BÀI TẬP NÂNG CAO TOÁN 4 THEO CHỦ ĐỀ Gia Sư Tài Năng Việt 1 BÀI TẬP NÂNG CAO TOÁN...
Transcript of BÀI TẬP NÂNG CAO TOÁN 4 THEO CHỦ ĐỀ Gia Sư Tài Năng Việt 1 BÀI TẬP NÂNG CAO TOÁN...
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
1
BÀI TẬP NÂNG CAO TOÁN 4 THEO CHỦ ĐỀ
1/Sè tù nhiªn - D·y sè tù nhiªn Bµi 11: T×m x , biÕt:
a) x lµ sè trßn chôc vµ 28 < x < 48
b) x lµ sè tù nhiªn vµ 145 < x < 150
c) x lµ sè ch½n vµ 200 < x < 210
d) x lµ sè tù nhiªn vµ x < 3
e) x lµ sè tù nhiªn vµ 2 < x < 5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 12: Sè tù nhiªn x gåm mÊy ch÷ sè, biÕt sè ®ã:
a) Cã ch÷ sè hµng cao nhÊt thuéc líp ngh×n?
b) Cã ch÷ sè hµng cao nhÊt thuéc líp triÖu?
c) BÐ h¬n 10?
d) BÐ h¬n 1 000 000 vµ lín h¬n 1 00 000?
e) §øng liÒn sau mét sè cã ba ch÷ sè?
f) §øng liÒn tríc mét sè cã ba ch÷ sè?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 13: ViÕt sè tù nhiªn nhá nhÊt, biÕt sè ®ã:
a) Gåm cã: - Mét ch÷ sè
- Ba ch÷ sè
- Ba ch÷ sè lÎ kh¸c nhau
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
2
b) Cã ®ñ n¨m ch÷ sè 5, 4, 7, 0, 1
c) Cã ba ch÷ sè mµ tæng c¸c ch÷ sè cña nã b»ng 20.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 14: T×m sè tù nhiªn x, biÕt:
a) x lµ sè tù nhiªn bÐ nhÊt;
b) x lµ sè liÒn sau sè 999;
c) x lµ sè liÒn tríc sè 1001;
d) x lµ sè võa lín h¬n 99 võa bÐ h¬n 1000;
e) x lµ sè cã hai ch÷ sè vµ lín h¬n 15;
f) x lµ sè cã ba ch÷ sè vµ bÐ h¬n 105;
g) x lµ sè ë gi÷a sè 1 vµ sè 11;
h) x lµ sè gi÷a sè tù nhiªn a vµ sè (a + 1)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 16: H·y viÕt tÊt c¶ c¸c sè cã 3 ch÷ sè mµ tæng c¸c ch÷ sè cña nã b»ng 3.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 17: Cho 3 ch÷ sè 1; 2; 3.
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
3
a) H·y viÕt tÊt c¶ c¸c sè cã 3 ch÷ sè kh¸c nhau tõ 3 ch÷ sè ®· cho.
b) TÝnh nhanh tæng c¸c sè võa viÕt ®îc.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 18: Víi bèn ch÷ sè 1,2,3,4;
a) H·y viÕt tÊt c¶ c¸c sè cã ®ñ bèn ch÷ sè Êy.
b) TÝnh tæng cña tÊt c¶ c¸c sè ë c©u a.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 19: Cho 5 ch÷ sè 0, 1, 2, 3, 6.
a) H·y lËp tÊt c¶ c¸c sè cã bèn ch÷ sè kh¸c nhau tõ 5 ch÷ sè trªn?
b) TÝnh nhanh tæng c¸c sè võa lËp ®îc?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 22: Cho d·y sè: 2, 3, 4, 5, ..., 30, 31, 32, 33, 34.
a) D·y sè trªn cã bao nhiªu sè h¹ng?
b) TÝnh nhanh tæng cña d·y sè trªn?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
4
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 25: Cho d·y sè ch½n liªn tiÕp 2, 4, 6, 8, 10, ... , 2468. Hái d·y cã:
a) Bao nhiªu sè h¹ng?
b) Bao nhiªu ch÷ sè ?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. BÀI TOÁN LIÊN QUAN DÃY SỐ THEO QUY LUẬT Cho các số 1;4;7;10;.....................
a.Số 2221;2234 có thuộc dãy số đó không ?
b.Số thứ 134 ,số thứ 205 là số nào ?
c.Tính tổng của 50 số đầu của dãy số. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3/CẤU TẠO SỐ D¹ng 1: ViÕt sè TN tõ nh÷ng ch÷ sè cho tríc Bµi 2 : Cho 5 ch÷ sè : 0; 1; 2; 3; 4.
a) H·y viÕt c¸c sè cã 4 ch÷ sè kh¸c nhau tõ 5 ch÷ sè ®· cho ? b) T×m sè ch½n lín nhÊt, sè lÎ nhá nhÊt cã 4 ch÷ sè kh¸c nhau ®îc viÕt tõ 5 ch÷ sè ®· cho ?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
5
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 1 : Cho bèn ch÷ sè : 0; 3; 8 vµ 9.
a) ViÕt ®îc tÊt c¶ bao nhiªu sè cã 4 ch÷ sè kh¸c nhau tõ 4 ch÷ sè ®· cho ? b) T×m sè lín nhÊt, sè nhá nhÊt cã 4 ch÷ sè kh¸c nhau ®îc viÕt tõ 4 ch÷ sè ®· cho? c) T×m sè lÎ lín nhÊt, sè ch½n nhá nhÊt cã 4 ch÷ sè kh¸c nhau ®îc viÕt tõ 4 ch÷ sè ®· cho ?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D¹ng 2: C¸c bµi to¸n gi¶i b»ng ph©n tÝch sè : Bµi 1: T×m 1 sè TN cã 2 ch÷ sè, biÕt r»ng nÕu viÕt thªm ch÷ sè 9 vµo bªn tr¸i sè ®ã ta ®îc mét sè lín gÊp 13 lÇn sè ®· cho ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 2: T×m mét sè cã 3 ch÷ sè, biÕt r»ng khi viÕt thªm ch÷ sè 5 vµo bªn ph¶i sè ®ã th× nã t¨ng thªm 1112
®¬n vÞ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 3: T×m mét sè cã 2 ch÷ sè, biÕt r»ng khi viÕt thªm sè 21 vµo bªn tr¸i sè ®ã ta ®îc mét sè lín gÊp 31
lÇn sè ph¶i t×m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
6
Bµi 4: T×m mét sè cã 2 ch÷ sè, biÕt r»ng khi viÕt thªm ch÷ sè 5 vµo bªn ph¶i sè ®ã ta ®îc sè míi lín h¬n
sè ph¶i t×m lµ 230 ®¬n vÞ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D¹ng 3: Nh÷ng bµi to¸n vÒ xÐt c¸c ch÷ sè tËn cïng cña sè Bµi 1: Kh«ng lµm tÝnh, h·y cho biÕt ch÷ sè tËn cïng cña mçi kÕt qu¶ sau :
a) ( 1991 + 1992 + ...+ 1999 ) – ( 11 + 12 + .....+ 19 ). b) ( 1981 + 1982 + ...+ 1989 ) ( 1991 + 1992 +....+ 1999 ) c) 21 23 25 27 – 11 13 15 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 2 : Kh«ng lµm tÝnh, h·y xÐt xem kÕt qu¶ sau ®©y ®óng hay sai ? Gi¶i thÝch t¹i sao ?
a) 136 136 – 42 = 1960
b) ab ab - 8557 = 0
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 3 : Kh«ng lµm tÝnh, h·y cho biÕt ch÷ sè tËn cïng cña mçi kÕt qu¶ sau :
a) ( 1999 + 2378 + 4545 + 7956 ) – ( 315 + 598 + 736 + 89 ) b) 56 66 76 86 – 51 61 71 81 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 4 : Kh«ng lµm tÝnh, h·y xÐt xem kÕt qu¶ sau ®©y ®óng hay sai ? Gi¶i thÝch t¹i sao ?
a) abc abc - 853467 = 0
b) 11 21 31 41 – 19 25 37 = 110
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
7
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. C¸c bµi to¸n vÒ d·y sè I. §iÒn thªm sè h¹ng vµo sau, gi÷a hoÆc tríc mét d·y sè Bµi 1. ViÕt tiÕp ba sè h¹ng vµo d·y sè sau :
a) 1; 3; 4; 7; 11; 18;... b) 0; 2; 4; 6; 12; 22;... c) 0 ; 3; 7; 12;... d) 1; 2; 6; 24;... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 2 : T×m sè h¹ng ®Çu tiªn cña c¸c d·y sè sau :
a).....; 17; 19; 21. b)......: 64; 81; 100. BiÕt r»ng mçi d·y cã 10 sè h¹ng. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
8
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 3 : ViÕt tiÕp hai sè h¹ng cña d·y sè sau :
a) 100; 93; 85; 76;..... b) 10; 13; 18; 26;... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
II. X¸c ®Þnh sè a cã thuéc d·y ®· cho hay kh«ng Bµi 1: H·y cho biÕt:
a) C¸c sè 50 vµ 133 cã thuéc d·y 90; 95; 100;...hay kh«ng ? b) Sè 1996 thuéc d·y 2;5;8;11;... hay kh«ng ? c) Sè nµo trong c¸c sè 666; 1000; 9999 thuéc d·y 3; 6; 12; 24;... hay kh«ng ? Gi¶i thÝch t¹i sao ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
III. T×m sè sè h¹ng cña d·y Bµi1. Cho d·y sè 11; 14; 17;.....;65; 68. a) H·y x¸c ®Þnh d·y sè trªn cã bao nhiªu sè h¹ng? b) NÕu ta tiÕp tôc kÐo dµi c¸c sè h¹ng cña d·y sè ®ã th× sè h¹ng thø 1996 lµ sè mÊy? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 2 . Trong c¸c sè cã ba ch÷ sè, cã bao nhiªu sè chia hÕt cho 4?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
9
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 3: Cã bao nhiªu sè : cã 3 ch÷ sè khi chia cho 5 d 1? D 2 ?
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
IV. T×m tæng c¸c sè h¹ng cña d·y sè Bµi 1 . TÝnh tæng cña 50 sè lÎ ®Çu tiªn .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bµi 2: T×m tæng cña :
a) C¸c sè cã 2 ch÷ sè chia hÕt cho 3. b) C¸c sè cã 2 ch÷ sè chia cho 4 d 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5. Bèn phÐp tÝnh víi sè tù nhiªn
5.1. PhÐp céng Bµi 1: T×m hai sè cã tæng b»ng 1149, biÕt r»ng nÕu gi÷ nguyªn sè lín vµ gÊp sè bÐ lªn 3 lÇn th× ta ®îc
tæng míi b»ng 2061. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 2: Hai sè cã tæng b»ng 6479, nÕu gi÷ nguyªn sè thø nhÊt, gÊp sè thø hai lªn 6 lÇn th× ®îc tæng míi
b»ng 6789. H·y t×m hai sè h¹ng ban ®Çu. ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
10
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 3: T×m hai sè cã tæng b»ng 140, biÕt r»ng nÕu gÊp sè h¹ng thø nhÊt lªn 5 lÇn vµ gÊp sè h¹ng thø hai
lªn 3 lÇn th× tæng míi lµ 508. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 4: T×m hai sè tù nhiªn cã tæng lµ 254. NÕu viÕt thªm mét ch÷ sè 0 vµo bªn ph¶i sè thø nhÊt vµ gi÷
nguyªn sè thø hai th× ®îc tæng míi lµ 362. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 5: T×m hai sè cã tæng b»ng 586. NÕu viÕt thªm ch÷ sè 4 vµo bªn ph¶i sè thø hai vµ gi÷ nguyªn sè thø
nhÊt th× tæng míi b»ng 716. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 36: Khi céng mét sè tù nhiªn víi 107, mét häc sinh ®· chÐp nhÇm sè h¹ng thø hai thµnh 1007 nªn
®îc kÕt qu¶ lµ1996. T×m tæng ®óng cña hai sè h¹ng.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 37: Hai sè cã tæng b»ng 6479, nÕu gi÷ nguyªn sè h¹ng thø nhÊt, gÊp sè h¹ng thø hai lªn 6 lÇn th×
®îc tæng míi b»ng 65789. H·y t×m hai sè h¹ng ban ®Çu.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 40: Cho sè cã hai ch÷ sè. NÕu viÕt sè ®ã theo thø tù ngîc l¹i ta ®îc sè míi bÐ h¬n sè ph¶i t×m. BiÕt
tæng cña sè ®ã víi sè míi lµ 143. T×m sè ®· cho.
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
11
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 41: Tæng cña hai sè thay ®æi thÕ nµo nÕu mét sè h¹ng cña nã t¨ng thªm 300 ®¬n vÞ vµ gi÷ nguyªn sè
h¹ng kia?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 42: Chu vi h×nh ch÷ nhËt sÏ thay ®æi thÕ nµo nÕu ta t¨ng chiÒu dµi thªm 3 mÐt vµ gi¶m chiÒu réng cña
nã ®i 3m.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 43: Tæng cña hai sè lµ 69, nÕu gÊp 3 lÇn sè thø hai vµ gi÷ nguyªn sè thø nhÊt th× tæng míi lµ 87. T×m
hai sè ®ã.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
5.2. PhÐp trõ Bµi 1: T×m hai sè cã hiÖu lµ 23, biÕt r»ng nÕu gi÷ nguyªn sè trõ vµ gÊp sè bÞ trõ lªn 3 lÇn th× ®îc hiÖu lµ
353. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Bµi 2: T×m hai sè cã hiÖu lµ 383, biÕt r»ng nÕu gi÷ nguyªn sè bÞ trõ vµ gÊp sè trõ lªn 4 lÇn th× ®îc hiÖu
míi lµ 158. ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
12
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 3: HiÖu cña hai sè tù nhiªn lµ 4441, nÕu viÕt thªm mét ch÷ sè 0 vµo bªn ph¶i sè trõ vµ gi÷ nguyªn sè
bÞ trõ th× ®îc hiÖu míi lµ 3298. ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ .................................................................................................................................................................................................................................................................................................................................................... Bµi 4: HiÖu cña hai sè tù nhiªn lµ 134. ViÕt thªm mét ch÷ sè vµo bªn ph¶i cña sè bÞ trõ vµ gi÷ nguyªn sè
trõ th× hiÖu míi lµ 2297. T×m ch÷ sè viÕt thªm vµ hai sè ®ã. ............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Bµi 45: TÝnh nhanh
a) 32 - 13- 17 c) 1732 - 513 - 732
b) 45 - 12 - 5 - 23 d) 2834 - 150 -834
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 50: T×m tæng hai sè, biÕt hiÖu cña hai sè ®ã lµ 37 vµ hiÖu ®ã b»ng nöa sè bÐ.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 51: HiÖu cña hai sè thay ®æi thÕ nµo nÕu ta cïng t¨ng thªm (hay bít ®i) hai sè ®ã cïng mét sè. Cho vÝ
dô?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 52: HiÖu cña hai sè lµ 27, nÕu ta cïng gÊp lªn ( hay gi¶m ®i) mçi sè ®ã 3 lÇn th× hiÖu míi lµ bao
nhiªu?
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
13
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 53: Kh«ng thùc hiÖn phÐp tÝnh, cã thÓ nãi ngay gi¸ trÞ biÓu thøc sau ®îc kh«ng?
a) A= 621 – ( 621 – 58) b) B = x- ( x- 60)
c) C= 720 + ( 3927 – 720) d) D = x + ( 390 – x)
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 54: T×m sè tù nhiÖn x, biÕt:
a) 35- x < 35 – 5 b) x – 10 < 35 – 10 c) x – 10 < 45
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
5.3. PhÐp nh©n Bµi 1: T×m tÝch cña 2 sè, biÕt r»ng nÕu gi÷ nguyªn thõa sè thø nhÊt vµ t¨ng thõa sè thø 2 lªn 4 lÇn th× ®îc
tÝch míi lµ 8400.
Bµi gi¶i
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
14
Bµi 2: T×m 2 sè cã tÝch b»ng 5292, biÕt r»ng nÕu gi÷ nguyªn thõa sè thø nhÊt vµ t¨ng thõa sè thø hai thªm
6 ®¬n vÞ th× ®îc tÝch míi b»ng 6048. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 3: T×m 2 sè cã tÝch b»ng 1932, biÕt r»ng nÕu gi÷ nguyªn mét thõa sè vµ t¨ng mét thõa sè thªm 8 ®¬n
vÞ th× ®îc tÝch míi b»ng 2604. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 58: Trong mét phÐp nh©n cã thõa sè thø hai lµ 64, khi thùc hiÖn phÐp nh©n mét ngêi ®· viÕt c¸c tÝch
riªng th¼ng cét víi nhau nªn kÕt qu¶ t×m ®îc lµ 870. T×m tÝch ®óng cña phÐp nh©n? Bµi 59: Kh«ng tÝnh tæng, h·y biÕn ®æi tæng sau thµnh tÝch cã hai thõa sè . a) 462+273+315+630 c) 5555+6767+7878 b) 209+187+726+1078 d) 1997,1997+1998,1998+1999,1999 .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 59: . So s¸nh A vµ B biÕt:
a. A=73 x 73 B=72 x 74 b. A=1991 x 1999 B=1995 x 1995 .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 60: TÝch cña hai sè thay ®æi thÕ nµo nÕu ta gÊp mét thõa sè lªn 2 lÇn vµ gi¶m thõa sè kia ®i 2 lÇn. Cho
vÝ dô? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 61: TÝch cña hai sè thay ®æi thÕ nµo nÕu mçi thõa sè ®Òu gÊp lªn 3 lÇn. Cho vÝ dô?
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
15
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 62: T×m x ( Kh«ng thùc hiÖn phÐp tÝnh)
a) 5x = 5195 b) ( x + 5) 2009 = ( 19 + 5) 2009 c) 35 x < 35 6 d) ( 15 – x) 79 < ( 15 – 2) 79 .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 63: TÝch cña hai sè tù nhiªn lµ 65. NÕu mét sè t¨ng thªm 30 ®¬n vÞ vµ gi÷ nguyªn sè kia th× tÝch míi
lµ 215.T×m hai sè ®ã. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 64: Khi nh©n mét sè víi 245, mét häc sinh ®· ®Æt c¸c tÝch riªng th¼ng cét nh trong phÐp céng nªn
t×m ra kÕt qu¶ lµ 4257. T×m tÝch ®óng cña phÐp nh©n ®ã. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 65: TÝnh gi¸ trÞ cña biÓu thøc sau b»ng c¸ch hîp lÝ:
a) 54 113 + 54113 + 113 b)( 532 7 - 26614) ( 5327 + 266) c) 117 ( 36 + 62) - 17 ( 62 + 36) d)( 145 99 + 145) – ( 143 101 – 143) 21. T×m 3 sè lÎ liªn tiÕp mµ tÝch cña chóng lµ 105. ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
16
..........................................................................................................................................................................
..........................................................................................................................................................................
22. Cho A= 12 + 23 + 34 + …+ 1920 TÝnh A3 = ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 66: TÝnh gi¸ trÞ biÓu thøc sau b»ng c¸ch hîp lÝ:
a) 2009 867 + 2009 133 b) 2008867 + 2009133 TÝch cña hai sè tù nhiªn liªn tiÕp tõ 1 ®Õn 76 tËn cïng b»ng bao nhiªu ch÷ sè 0? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 67: TÝnh gi¸ trÞ biÓu thøc sau b»ng c¸ch hîp lÝ:
a) A = 1 + 1 + 1 + ...+ 1 – 999( cã 1000 sè 1) b) 411325 - 5112 20 c) ( 100 – 99 + 97 – 80 + 15) ( 16 – 2 8) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 69: TÝnh b»ng c¸ch thuËn tiÖn
a) 317 + 325 - 32 b) 12315 - 1235 c) 246 4 - 2463 – 246 d) 7899 - 7898 .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
5.4. PhÐp CHIA Bµi 73: §Æt tÝnh råi tÝnh
a) 256075 : 5 b) 369090 : 6 c)498479: 7 .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
17
Bµi 74: T×m x:
a) x5 = 106570 b) 450906 : x = 6 .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 76: TÝnh ( Theo mÉu)
MÉu: 60 : 30 = 60 : ( 10 3) = 60 : 10 : 3 = 6 : 3 = 2 a) 90 : 30 b) 180 : 60 .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 77: §Æt tÝnh råi tÝnh
552 : 24 450 : 27 540 : 45 .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 79: §Æt tÝnh råi tÝnh
4725 : 15 8058: 34 5672 : 42 .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 80: Ngêi ta xÕp c¸c gãi kÑo vµo c¸c hép, mçi hép 30 gãi. Hái cã thÓ xÕp 2000 gãi kÑo vµo nhiÒu
nhÊt bao nhiªu hép vµ cßn thõa bao nhiªu gãi kÑo? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 81: §Æt tÝnh råi tÝnh
3621: 213 8000 : 308 1682 : 209 .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
18
Bµi 84: Mua 52 bót bi hÕt 78 000 ®ång. Hái nÕu mçi bót bi ®ã gi¶m gi¸ 300 ®ång th× víi sè tiÒn 78 000
®ång sÏ mua ®îc bao nhiªu bót bi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 85: Nam lµm mét phÐp chia cã d lµ sè d lín nhÊt cã thÓ cã. Sau ®ã Nam gÊp c¶ sè bÞ chia vµ sè chia
lªn 3 lÇn. ë phÐp chia míi nµy, sè th¬ng lµ 12 vµ sè d lµ 24. T×m phÐp chia Nam thùc hiÖn ban ®Çu? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 86: Sè A chia cho 12 th× d 8. NÕu gi÷ nguyªn sè chia th× sè A ph¶i thay ®æi thÕ nµo ®Ó th¬ng t¨ng
thªm 2 ®¬n vÞ vµ phÐp chia kh«ng cã d? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 87: Mét phÐp chia cho 18 d 8. §Ó phÐp chia kh«ng cßn d vµ th¬ng gi¶m ®i 2 lÇn th× ph¶i thay ®æi
sè bÞ chia nh thÕ nµo? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 88: Th¬ng cña hai sè thay ®æi thÕ nµo nÕu ta gÊp sè bÞ chia vµ sè chia lªn cïng mét sè lÇn? Cho vÝ
dô. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 89: Kh«ng thùc hiÖn phÐp tÝnh, t×m x:
a) 2009 : x = 2009 : 2 b) ( x + 2) : 2009 = (2345 + 2) : 2009 c) x : 5 < 15 : 5 d) 35 : x > 35 : 5 ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
19
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 89: TÝnh gi¸ trÞ biÓu thøc sau b»ng c¸ch hîp lÝ:
a) 1875 : 2 + 125 : 2 b) 0 : 36 ( 32 + 17 + 99 – 68 + 1) c) ( m : 1 - m1) : ( m2009 + m + 1) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 90: H·y ®Æt dÊu ngoÆc vµo biÓu thøc : 315 + 18 : 6+ 3 ®Ó gi¸ trÞ cña biÓu thøc lµ :
a) 47 b) Sè bÐ nhÊt cã thÓ cã c) Sè lín nhÊt cã thÓ cã. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 91: TÝnh gi¸ trÞ biÓu thøc sau víi x = 1 vµ y = 0:
a) A = ( 15 : x + 15x) + 2009 y b) B = y : ( 119 x + 4512) + (756 : x – y) c) C = ( 10 + y) : ( 10 – y) – x + 10x – 10 : x + y .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
6. DẠNG TOÁN TRUNG BÌNH CỘNG 4. Trong c¸c sè, nÕu cã mét sè lín h¬n møc trung b×nh céng cña c¸c sè n ®¬n vÞ th× trung b×nh céng
cña c¸c sè ®ã b»ng tæng c¸c sè cßn l¹i céng víi n ®¬n vÞ råi chia cho sè lîng c¸c sè h¹ng cßn l¹i ®ã.
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
20
VD: An cã 20 viªn bi, B×nh cã sè bi b»ng 2
1 sè bi cña An. Chi cã sè bi h¬n møc trung b×nh céng cña ba
b¹n lµ 6 viªn bi. Hái Chi cã bao nhiªu viªnn bi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
5. Trong c¸c sè , nÕu mét sè kÐm trung b×nh céng cña c¸c sè ®ã n ®¬n vÞ th× trung b×nh céng cña c¸c
sè ®ã b»ng tæng c¸c sè cßn l¹i trõ ®i n ®¬n vÞ råi chia sè c¸c sè h¹ng cßn l¹i.
VD: An cã 20 bi, B×nh cã 20 bi. Chi cã sè bi kÐm trung b×nh céng cña c¶ ba b¹n lµ 6 bi. Hái Chi cã bao
nhiªu bi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
6. Bµi to¸n cã thªm mét sè h¹ng ®Ó møc trung b×nh céng cña tÊt c¶ t¨ng thªm n ®¬n vÞ, ta lµm nh
sau:
VD: Mét « t« trong ba giê ®Çu, mçi giê ®i ®îc 40km, trong ba giê sau, mçi giê ®i ®îc 50 km. NÕu
muèn t¨ng trung b×nh céng mçi giê t¨ng thªm 1 km n÷a th× ®Õn giê thø 7, « t« ®ã cÇn ®i bao nhiªu km n÷a? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... VÝ dô 1:
H·y t×m sè trung b×nh céng cña 1, 2, 3, 4, 5, 6, 7, 8, 9. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... VÝ dô3:
An cã 20 nh·n vë, B×nh cã 20 nh·n vë. Chi cã sè nh·n vë kÐm trung b×nh céng cña ba b¹n lµ 6 nh·n vë. Hái Chi cã bao nhiªu n·nh vë? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
VÝ dô 4:
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
21
Cã bèn b¹n An, B×nh, Dòng, Minh cïng ch¬i bi. BiÕt An cã 18 viªn bi, B×nh cã 16 viªn bi, Dòng cã sè bi b»ng trung b×nh céng sè bi cña An vµ B×nh. Minh cã sè bi b»ng trung b×nh céng sè bi cña c¶ bèn b¹n. Hái B¹n Minh cã bao nhiªu viªn bi?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 1: T×m sè trung b×nh céng cña c¸c sè c¸ch ®Òu nhau 4 ®¬n vÞ : 3, 7, 11, …,95, 99, 103.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 2: T×m sè trung b×nh céng cña c¸c sè : 4, 6, 8, 10, 12, 14, 16, 18.
Em cã c¸ch nµo tÝnh nhanh sè trung b×nh céng cña c¸c sè trªn kh«ng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 3: Trung b×nh céng tuæi cña bè, mÑ, B×nh vµ Lan lµ 24 tuæi, trung b×nh céng tuæi cña bè. mÑ vµ Lan lµ
28 tuæi. T×m tuæi cña mçi ngêi, biÕt tuæi B×nh gÊp ®«i tuæi Lan,
tuæi Lan b»ng 6
1tuæi mÑ.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 5: Hai ngêi ®i xe m¸y khëi hµnh cïng mét lóc tõ hai đ Þa ®iÓm c¸ch nhau 216km vµ ®i ngîc chiÒu
nhau. Hä ®i sau 3 giê th× gÆp nhau. Hái trung b×nh mét giê mçi ngêi ®i ®i ®îc bao nhiªu ki- l«-mÐt?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
22
Bµi 6: Con lîn vµ con chã nÆng 102kg, con lîn vµ con bß nÆng 231kg, con chã vµ con bß nÆng 177kg.
Hái trung b×nh mçi con nÆng bao nhiªu ki-l«-gam? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 7: T×m sè cã ba ch÷ sè, biÕt trung b×nh céng ba ch÷ sè cña sè ®ã b»ng 6 vµ ch÷ sè hµng tr¨m gÊp ba
ch÷ sè hµng chôc, ch÷ sè hµng chôc kÐm ch÷ sè hµng ®¬n vÞ lµ 2. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 8: Ba sè cã trung b×nh céng lµ 60. T×m ba sè ®ã, biÕt nÕu viÕt thªm mét ch÷ sè ch÷ sè 0 vµo bªn ph¶i
sè thø nhÊt th× ta ®îc sè thø hai vµ sè thø nhÊt b»ng 4
1 sè thø ba.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 12: ViÖt cã 18 bi, Nam cã 16 bi, Hoµ cã sè bi b»ng trung b×nh céng cña ViÖt vµ Nam, B×nh cã sè bi
kÐm trung b×nh céng cña 4 b¹n lµ 6 bi. Hái B×nh cã bao nhiªu bi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 13: Nh©n dÞp khai gi¶ng, Mai mua 10 quyÓn vë, Lan mua 12 quyÓn vë, §µo mua sè vë b»ng trung
b×nh céng cña 2 b¹n trªn, Cóc mua h¬n trung b×nh céng cña c¶ 3 b¹n lµ 4 quyÓn. Hái Cóc mua bao nhiªu quyÓn vë?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 14: Tuæi trung b×nh 11 cÇu thñ cña mét ®éi bãng ®¸ lµ 22 tuæi . NÕu kh«ng kÓ thñ m«n th× tuæi trung
b×nh cña 10 cÇu thñ lµ 21 tuæi. Hái thñ m«n bao nhiªu tuæi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
23
Bµi 103: T×m trung b×nh céng cña c¸c sè : 4, 6, 8, 10, 12 14, 16, 18. Em cã c¸ch nµo tÝnh nhanh sè trung
b×nh céng cña c¸c sè trªn kh«ng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 104: T×m sè cã ba ch÷ sè, biÕt truug b×nh céng ba ch÷ sè cña nã b»ng 5 vµ ch÷ sè hµng tr¨m gÊp ba
ch÷ sè hµng chôc, ch÷ sè hµng chôc h¬n ch÷ sè hµng ®¬n vÞ lµ 1. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 105: Trung b×nh céng tuæi cña bè, mÑ, B×nh vµ Lan lµ 24 tuæi, trung b×nh céng tuæi cña bè, mÑ vµ Lan
lµ 28 tuæi. T×m tuæi mçi ngêi, biÕt tuæi B×nh gÊp ®«i tuæi Lan, tuæi Lan b»ng 6
1 tuæi mÑ.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 106: Cã 4 b¹n An, B×nh, Dòng, Minh ch¬i bi. An cã 18 viªn, B×nh cã 16 viªn, Dòng cã sè bi b»ng
TBC sè bi cña An vµ B×nh, Minh cã sè bi b»ng TBC sè bi cña c¶ 4 b¹n. Hái Minh cã bao nhiªu viªn bi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 107: TBC sè tuæi cña «ng , bè vµ ch¸u lµ 36 tuæi, TBC sè tuæi cña bè vµ cña ch¸u lµ 23, «ng h¬n
ch¸u 54 tuæi. T×m tuæi mçi ngêi. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 108: T×m 3 sè cã TBC b»ng 60, biÕt r»ng nÕu viÕt thªm 1 ch÷ sè 0 vµo bªn ph¶i sè thø nhÊt th× ®îc
sè thø hai vµ sè thø 3 gÊp 4 lÇn sè thø nhÊt. ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
24
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 109: ViÖt cã 18 viªn bi, Nam cã 16 bi, Hßa cã s« bi b»ng trung b×nh céng cña ViÖt vµ Nam, B×nh cã
sè bi kÐm trung b×nh céng cña 4 b¹n lµ 6 bi. Hái B×nh cã bao nhiªu viªn bi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 110: Nh©n dÞp khai gi¶ng, Mai mua 10 quyÓn vë, Lan mua 12 quyÓn vë, §µo mua sè vë b»ng trung
b×nh céng cña hai b¹n trªn, Cóc mua h¬n trung b×nh céng cña c¶ 3 b¹n lµ 4 quyÓn vë. Hái Cóc mua bao nhiªu quyÓn vë? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 112: Tuæi trung b×nh cña 11 cÇu thñ cña ®éi bãng ®¸ lµ 22 tuæi. NÕu kh«ng kÓ thñ m«n th× tuæi trung
b×nh cña 10 cÇu thñ lµ 21 tuæi. Hái thñ m«n bao nhiªu tuæi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 113: Mét th¸ng ®iÓm cã 20 lÇn kiÓm tra, sau 10 lÇn kiÓm tra b¹n An thÊy ®iÓm trung b×nh cña m×nh lµ
7 ®iÓm. Hái cßn 10 lÇn kiÓm tra n÷a b¹n An ph¶i ®¹t ®îc tÊt c¶ bao nhiªu ®iÓm ®Ó ®iÓm trung b×nh cña th¸ng lµ 8 ®iÓm. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài tập 1: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở bằng trung bình
cộng 3 xe . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài tập 2: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở hơn trung bình
cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng?
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
25
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài tập 3: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở kém trung bình
cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài tập 4: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở bằng trung bình
cộng 3 xe . Hỏi xe thứ 3 chở bao nhiêu tấn hàng?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài tập 5: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở hơn trung bình
cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài tập 6: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở kém trung bình
cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài tập 7: Trung bình cộng của n số là 80 biết 1 trong các số đó là 100 .Nếu bỏ số 100 thì trung bình
cộng các số còn lại là 78 tìm n. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài tập 8: Có ba con ; gà, vịt, ngan . Hai con gà và vịt nặng tất cả là 5 kg . Hai con gà và ngan nặng tất cả
là 9 kg . Hai con ngan và vịt nặng tất cả là 10 kg . Hỏi trung bình một con nặng mấy kg ? ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
26
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài tập 10: Trung bình cộng của ba số là 50 . Tìm số thứ ba biết rằng nó bằng trung bình cộng của hai
số đầu .
Hướng dẫn giải .Dùng sơ đồ .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài tập 11: Trung bình cộng của ba số là 35 . Tìm ba số đó biết rằng số thứ nhất gấp đôi số thứ hai, số
thứ hai gấp đôi số thứ ba?
Gợi ý Dùng sơ đồ .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài tập 12: Tìm sáu số chẵn liên tiếp biết tổng của chúng là 90. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài tập 13: Tìm trung bình cộng của tất cả các số có hai chữ số , mà chia hết cho 4 . .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài tập 14: Trung bình cộng số tuổi của hai anh em ít hơn tuổi anh là 4 tuổi . Hỏi anh hơn em mấy tuổi ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài tập 15: Lớp 4 A có 40 học sinh , lớp 4B có 36 học sinh . Lóp 4 C có số học sinh ít hơn trunh bình
cộng số học sinh của cả ba lớp là hai bạn . Tính số học sinh lớp 4 B.
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
27
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài tập 16: Hai lớp 3A và 3B có tất cả 37 h/s .Hai lớp 3B và 3B có tất cả là 83 h/s. Hai lớp 3C vàg 3A có
tất cả là 86 h/s .
Hỏi: trung bình mỗi lớp có bao nhiêu học sinh ? Số học sinh của mỗi lớp là bao nhiêu em ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài tập 17: Tuổi trung bình cộng của một đội bóng đá (11 người) là 22 tuổi. Nếu không kể đội trưởng, thì
tuổi trung bình của 10 cầu thủ còn lại chỉ là 2. Tính tuổi của đội trưởng ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài tập 18: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở bằng trung bình
cộng 3 xe . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài tập 19: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở hơn trung bình
cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài tập 20: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở kém trung bình
cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
28
Bài tập 21: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở bằng trung bình
cộng 3 xe . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài tập 22: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở hơn trung bình
cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài tập 23: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở kém trung bình
cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài tập 24: Ba lớp 4a;4b;4c; đi trồng cây . số cây của lớp 4a và 4b trồng được là 41 cây .Số cây của lớp
4b và lớp 4c trồng được là 43 cây . Số cây của 4c và 4a trồng được là 42 cây . Hỏi mỗi lớp trồng được bao
nhiêu cây?
.BàiGiải.
Cả 3 lớp trồng được số cây là:
(41+42+43 ): 2 =63 cây
Lớp 4c trồng được số cây là
63- 41=22cây
Lớp 4 b trồng số cây là:
43 -22= 21(Cây)
Lớp 4 a trồng số cây là:
42 – 22 = 20 (cây)
Đáp Số:
Bài tập 25: An,Bình ,Chi đi câu cá . Cả ba bạn câu được 37 con cá . Nếu An câu thêm được 5 con cá và
Bình câu giảm đi 3 con cá thí số cá ba bạn bằng nhau . Hỏi mỗi bạn câu được bao nhiêu con cá? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Ví dụ 1 : Tìm 3 số có trung bình cộng lớn hơn số thứ nhất 540, bé hơn số thứ hai là 1260 và gấp 31 lần số
thứ ba. ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
29
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Ví dụ 2 : Đội tuyển học sinh giỏi khối 5 của một trường Tiểu học có 16 bạn. Biết rằng 2/5 số bạn nam
nhiều hơn 1/2 số bạn nữ là 1 bạn. Hỏi đội tuyển có bao nhiêu bạn nam, bao nhiêu bạn nữ ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. Ví dụ 3 : Một trường Tiểu học có số học sinh nam nhiều hơn số học sinh nữ là 40 học sinh. Trong đó 3/4
số bạn nam và 1/2 số bạn nữ đạt danh hiệu học sinh tiên tiến. Tính số học sinh nam và số học sinh nữ của
trường đó. Biết số học sinh tiên tiến của trường đó là 530 bạn. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
7. DẠNG TÌM HAI SỐ KHI BIẾT TỔNG VÀ HIỆU Bµi 1: Cã mét hép bi xanh vµ mét hép bi ®á, tæng sè bi cña 2 hép lµ 48 viªn bi. BiÕt r»ng nÕu lÊy ra ë hép
bi ®á 10 viªn vµ lÊy ra ë hép bi xanh 2 viªn th× sè bi cßn l¹i trong 2 hép b»ng nhau. T×m sè bi cña mçi hép lóc ®Çu.
Bµi gi¶i: ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................§¸p sè : 18 vµ 20
Bµi 2: Lan cã nhiÒu h¬n Hång 12 quyÓn truyÖn nhi ®ång. NÕu Hång mua thªm 8 quyÓn vµ Lan mua thªm
2 quyÓn th× 2 b¹n cã tæng céng 46 quyÓn. Hái mçi b¹n cã bao nhiªu quyÓn truyÖn nhi ®ång? .......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... §¸p sè : 12 vµ 24
Bµi 3: Hai hép bi cã tæng céng 115 viªn, biÕt r»ng nÕu thªm vµo hép bi thø nhÊt 8 viªn vµ hép thø hai 17
viªn th× 2 hép cã sè bi b»ng nhau. Hái mçi hép cã bao nhiªu viªn bi? ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
§¸p sè 78 vµ 37
Bµi 4: T×m hai sè cã hiÖu b»ng 129, biÕt r»ng nÕu lÊy sè thø nhÊt céng víi sè thø hai råi céng víi tæng cña
chóng th× ®îc 2010. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
30
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 5: T×m hai sè ch½n cã tæng b»ng 216, biÕt gi÷a chóng cã 5 sè ch½n
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 6: Tæng sè tuæi hiÖn nay cña bµ, cña HuÖ vµ cña H¶i lµ 80 tuæi. C¸ch ®©y 2 n¨m, tuæi bµ h¬n tæng sè
tuæi cña HuÖ vµ H¶i lµ 54 tuæi, HuÖ nhiÒu h¬n H¶i 6 tuæi. Hái hiÖn nay mçi ngêi bao nhiªu tuæi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 7: Hai ®éi trång c©y nhËn kÕ ho¹ch trång tÊt c¶ 872 c©y. Sau khi mçi ®éi hoµn thµnh 4
3 kÕ ho¹ch cña
m×nh, ®éi 1 trång nhiÒu h¬n sè c©y ®éi 2 trång lµ 54 c©y. Hái mçi ®éi nhËn trång theo kÕ ho¹ch lµ bao nhiªu c©y?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 115: T×m hai sè, biÕt tæng hai sè lµ sè lín nhÊt cã hai ch÷ sè. HiÖu hai sè lµ sè lÎ bÐ nhÊt cã hai ch÷ sè. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 116: T×m hai sè biÕt tæng hai sè lµ 100 vµ hiÖu hai sè lµ sè bÐ nhÊt cã hai ch÷ sè. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 117: T×m hai sè biÕt hiÖu hai sè lµ sè lín nhÊt cã 1 ch÷ sè vµ tæng hai sè lµ sè lín nhÊt cã ba ch÷ sè. ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
31
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 118: T×m hai sè ch½n cã tæng b»ng 220, biÕt r»ng ë gi÷a chóng cã 3 sè ch½n. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 119: Tæng cña hai sè ch½n lµ 38. H·y t×m hai sè biÕt r»ng gi÷a chóng chØ cã 3 sè lÎ. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 120: Tæng cña ba sè lÎ liªn tiÕp lµ 75,h·y t×m ba sè ®ã. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 121: Anh h¬n em 5 tuæi. BiÕt r»ng 5 n¨m n÷a th× tæng sè tuæi cña hai anh em lµ 25. TÝnh sè tuæi cña mçi ngêi hiÖn nay? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 122: TÝnh diÖn tÝch cña miÕng ®Êt h×nh ch÷ nhËt cã chu vi lµ 256 m vµ chiÒu dµi h¬n chiÒu réng 32m .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 123: Mét m¶nh vên h×nh ch÷ nhËt cã chu vi b»ng chu vi thöa ruéng h×nh vu«ng c¹nh 80m. NÕu gi¶m chiÒu dµi m¶nh vên ®i 30m vµ t¨ng chiÒu réng thªm 10m th× m¶nh vên sÏ cã h×nh vu«ng. TÝnh diÖn tÝch m¶nh vên. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 124: T×m hai sè cã hiÖu b»ng 129, biÕt r»ng nÕu lÊy sè thø nhÊt céng víi sè thø hai råi céng tæng cña chóng th× ®îc 2010 ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
32
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
8. DẠNG TÌM HAI SỐ KHI BIẾT 2 HIỆU SỐ Bài toán: Để chuẩn bị cho năm học mới, hai bạn Vĩnh và Kim đi mua sắm sách vở. Vĩnh mua 15
quyển vở, Kim mua nhiều hơn hơn Vĩnh 5 quyển vở cùng loại và phải trả nhiều hơn Vĩnh 20.000 đồng.
Hỏi mỗi bạn phải trả bao nhiêu tiền mua vở? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... 3. Bài tập cần luyện:
*Bài tập 1: Một hiệu sách, lần thứ nhất bán được 27 quyển vở. Lần thứ hai bán được 40 quyển vở
cùng loại và nhận nhiều tiền hơn lần trước 52.000 đồng. Hỏi mỗi lần bán hiệu sách nhận bao nhiêu tiền?
(GV phân tích tương tự như bài toán trên). .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... *Bài tập 2: Hồng mua 3 cái bút và 5 quyển vở hết 39.000 đồng. Hoa mua 3 cái bút và 9 quyển vở
cùng loại như Hồng hết 51.000 đồng. Tính giá tiền một cây bút, một quyển vở? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
4. Bài tập về nhà:
Chị Vĩnh mua 2 mét vải xanh và 6 mét vải hoa. Chị Linh mua 2 mét vải xanh và 9 mét vải hoa
cùng loại. Chị Vĩnh phải trả 380.000 đồng. Chị Linh phải trả 530.000 đồng. Tính giá tiền một mét vải mỗi
loại? ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
33
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 1: Hiện nay, Minh 10 tuổi ,em Minh 6 ,còn mẹ của Minh 36 tuổi .Hỏi bao nhiêu năm nữa tuổi mẹ
bằng tổng số tuổi của hai anh em. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 2 : Bể thứ nhất chứa 1200 lít nước . Bể thứ 2 chứa 1000 lít nước .Khi bể không có nứớc người ta cho
2 vòi cùng chảy 1 lúc vào 2 bể . Vòi thứ nhất mỗi giờ chảy được 200 lít .Vòi thứ 2 mỗi giờ chảy được 150
lít. Hỏi sau bao lâu số nước còn lại ở 2 bể bằng nhau. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 3: Cùng 1 lúc xe máy và xe đạp cùng đi về phía thành phố xe máy cách xe đạp 60km. Vận tốc xe máy
là 40 km/h vận tốc xe đạp là 25 km/h.
Hỏi sau bao lâu xe máy đuổi kịp xe đạp. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 4 : Một con Chó Đuổi theo một con thỏ .Con chó cách con thỏ 20m.Mỗi bước con thỏ nhẩy được
30cm,con chó nhảy được 50 cm.Hỏi sau bao nhiêu bước con chó bắt được con thỏ ? Biết rằng con thỏ
nhảy được 1 bước thì con chó cũng nhảy được 1 bước. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 5 Hai bác thợ mộc nhận bàn ghế về đống .Bác thứ nhất nhận 60 bộ .Bác thứ 2 nhận 45 bộ . Cứ 1
tuần bác thứ nhất đóng được 5 bộ ,bác thứ hai đóng được 2 bộ . Hỏi sau bao lâu số ghế còn lại của 2 bác
bằng nhau. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
34
Bài 6:Hai bác thợ mộc nhận bàn ghế về đống .Bác thứ nhất nhận 120 bộ .Bác thứ 2 nhận 80 bộ . Cứ 1
tuần bác thứ nhất đóng được 12 bộ ,bác thứ hai đóng được 4 bộ .Hỏi sau bao lâu số ghế còn lại của bác
thứ nhất bằng 1/2 số bộ bàn ghế của bác thứ 2. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 7: Hai bể nước có dung tích bằng nhau .Cùng 1 lúc người ta cho 2 vòi nước chảy vào 2 bể .Vòi thứ
nhất mỗi giờ chảy được 50 lít nước .Vòi thứ 2 mỗi giờ chảy được 30 lít nước . Sau khi bể thứ nhất đầy
nước thì bể thứ 2 phải chảy thêm 600 lít nữa mới đầy .Hỏi dung tích của bể là bao nhiêu lít nước?
(Tham khảo thêm Đề thi và phần Bài tập mở rộng) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
9. DẠNG TOÁN LIÊN QUAN ĐẾN CHIA HẾT Bµi 1: Tõ 3 ch÷ sè 0, 1, 2. H·y viÕt tÊt c¶ c¸c sè cã 3 ch÷ sè kh¸c nhau chia hÕt cho 2.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
........................................................ Bµi 2: ViÕt tÊt c¶ c¸c sè chia hÕt cho 5 cã 4 ch÷ sè kh¸c nhau tõ 4 ch÷ sè 0, 1, 2 , 5.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 3: Em h·y viÕt vµo dÊu * ë sè 86* mét ch÷ sè ®Ó ®îc sè cã 3 ch÷ sè vµ lµ sè:
a) Chia hÕt cho 2 b) chia hÕt cho 3 c) Chia hÕt cho 5 d) chia hÕt cho 9 e) Chia hÕt cho c¶ 2 vµ 5 g) Chia hÕt cho c¶ 3 vµ 9
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
........................................................
Bµi 4: H·y t×m c¸c ch÷ sè x, y sao cho yx817 chia hÕt cho 5 vµ 9.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
35
..........................................................................................................................................................................
........................................................
Bµi 5: T×m x, y ®Ó yx765 chia hÕt cho 3 vµ 5.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
........................................................
§¸p sè: Y = 0 ta cã c¸c sè : x= 3, 6 9
Y = 5 ta cã x = 14,7
Bµi 6: T×m x vµ y ®Ó sè xy1996 chia hÕt cho 2, 5 vµ 9.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
........................................................
Bµi 7: T×m a vµ b ®Ó ba356 chia hÕt cho 36.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
........................................................
§¸p sè: ( Chia hết cho 36 thì tổng của 56a3b chia hết cho 4 và 9)
Bµi 8: T×m tÊt c¶ c¸c ch÷ sè a vµ b ®Ó ph©n sè 45
831 ba lµ sè tù nhiªn.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
........................................................
§¸p sè: ( Chia hết cho 45 thì tổng của 45
831 ba chia hết cho 5 và 9)
Bµi 9: T×m x ®Ó 5237 x chia hÕt cho 3.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
........................................................
§¸p sè: 37 + 2 + 5 = 41 vËy x = 1, 4 , 7
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
36
Bµi 10: T×m a vµ b ®Ó sè ba391 chia hÕt cho 9 vµ chia cho 5 d 1.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 11: T×m tÊt c¶ c¸c sè cã 3 ch÷ sè kh¸c nhau abc , biÕt: 3
2
7
b
ac.
B= 2 th× ac = 2 x 9 = 18 B= 5 th× ac = 2 x 19 = 39 B= 8 th× ac = 2 x 29 = 54 ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
1. ViÕt c©c sè tù nhiªn theo dÊu hiÖu chia hÕt Bµi 2 : Cho 4 ch÷ sè 0; 1; 5; 8. H·y lËp c¸c sè cã 3 ch÷ sè kh¸c nhau tõ 4 ch÷ sè ®· cho tho¶ m·n ®iÒu kiÖn: a) Chia hÕt cho 3 ? b) Chia hÕt cho 2 vµ 5 ? ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
2. Dïng dÊu hiÖu chia hÕt ®Ó ®iÒn c¸c ch÷ sè cha biÕt. Bµi 2:
Cho sè b = 2008xy thay x vµ y sao cho sè b chia hÕt cho 2, 5 vµ 3.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
3.bµi to¸n vÒ vËn dông tÝnh chÊt chia hÕt cña mét tæng vµ mét hiÖu. Bµi 1: Kh«ng lµm phÐp tÝnh, h·y xÐt xem c¸c tæng vµ hiÖu díi ®©y cã chia hÕt cho 3 hay kh«ng?
a) 240 + 123 b) 240 – 123 c) 459 + 690 + 1236 d) 2454 + 374 ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
37
Bµi 2:
Tæng kÕt n¨m häc 2007- 2008, mét trêng tiÓu häc cã 462 häc sinh tiªn tiÕn vµ 195 häc sinh giái. Ban gi¸m hiÖu dù ®Þnh thëng cho mçi häc sinh giái nhiÒu h¬n häc sinh tiªn tiÕn 2 quyÓn vë. C« v¨n phßng nhÈm tÝnh ph¶i mua 1996 quyÓn th× ®ñ ph¸t thëng. Hái c« v¨n phßng ®· tÝnh ®óng hay sai? Gi¶i thÝch t¹i sao ? ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
4.C¸c bµi to¸n vÒ phÐp chia cã d.
Cho a = xy5 . H·y thay x, y b»ng nh÷ng ch÷ sè thÝch hîp ®Ó dîc mét sè cã 3 ch÷ sè kh¸c nhau chia
cho 2,3 vµ 5 ®Òu d 4. ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
5. VËn dông tÝnh chÊt chia hÕt vµ phÐp chia cã d ®Ó gi¶i c¸c bµi to¸n cã lêi v¨n. Bµi 3: Mét cöa hµng då s¾t cã 7 thïng ®ùng 2 lo¹i ®inh 5 ph©n vµ 10 ph©n (mçi thïng chØ ®ùng mét lo¹i
®inh). Sè ®inh trong mçi thïng theo thø tù lµ 24kg, 26kg, 30kg, 37kg, 41kg, 55kg vµ 58 kg. Sau khi b¸n hÕt 6 thïng vµ chØ cßn mét thïng ®inh 10 ph©n, ngêi b¸n hµng thÊy r»ng trong sè ®inh ®· b¸n, ®inh 10 ph©n gÊp 3 lÇn ®inh 10 ph©n. Hái cöa hµng ®· cã bao nhiªu kil«gam ®inh mçi lo¹i? ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Bài 1: Trong giờ tập thể dục của lớp 4a thầy giáo cho các bạn học sinh xép hàng .lúc thì cho xép hàng 8
,lúc xép hàng 6,lúc lại xép hàng 4,hàng 3 hàng 2 vẫn thấy vừa đủ .Các bạn tính xem lớp 4a có bao nhiêu
bạn biết biết số học sinh là số nhỏ hơn 48. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 2:Mẹ có một số táo mẹ xếp vào đĩa .Khi xếp vào đĩa mẹ nhận thấy nếu xếp mỗi đĩa 9 quả hay 12 quả
thì cũng vừa hết .Hỏi mẹ có bao nhiêu quả táo ? biết số táo lớn hơn 30 nhỏ hơn 40
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài 3:ở một bến cảng có ba con tàu A,B,C Tàu a cứ 3 ngày cặp bến 1 lần ,tàu B là 4 ngày cặp bến 1 lần
,tàu C là 5 ngày .Nếu một hôm nào đó cả ba tàu cùng cặp bến thì hỏi sau bao nhiêu ngày ba tàu lại cùng
cặp bến.
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
38
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 4:Trong giờ tập thể dục của lớp 4 b thầy giáo cho các bạn học sinh xép hàng .lúc thì cho xép hàng 8
,lúc xép hàng 6,lúc lại xép hàng 4,hàng 3 hàng 2 đều thấy hàng cuối thiếi 1 người .Các bạn tính xem lớp
4b có bao nhiêu bạn .Biết biết số học sinh là số nhỏ hơn 48. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 5:Trong giờ tập thể dục của lớp 4C thầy giáo cho các bạn học sinh xếp hàng .lúc thì cho xếp hàng 8,
lúc xếp hàng 6, lúc lại xếp hàng 4, hàng 3 hàng 2 đều thấy thừa 1 người .Các bạn tính xem lớp 4c có bao
nhiêu bạn biết số học sinh là số nhỏ hơn 48. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 6 : Mẹ có một số táo mẹ xếp vào đĩa .Khi xếp vào đĩa mẹ nhận thấy nếu xếp mỗi đĩa 9 quả hay 12 quả
thì đĩa cuối đều thiếu 2 quả .Hỏi mẹ có bao nhiêu quả táo ? biết số táo lớn hơn 30 nhỏ hơn 40. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 7: Một ông tướng cầm quân đi dẹp giặc .Ông cho quân xép hàng 10 thì thấy hàng cuối thiếu 1 người,
thấy vậy ông lại cho quân xếp hàng 9 thì thấy hàng cuối vẫn thiếu 1 người; thế là ông lại cho quân xếp
hàng 8 thì hàng cuối vẫn thiếu 1 người. Ông bèn cho xếp hàng 7;6;5;4;3;2 đều vẫn như vậy .
Tính hộ xem ông tướng có bao nhiêu quân biết số quân của ông ít hơn 5000 .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
39
10. BÀI TOÁN CÓ NỘI DUNG HÌNH HỌC Bài 3:Một thửa ruộng hình chữ nhật có chu vi 100m .Người ta tăng chiều dài lên 1/3 chiều dài thì chu vi
hình chữ nhật mới là 120m.
Tính diện tích thửa ruộng ban đầu . .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 4:Một thửa ruộng hình chữ nhật có chu vi 100m .Người ta giảm chiều dài đi 1/3 chiều dài thì chu vi
hình chữ nhật mới là 80m.
Tính diện tích thửa ruộng ban đầu . .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 5:Một thửa ruộng hình chữ nhật có chu vi 110m . Nếu tăng chiều rộng 5 m và giảm chiều dài 5 m thì
diện tích thửa ruộng không thay đổi .Tính diện tích thửa ruộng
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
40
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 6:Một thửa đất hình vuông trên thửa đất đó người ta đào một cái ao hình vuông cạnh cái ao cách đều
cạnh thửa đất .Chu vi cái ao kém chu vi thửa đất là 64 m.Tính diện tích cái ao biết diện tích phần dất còn
lại là 600m2.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài 7:Bác An có một mảnh đất vườn chữ nhật .ở một góc vườn bác đào một cái ao hình vuông có 1 cạnh
cách chiều rộng mảnh vườn 33 m còn cạnh kia cách chiều dài mảnh vườn là 17 m .Biết diện tích phần đất
còn lại là 1311m2 . Tính diện tích mảnh vườn.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 8:Một thửa ruộng hình chữ nhật có chu vi 200 m .chiều dài hình chữ nhật hơn 2 lần chiều rộng là
10m.Tính diện tích thửa ruộng. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 9:Một thửa ruộng hình chữ nhật có chu vi 160 m .chiều dài hình chữ nhật kém 2 lần chiều rộng là
10m.Tính diện tích thửa ruộng. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 10:Một thửa ruộng hình chữ nhật có chu vi 200 m Dọc theo chiều dài người ta ngăn thửa ruộng thành
2 thửa ruộng nhỏ .Biết 1 trong 2 thửa ruộng là hình vuông và chu vi thửa ruộng hình vuông nhỏ hơn chu
vi thửa ruộng hình chữ nhật nhỏ là 20m Tính diện tích thửa ruộng ban đầu. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
41
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 11:Một thửa ruộng hình chữ nhật có chu vi 160 m Dọc theo chiều dài người ta ngăn thửa ruộng thành
2 thửa ruộng nhỏ .Biết 1 trong 2 thửa ruộng là hình vuông và chu vi thửa ruộng hình vuông lớn hơn chu
vi thửa ruộng hình chữ nhật nhỏ là 20m Tính diện tích thửa ruộng ban đầu. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 12:Một thửa ruộng hình chữ nhật có chiều dài gấp 3 lần chiều rộng . Nếu tăng chiều rộng 5m và
giảm chiều dài 5 m thì diện tích tăng thêm 300m2
. Tính diện tích thửa ruộng ban đầu
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài 13: Một hình chữ nhật, nếu tăng chiều rộng để bằng chiều dài của nó thì diện tích tăng thêm 20m
2,
còn khi giảm chiều dài cho bằng chiều rộng thì diện tích giảm 16 m2. Tính diện tích hình chữ nhật
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 14 Một hình chữ nhật có diện tích 135m2
. Chiều dài bằng 3/5 chiều rộng .Tính chu vi hình chữ nhật. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 15: Một cái sân hình chũ nhật có chu vi 110m. Người ta tăng chiều rộng lên 5m thì sân trở thành hình
vuông . tính diện tích cái sân ban đầu. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 16 Một mảnh vườn hình chữ nhật có chu vi 180 m nếu giảm chiều dài 10 m thì mảnh vườn trở thành
mảnh vườn hình vuông .Tính diện tích mảnh vườn ban đầu . ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
42
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài 17 Một mảnh vườn hình chữ nhật có chu vi 150 m .Nếu giảm chiều dài 10m và tăng chiều rộng 5m
thì được một hình chữ nhật mới có chiều dài gấp 4 chiều rộng .Tính diện tích mảnh vườn. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 18 Một hình chữ nhật có chiều dài gấp 3 chiều rộng . Nếu tăng chiều rộng lên 24 m thì được hình chữ
nhật mới có chiều dài gấp 3 chiều rộng. Tính diện tích hình chữ nhật. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 19 Một mảnh vườn hình chữ nhật có chiều dài gấp 4 lần chiều rộng . Nếu tăng chiều dài 5m và giảm
chiều rộng 5 m thì diện tích giảm đi 256m2. Tính diện tích mảnh vườn.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 20 Một cái ao hình chữ nhật có chu vi 120 m .Dọc theo chiều dài người ta ngăn cái ao thành 2 ao nhỏ
(Hình vẽ). Tổng chu vi 2 ao mới tạo thành la 180 m .Tính diện tích cái ao ban đầu.
.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 21 Sân trường em hình vuông .Để tăng thêm diện tích nhà trường đã mở rộng về mỗi phía 3m thì diện
tích tăng thêm là 196 m2 . Hỏi trước đây sân trường em có diện tích là bao nhiêu m
2?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
43
Bài 22: Bác Hà có hai tấm kính hình chữ nhật. Chiều rộng của mỗi tấm kính bằng 1/2 chiều dài của nó
và chiều dài của tấm kính nhỏ đúng bằng chiều rộng của tấm kính to. Bác ghép hai tấm kính sát vào nhau
và đặt lên bàn có diện tích 90 dm2 thì vừa khít. Hãy tính kích thước của mỗi tấm kính đó.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 23: Khu vườn hình chữ nhật có nửa chu vi 108m. Nếu giảm chiều dài 3m và tăng chiều rộng thêm 3m
thì được hình vuông . Tính diện tích hình vuông. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 24: Hình chữ nhật có chu vi 84m. Nếu bớt chiều rộng 5m và bớt chiều dài 7m thì được hình vuông.
Tính chiều dài và chiều rộng hình chữ nhật. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 25: Hình chữ nhật có nửa chu vi 86m. Nếu giảm chiều dài 9m và tăng chiều rộng thêm 5m thì được
hình vuông . Tính diện tích hình chữ nhật. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 26: Hình chữ nhật có chu vi 216m. Nếu giảm chiều rộng 5m và giảm chiều dài 21m thì được hình
vuông. Tính diện tích hình vuông đó. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 27: Hình chữ nhật có chu vi gấp 10 lần chiều rộng. Chiều dài bằng 88m. Tính chiều rộng. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 28: Hình chữ nhật có chu vi gấp 12 lần chiều rộng. Chiều dài bằng 120m. Tính diện tích hình chữ
nhật.
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
44
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 29: Hình chữ nhật có chu vi gấp 14 lần chiều rộng. Chiều dài hơn chiều rộng 80m. Tính chiều dài và
chiều rộng hình chữ nhật. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 30: Hình chữ nhật có chu vi gấp 16 lần chiều rộng. Chiều dài hơn chiều rộng 198m. Tính diện tích
hình chữ nhật đó. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 31: Hình chữ nhật có nửa chu vi 99m. Nếu tăng chiều rộng thêm 5m và giảm chiều dài đi 5m thì diện
tích không thay đổi. Tính chiều dài và chiều rộng hình chữ nhật. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 32: Hình chữ nhật có chu vi 160m. Nếu tăng chiều rộng thêm 10m và giảm chiều dài đi 10m thì diện
tích không thay đổi. Tính diện tích hình chữ nhật đó. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 33: Hình chữ nhật có chu vi gấp 3 lần chiều dài. Chiều rộng bằng 5m. Tính diện tích hình chữ nhật
đó. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
45
Bài 34: Hình chữ nhật có chu vi gấp 3 lần chiều dài. Chiều rộng kém chiều dài 5m. Tính diện tích hình
chữ nhật đó. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 35: Hình chữ nhật có chu vi 48m. Nếu tăng chiều dài 6m thì được hình chữ nhật mới có chiều dài gấp
2 lần chiều rộng. Tính chiều dài và chiều rộng hình chữ nhật ban đầu. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 36: Hình chữ nhật có chu vi 64cm. Nếu giảm chiều rộng 2cm, thêm chiều dài 2cm thì được hình chữ
nhật mới có chiều dài gấp 3 lần chiều rộng. Tính chiều dài và chiều rộng hình chữ nhật ban đầu. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 37: Trung bình cộng chiều dài và chiều rộng hình chữ nhật là 18m, chiều dài hơn chiều rộng 6m.
Tính chiều dài và chiều rộng hình chữ nhật. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 38: Trung bình cộng chiều dài và chiều rộng hình chữ nhật là 32m, chiều dài gấp 3 lần chiều rộng
6m. Tính diện tích hình chữ nhật. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 39: Hình chữ nhật có chiều dài gấp 3 lần chiều rộng. Nếu giảm chiều rộng đi 2m và tăng chiều dài
thêm 2m thì diện tích giảm đi 68m2 . Tính diện tích hình chữ nhật ban đầu.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
46
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 40: Hình chữ nhật có chiều dài gấp 4 lần chiều rộng. Nếu giảm chiều dài đi 3m và tăng chiều rộng
thêm 3m thì diện tích tăng thêm 108m2 . Tính chiều dài và chiều rộng hình chữ nhật ban đầu.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài 41: Hình chữ nhật có chiều dài gấp 5 lần chiều rộng. Nếu giảm chiều rộng đi 2m và giảm chiều dài đi
2m thì diện tích giảm đi 140m2 . Tính diện tích hình chữ nhật ban đầu.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài 42: Hình chữ nhật có chiều dài gấp 5 lần chiều rộng. Nếu tăng chiều dài thêm 5m và tăng chiều rộng
thêm 5m thì diện tích tăng thêm 475m2 . Tính diện tích hình chữ nhật ban đầu.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài 43: Một thửa hình chữ nhật có chiều rộng bằng 1/2 chiều dài. Tính diện tích thửa đất. Biết rằng nếu
tăng chiều rộng 15m và giảm chiều dài 9m thì thửa đất trở thành hình vuông. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 44: Nếu bớt một cạnh hình vuông là 7m và bớt một cạnh khác 25m thì được hình chữ nhật có chiều
dài gấp 3 lần chiều rộng. Tính chu vi và diện tích của hình vuông. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 45: Trên một miếng đất hình vuông, người ta đào một cái ao hình vuông để thả cá. Sau khi đào xong
thì diện tích còn 1280m2. Tính diện tích miếng hình vuông ban đầu. Biết rằng cạnh ao kém cạnh miếng
đất 32m. ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
47
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài 46: Cho hai hình chữ nhật A và B. Diện tích hình A hơn hình B là 300m
2, chu vi hình A hơn hình B
là 20m. Tính diện tích mỗi hình chữ nhật. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 47: Một mảnh đất hình chữ nhật có chiều rộng bằng 1/5 chiều dài, nếu tăng mỗi chiều thêm 5m thì
mảnh đất hình chữ nhật có diện tích mới hơn diện tích cũ là 300m2. Tính diện tích mảnh đất hình chữ nhật
sau khi mở rộng. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 48: Một mảnh đất hình chữ nhật có chiều dài hơn chiều rộng 15m, nếu tăng mỗi chiều thêm 5m thì
mảnh đất hình chữ nhật có diện tích mới hơn diện tích cũ là 600m2. Tính diện tích mảnh đất hình chữ nhật
ban đầu. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 49: Ở chính giữa một mảnh đất hình vuông người ta đào một cái ao cũng hình vuông. Cạnh ao song
song và cách đều đám đất 2m. Tính diện tích cái ao biết diện tích mảnh đất hơn diện tích cái ao là 64m2.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 50: Tính diện tích hình chữ nhật biết 3 lần chiều rộng 2 lần chiều dài bằng 62m, 2 lần chiều rộng 3
lần chiều dài bằng 68m. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 51: Một khu đất hình chữ nhật có chu vi bằng 286m. CHiều dài hơn chiều rộng 5m. Người ta mở
rộng chiều dài và chiều rộng khu đất them một đoạn bằng nhau để được khu đất mới có chiều dài gấp đôi
chiều rộng. Tính diện tích khu đất mới.
(Tham khảo thêm Đề thi và phần Bài tập mở rộng)
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
48
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
11/®¬n vÞ ®o
Bµi 28: C« Mai cã 2kg ®êng, c« ®· dïng 4
1 sè ®êng ®ã ®Ó lµm b¸nh. Hái c« Mai cßn l¹i bao nhiªu gam
®êng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
49
Bµi 29: ViÕt sè thÝch hîp vµo chç chÊm:
1 phót = ...gi©y 3 phót = .........gi©y 2 phót 10 gi©y = ...gi©y
6
1phót = .......gi©y
5
1thÕ kØ = .....n¨m
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 30: ViÕt tiÕp vµo chç chÊm:
a) N¨m 40, Hai Bµ Trng phÊt cê khëi nghÜa chèng l¹i ¸ch thèng trÞ cña nhµ H¸n, n¨m ®ã thuéc thÕ kØ ... b)Lª Lîi lªn ng«i vua vµo n¨m 1428. N¨m ®ã thuéc thÕ kØ ... .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 31: Khoanh vµo ch÷ ®Æt tríc c©u tr¶ lêi ®óng:
Ngµy 23 th¸ng 5 lµ thø 3. Ngµy 1 th¸ng 6 cïng n¨m ®ã lµ: A. Thø t B. Thø n¨m C. Thø s¸u D. Thø b¶y .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
12. DẠNG TOÁN LIÊN QUAN ĐẾN CHUYỂN TỪ A
SANG B ; B SANG C; C SANG ... Bài 1: Ba kho chứa 560 tấn thóc .Nếu chuyển 30 tấn từ kho thứ nhất sang kho thứ 2 Sau đó chuyển 25 tấn
từ kho thứ 2 sang kho thứ 3 rồi chuyển 12 tấn từ kho thứ 3 sang kho thứ nhất thì số thóc ở 3 kho bằng
nhau .Tính số thóc mỗi kho. ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
50
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 2 Ba kho chứa 240 tấn thóc .Nếu chuyển 25 tấn từ kho thứ nhất sang kho thứ 2 Sau đó chuyển 35 tấn
từ kho thứ 2 sang kho thứ 3 thì số thóc ở 3 kho bằng nhau .Tính số thóc mỗi kho. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 3: Ba lớp 4a;4b;4c. đi trồng cây cả 3 lớp trồng được 120 .Số cây lớp 4a và 4 b trồng được là 70 cây
;số cây lớp 4b và 4c là 90 cây ;số cây lớp 4c và 4a là 80 cây . Tính số cây mỗi lớp .
(Tham khảo thêm Đề thi và phần Bài tập mở rộng) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
13.DẠNG TOÁN KHỬ Bài 1: Mua 3 lọ mực và 4 cái bút hết 25000 đồng . Mua 5 lọ mực và 4 cái bút hết 31000 đồng .
Tính giá tiền mỗi loại. ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
51
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 2: Minh mua 5 quyển vở và 8 quyển sách hết 75500 đồng. Tâm mua 3 quyển sách và 10 quyển vở hết
73000 đồng. Tính giá tiền mỗi loại. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 3: Mua 3 m vải hoa và 7 m vải xanh hết 370 000 đồng . Mua 4 m vải hoa và 5 m vai xanh phải trả
320 000 Đồng. Tính giá tiền 1m vải mỗi loại. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 4: Minh mua 5 quyển vở và 8 quyển sách hết 42000 đồng. Biết một quyển sách có giá gấp 2 lần 1
quyển vở. Tính giá tiền mỗi loại .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... *Bài tập 1: Để học thủ công, tổ Một mua 10 cái kéo và 5 túi giấy màu hết tất cả 50.000 đồng. Tổ
Hai cũng mua 8 cái kéo và 10 túi giấy màu như thế hết tất cả 52.000 đồng. Tính giá tiền một cái kéo, giá
tiền một túi giấy màu? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
*Bài tập 2: Văn phòng trường em lần đầu mua 24 cây bút bic và 12 cây bút chì hết tất cả 60.000
đồng. Lần sau mua 10 cây bút bic và 8 cây bút chì hết tất cả 28.000 đồng. Hãy tính giá tiền mỗi cây bút
từng loại? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
*Bài tập 3: Cô Thu mua 1 mét lụa và 1 mét vải hết tất cả 50.000 đồng. Cô Đông mua 2
1 mét lụa
và 5
2 mét vải cùng loại như thế hết tất cả 23.000 đồng. Hỏi cô Xuân mua 8 mét lụa và 15 mét vải cùng
loại như thế phải trả bao nhiêu tiền? ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
52
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
4. Bài tập về nhà: Bạn Mai mua 3 lọ mực đỏ và 2 lọ mực xanh giá 23.000 đồng. Bạn Lan cũng
mua 2 lọ mực đỏ và 3 lọ mực xanh mực như thế hết 22.000 đồng. Tính giá tiền một lọ mực mỗi loại? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
14. MỘT SỐ BÀI TOÁN VỀ TÍNH TUỔI Bài 1: Năm nay con 4 tuổi và kém cha 35 tuổi. Hỏi sau bao nhiêu năm nữa thì 2 lần tuổi cha bằng 7 lần
tuổi con ? ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
53
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài 2: Cách đây 3 năm, em lên 5 tuổi và kém anh 8 tuổi. Hỏi cách đây mấy năm thì tuổi anh gấp 3 lần
tuổi em ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 3: Tuổi cha năm nay gấp 4 lần tuổi con và tổng số tuổi của 2 cha con cộng lại là 50 tuổi. Hãy tính
tuổi của 2 cha con khi tuổi cha gấp 4 lần tuổi con. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 4: Hùng hơn Cường 6 tuổi, biết rằng 7
4 tuổi của Hùng bằng
3
2tuổi của Cường. Tính tuổi của mỗi
người. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 5: Năm nay tuổi mẹ gấp 3 lần tuổi con. 8 năm trước tuổi mẹ gấp 7 lần tuổi con.Tìm tuổi mỗi người
hiện nay. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 6: Tuổi của bà, của mẹ và của Mai năm nay cộng được 100 năm.Bạn hãy tính tuổi của mỗi người,
biết rằng, tuổi của Mai có bao nhiêu ngày thì tuổi của mẹ có bấy nhiêu tuần và tuổi của Mai có bao nhiêu
tháng thì tuổi của bà có bấy nhiêu năm. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 7: Tuổi em năm nay nhiều hơn hiệu số tuổi của 2 chị em là 15. Tổng số tuổi của 2 chị em cùng nhỏ
hơn 2 lần tuổi của chị là 3. Tính tuổi mỗi người. ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
54
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bài 8: 8 năm về trước tổng số tuổi của ba cha con cộng lại là 48. 8 năm sau cha hơn con lớn 26 tuổi và
hơn con nhỏ 34 tuổi. Tính tuổi của mỗi người hiện nay. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 9: Hai năm trước đây tuổi hai chú cháu cộng lại bằng 24. Hỏi sau mấy năm nữa thì tuổi chú gấp 4 lần
tuổi cháu? Biết rằng 2 năm trước tuổi cháu có bao nhiêu ngày thì tuổi chú có bấy nhiêu tuần . .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 10: Tuổi em hiện nay gấp 2 lần tuổi em khi anh bằng tuổi em hiện nay.Khi tuổi em bằng tuổi anh
hiện nay thì 2 lần tuổi em lớn hơn tuổi anh lúc đó 15 tuổi. Tính tuổi hiện nay của mỗi người. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 11: Khi tuổi chị bằng tuổi em hiện nay thì tuổi chị lớn hơn 3 lần tuổi em là 3 tuổi. đến khi chị 34 tuổi
thì tuổi em bằng tuổi chị hiện nay.Tìm tuổi của 2 chị em hiện nay. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 12: Tuổi bố năm nay gấp 2,3 lần tuổi con. 25 năm về trước, tuổi bố gấp 8,3 lần tuổi con. Hỏi khi tuổi
bố gấp 3 lần tuổi con thì con bao nhiêu tuổi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 13: Hai người bạn gặp nhau. Một người hỏi bạn mình :" Các con của anh bao nhiêu tuổi?" Người thứ
hai trả lời:
"Tôi có hai đứa con trai : tuổi tôi gấp 4 lần tuổi đứa thứ nhất và gấp 7lần đứa thứ hai".
Hỏi ông bố bao nhiêu tuổi và các con của ông bao nhiêu tuổi?
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
55
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 14: Ba người có tên là A, B, C cùng ở trong 1 buồng của toa xe lửa. Trong khi trò
chuyện mới biết rằng:
- Nếu đổi chỗ các chữ số trong tuổi của A thì được tuổi của B
- Hiệu của tuổi giữa A và B gấp đôi số tuổi của C
- Tuổi của B gấp 10 lần tuổi của C
Hỏi mỗi người bao nhiêu tuổi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 15 : Người ta hỏi một ông già rằng ông đã tham gia quân đội trong bao lâu, ông trả lời:Số năm tham
gia quân đội của tôi bằng 1/27 tuổi của tôi hay bằng 1/7 tuổi của cháu tôi hoặc bằng đúng tuổi của con trai
tôi. Ngoài ra tuổi của tôi gần số 90 hơn là gần số 100. Hỏi ông già đã tham gia quân đội trong bao lâu? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 16 : An hỏi Hà: “ Năm nay anh bao nhiêu tuổi? ” Anh Hà trả lời: “ Nếu sang năm lấy tuổi của anh
nhân với 6 sẽ được một số có 3 chữ số trong đó chữ số hàng trăm là 1, còn chữ số hàng chục và chữ số
hàng đơn vị chính là chữ số hàng hàng chục và chữ số hàng đơn vị của tuổi anh khi đó”. Hỏi anh Hà năm
nay bao nhiêu tuổi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 17: Vào năm mới tuổi bố nhiều hơn tuổi anh là 29, tuổi mẹ nhiều hơn tuổi em là 25, hiệu của tuổi bố
và tuổi mẹ gấp đôi hiệu của tuổi anh và tuổi em. Tính tuổi của mỗi người (bố, mẹ, anh và em) biết rằng
tổng số tuổi của bốn người là 90. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 18: Ngày đầu năm 1991, bác Nam hỏi anh Việt:
- Năm nay cháu bao nhiêu tuổi?
- Tuổi cháu năm nay đúng bằng tổng các chữ số của năm sinh - anh Việt trả lời.
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
56
Thế mà bác Nam tính ra ngay tuổi của anh Việt. Bác gật gù nói:
- Lúc bác bằng tuổi cháu hiện nay, bác đang tham gia kháng chiến chống Pháp, và năm ấy cũng có tổng
các chữ số bằng tuổi cháu.
Anh Việt cũng tính đúng tuổi của bác Nam.
Hỏi anh Việt và bác Nam sinh năm nào? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 19: Trả lời về tuổi của mình, 1 người đàn ông nói như sau: "Cứ vào sinh nhật của tôi, cha tôi lại giết 1
con cừu để ăn mừng, bộ da cừu ông xếp vào 1 chỗ. Tôi lớn lên lấy vợ cũng sinh được 1 thằng con trai,
vào sinh nhật nào của nó tôi cũng lại giết cừu, cất bộ da vào 1 chỗ. Năm nay số da cừu của tôi bằng số da
cừu của nó.
Hỏi tuổi người đàn ông và con trai của ông ta là bao nhiêu? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 20: Trong giờ nghỉ ở một hội nghị, các đồng nghiệp hỏi một giáo sư xem ông ta có mấy con và chúng
bao nhiêu tuổi. Giáo sư trả lời:
- Tôi có 3 con trai. Có sự trùng hợp lý thú là ngày sinh của chúng đều là ngày hôm nay, tuổi chúng cộng
lại bằng ngày hôm nay và đem nhân với nhau thì tích là 36.
Một đồng nghiệp nói:
- Chỉ như vậy thì chưa xác định được tuổi của bọn trẻ.
- Ồ, đúng vây. Tôi quên không nói thêm rằng: Khi chúng tôi chờ sinh đứa thứ 3 thì 2 đứa lớn đã được gửi
về quê với ông bà.
- Xin cám ơn ngài, giờ thì tôi đã biết tuổi của bọn trẻ rồi.
Vậy tuổi của mỗi cậu con trai là bao nhiêu và ngày hôm đó là ngày nào trong tháng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 1 Hiện nay tuổi em bằng 2/3 tuổi anh .Đến khi tuổi em bằng tuổi anh hiện nay thì tổng số tuổi của hai
anh em là 49 tuổi .
tính tuổi hiện nay của mỗi người. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 2 Hiện nay bố gấp 6 lần tuổi con . 4 năm nữa bố gấp 4 lần tuổi con .Tính tuổi hiên nay của mỗi
người.
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
57
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 3 Tổng số tuổi của ông ,bố và cháu là 120 tuổi .Tính tuổi mỗi người biết tuổi ông là bao nhiêu năm
thì cháu bấy nhiêu tháng và cháu bao nhiêu ngày thì bố bấy nhiêu tuần .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 4 Hiện nay tuổi mẹ gấp 4 lần tuỏi con . Năm năm nữa tuổi mẹ gấp 3 lần tuổi con .Tính tuổi hiện nay
của mỗi người. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 5: Tuổi của con hiện nay bằng 1/2 hiệu tuổi của bố và tuổi con. Bốn năm trước, tuổi con bằng 1/3
hiệu tuổi của bố và tuổi con. Hỏi khi tuổi con bằng 1/4 hiệu tuổi của bố và tuổi của con thì tuổi của mỗi
người là bao nhiêu ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
58
15. BÀI TOÁN GIẢ THIẾT TẠM VÝ dô 2: 12 con võa gµ võa thá, c¶ th¶y ®Õm ®îc 32 ch©n. Hái cã bao nhiªu con gµ, bao nhiªu con
thá. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
VÝ dô: Cã 18 « t« gåm 3 lo¹i: Lo¹i 4 b¸nh chë ®îc 5 tÊn, lo¹i 6 b¸nh chë ®îc 6 tÊn vµ lo¹i 8 b¸nh
chë ®îc 6 tÊn. 18 xe ®ã chë ®îc tÊt c¶ 101 tÊn hµng, vµ cã tÊt c¶ 106 b¸nh xe. Hái mçi lo¹i cã bao nhiªu xe? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi to¸n 1:
Cã 10 xe chë g¹o gåm hai lo¹i. Lo¹i 1 xe chë ®îc 43 t¹ vµ lo¹i 1 xe chë ®îc 32 t¹. TÊt c¶ ®· chë ®îc 39 tÊn 8 t¹ g¹o. Hái cã bao nhiªu xe mçi lo¹i? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi to¸n 2:
Cã 8 sät ®ùng tÊt c¶ 1120 qu¶ võa cam võa quýt. Mçi sät cam ®ùng ®îc 75 qu¶, mçi sät quýt ®ùng ®îc 179 qu¶. Hái mçi lo¹i cã bao nhiªu qu¶? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi to¸n 3:
Mét bÕp ¨n mua 200 con võa Õch võa cua bÓ. Tæng sè ch©n ®Õm ®îc lµ 1400 ch©n (cµng cua xem nh ch©n cua). Hái cã bao nhiªu con mçi lo¹i. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
59
Bµi to¸n 4:
Cã 15 « t« gåm 3 lo¹i: Lo¹i 4 b¸nh chë ®îc 5 tÊn, lo¹i 6 b¸nh chë ®îc 10 tÊn vµ lo¹i 6 b¸nh chë ®îc 8 tÊn. 15 xe ®ã chë ®îc tÊt c¶ 121 tÊn hµng, vµ cã tÊt c¶ 84 b¸nh xe. Hái mçi lo¹i cã bao nhiªu xe. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi to¸n 5: Cã 15 « t« gåm 3 lo¹i, lo¹i 4 b¸nh chë 5 tÊn, lo¹i 4 b¸nh chë 6 tÊn, lo¹i 6 b¸nh chë 8
tÊn. Hái sè xe mçi lo¹i lµ bao nhiªu, biÕt tæng sè b¸nh xe lµ 70 b¸nh, tæng sè hµng chë ®îc lµ 93 tÊn. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
16. CÁC BÀI TOÁN LIÊN QUAN TRỒNG CÂY
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
60
17. MỘT SỐ BÀI TOÁN GIẢI NGƯỢC TỪ CUỐI Bài 1: Lan có một số nhãn vở .Lan tặng Mai 1/2 số nhãn vở và 1chiếc .Lan tặng Hoà 1/2 số nhãn vở còn lại và 2 chiếc .Lan tặng Nga 1/2 số nhãn vở còn lại sau 2 lần và 3 chiếc .Cuối cùng Lan còn
lại 6 chíêc cho Mình .Hỏi Lan có tất cả bao nhiêu nhãn vở ,và tặng mỗi bạn bao nhiêu nhãn vở. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 2, Một bà đem trứng đi chợ bán .Lần đầu bà bán 1/2 số trứng và 1/2 quả trứng .Lần 2 bà bán 1/2 số
trứng còn lại và 1/2 quả trứng .Lần thứ 3 bà bán 1/2 Số trứng còn lại sau 2 lần đầu và 1/2 quả trứng nữa
thì vừa hết . Hỏi bà đem ra chợ bán bao nhiêu quả trứng. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 3: Mai có một số bông hồng ,Mai tặng Nga 1/2 số hoa Mai có .Tặng Đào 1/2 số còn lại .Cuối cùng
Mai còn 7 Bông dành cho mình .Hỏi Mai đã tặng mỗi bạn bao nhiêu bông hoa.
(Tham khảo thêm Đề thi và phần Bài tập mở rộng) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... 1. T×m mét sè biÕt r»ng, sè ®ã trõ 80, ®îc bao nhiªu nh©n víi 5 råi céng víi 192 th× b»ng 792. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... 2. MÑ cho hai anh em mét sè tiÒn ®Ó mua s¸ch. NÕu anh cho em mét sè tiÒn ®óng b»ng sè tiÒn cña em, råi em l¹i cho anh mét sè tiÒn ®óng b»ng sè tiÒn cßn l¹i cña anh th× em cã 35000 ®ång vµ anh cã 30000 ®ång. Hái mÑ ®· cho mçi ngêi bao nhiªu tiÒn ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
61
3. Cã ba hép bi A, B, C. LÇn ®Çu chuyÓn 10 bi tõ hép A sang hép B vµ 15 bi tõ hép C sang hép B. LÇn thø hai chuyÓn 6 bi tõ hép A sang hép B vµ 9 bi tõ hép B sang hép C. LÇn thø ba chuyÓn 20 bi tõ hép C sang hép A vµ 18 bi tõ hép B sang hép A. LÇn thø t chuyÓn 9 bi tõ hép A sang hép B vµ 7 bi tõ hép C sang hép B, th× cuèi cïng hép A cã 190 bi, hép B cã 350 bi, hép C cã 280 bi. Hái lóc ®Çu mçi hép cã bao nhiªu bi ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... 4. Mét ngêi ra chî b¸n cam. LÇn thø nhÊt b¸n 1/2 sè cam céng thªm 1/2 qu¶. LÇn thø hai b¸n 1/2 sè cam cßn l¹i céng thªm 1/2 qu¶. LÇn thø ba b¸n 1/2 sè cam cßn l¹i céng thªm 1/2 qu¶. LÇn thø t b¸n 1/2 sè cam cßn l¹i céng 1/2 qu¶ th× võa hÕt. TÝnh sè cam ngêi ®ã ®em b¸n. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... 5. (To¸n cæ). Mét tªn tham lam gÆp mét con quû ë c¹nh chiÕc cÇu. Tªn nµy than phiÒn vÒ nçi nghÌo khæ cña m×nh. Con quû nãi r»ng " T«i cã thÓ gióp anh. Cø mçi lÇn anh ®i qua cÇu th× sè tiÒn cña anh sÏ ®îc t¨ng gÊp ®«i; nhng ngay sau ®ã anh ph¶i tr¶ cho t«i 24 xu. B»ng lßng chø ?". Tªn tham lam b»ng lßng nh thÕ. Sau khi h¾n ®i qua cÇu ba lÇn th× thÊy trong tói cña m×nh kh«ng cßn mét xu nµo. Hái lóc ®Çu tªn tham lam cã bao nhiªu tiÒn ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... 6. Trong mét buæi lao ®éng trång c©y ®Çu xu©n, líp 5A ®· chia sè c©y cho c¸c tæ lÇn lît nh sau: Tæ Mét trång 20 c©y vµ 4/ 100 sè c©y cßn l¹i; Tæ Hai trång 21 c©y vµ 4/100 sè c©y cßn l¹i; Tæ Ba trång 22 c©y vµ 4/100 sè c©y cßn l¹i;
…………………………………………………. Cø chia nh vËy cho ®Õn tæ cuèi cïng th× võa hÕt sè c©y vµ sè c©y mçi tæ ®em trång ®Òu b»ng nhau. Hái líp 5 A cã mÊy tæ vµ mçi tæ ®îc chia bao nhiªu c©y ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... 7. Trong hép cã 130 bi. Hai b¹n ch¬i trß bèc bi. Mçi lÇn cã thÓ lÊy tõ 1 ®Õn 6 bi. Ai lÊy ®îc viªn bi cuèi cïng ngêi ®ã th¾ng cuéc. B¹n ®îc bèc tríc, theo b¹n nªn lÊy nh thÕ nµo ®Ó b¹n lu«n lµ ngêi th¾ng cuéc ? ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
62
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
18. DẠNG TOÁN CÔNG VIỆC Bài 1:Bác An làm một công việc hết 8 giờ .Bác Bình cũng công việc ấy hết 5 giờ .Hỏi nếu 2 bác cùng
làm công việc ấy thi sau bao nhiêu giờ sẽ hoàn thành? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 2: Nếu bể không có nước vòi thứ nhất chảy trong 3 giờ sẽ đầy bể.Nếu bể không có nước vòi thứ 2
chảy trong 5 giờ sẽ đầy bể .Hỏi nếu bể không có nước cùng 1 lúc cho cả 2 vòi chảy trì trong bao lâu sẽ
đầy bể? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 3: Bác Minh làm Một công việc hết 8 giờ .Bác Tâm cũng công việc ấy làm hết 5 giờ . Đầu tiên bác
Minh làm một mình sau khi làm được 4 giờ thì bác Tâm đến làm cùng với bác Minh .Hỏi sau bao nhiêu
lâu nữa thì hai bác làm xong công việc đó?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 4:Bác An làm một công việc hết 8 giờ .Bác Bình cũng công việc ấy hết 5 giờ .Lúc đâu 2 bác cùng
làm nhưng sau khi làm được 3 giờ do bận công việc nên bác Bình phải đi làm việc khác .Hỏi bác An còn
phải làm bao lâu nữa mới hoàn thành công việc ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 5: Nếu bể không có nước vòi thứ nhất chảy trong 4 giờ sẽ đầy bể.Nếu bể không có nước vòi thứ 2
chảy trong 5 giờ sẽ đầy bể .Khi bể không có nước người ta cho 2 vòi cùng chảy vào bể sau khi chảy được
2 giờ người ta tắt vòi thứ nhất để vòi thứ 2 chảy tiếp .Hỏi sau bao nhiêu thời gian nữa thì bể đầy nước?
(Tham khảo thêm Đề thi và phần Bài tập mở rộng) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
63
Bài 1 : Sơn và Hải nhận làm chung một công việc. Nếu một mình Sơn làm thì sau 3 giờ sẽ xong việc, còn
nếu Hải làm một mình thì sau 6 giờ sẽ xong công việc đó. Hỏi cả hai người cùng làm thì sau mấy giờ sẽ
xong công việc đó. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 2 : Hai vòi nước cùng chảy vào bể nước thì sau 1 giờ 12 phút sẽ đầy bể. Nếu một mình vòi thứ nhất
chảy thì sau 2 giờ sẽ đầy bể. Hỏi nếu một mình vòi thứ hai chảy thì mấy giờ đầy bể ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 3 : Ba người dự định đắp xong một con đường. Người thứ nhất có thể đắp xong con đường đó trong 3
tuần. Người thứ hai có thể đắp xong một con đường dài gấp 3 lần con đường đó trong 8 tuần. Người thứ
ba có thể đắp xong một con đường dài gấp 5 lần con đường đó trong 12 tuần. Hỏi cả ba người cùng đắp
con đường dự định ban đầu thì sẽ hoàn thành trong bao nhiêu giờ, nếu mỗi tuần làm việc 45 giờ ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
64
19.BÀI TOÁN CHIA GIA TÀI *Đề : Một ông nhà giàu khi vợ đang mang thai thì mắc bệnh hiểm nghèo, trước lúc lâm chung ông ta để
lại “Di chúc ” : Sau khi qua đời nếu vợ sinh con trai thì gia tài cho con trai 2/3 và vợ 1/3; Nếu sinh con
gái thì con gái 1/3; vợ 1/3; còn lại 1/3 làm từ thiện. Nhưng thực tế sau khi ông ta chết, vọ sinh đôi : 1 con
trai và 1 con gái.
Hỏi Tòa án dân sự phải xử chia gia tài cho họ như thế nào ? Mỗi người được hưởng bao nhiêu phần ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
*Đề : Một ông nhà giàu khi vợ đang mang thai thì mắc bệnh hiểm nghèo, trước lúc lâm chung ông ta để
lại “Di chúc ” : Sau khi qua đời nếu vợ sinh con trai thì gia tài cho con trai 2/3 và vợ 1/3; Nếu sinh con
gái thì con gái 1/3; vợ 1/3; còn lại 1/3 làm từ thiện. Nhưng thực tế sau khi ông ta chết, vọ sinh đôi : 1 con
trai và 1 con gái.
Hỏi Tòa án dân sự phải xử chia gia tài cho họ như thế nào ? Mỗi người được hưởng bao nhiêu phần ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
65
20.DÙNG SƠ ĐỒ DIỆN TÍCH ĐỂ GIẢI TOÁN BA ĐẠI
LƯỢNG Bài 1: Một ôtô đi từ Vinh đến Hà Nội dự định đi với vận tốc 30 km/h. Nhưng do trời mưa nên chỉ đi được
25 km/h, nên đến Hà Nội muộn mất 2 giờ so với thời gian dự định. Tính quãng đường Vinh - Hà Nội? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 2: Bố bạn An năm nay 30 tuổi. Nếu lấy số tuổi bố bạn An cách đây 5 năm và số tuổi của An bây giờ
cộng với 2 rồi nhân hai số đó với nhau thì cũng bằng số tuổi bố bạn An bây giờ nhân với số tuổi bạn An
bây giờ. Tính tuổi bạn An bây giờ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
66
TOÁN 4 – HỌC KÌ 2
NÂNG CAO THEO CHỦ ĐỀ
ph©n sè
21/ph©n sè - RÚT GỌN PHÂN SỐ
Bài 137: Viết các phân số sau theo thứ tự từ bé đến lớn: 7
6;
7
3;
7
4
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 141: So sánh
a) 4
3 +
4
2 b)
8
7
8
3 c)
10
9
10
8
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 149: Khu đất nhà Lan có 5
3 diện tích đất làm nhà,
7
2 diện tích dùng để trồng rau. Hỏi:
a)Diện tích đất làm nhà và trồng rau bằng bao nhiêu phần diện tích của khu vườn?
a) Diện tích làm nhà nhiêu hơn diện tích trồng rau bao nhiêu phần diện tích khu đất? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 150: Tìm x
a) 3
4
4
3x b)
2
3
12
7 x c)
22
9
11
3x d)
9
2
2
9 x
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
67
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 151: Trong số các bài kiểm tra giữa kì II của khối lớp 4, có 7
3 số bài đạt điểm khá. Biết số bài đạt
điểm khá và giỏi là 35
29
số bài kiểm tra. Hỏi số bài đạt điểm giỏi chiếm bao nhiêu phân số bài kiểm tra? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 154: T×m sè tù nhiªn x sao cho: 7
5
107
4
x
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 155: T×m hai ph©n sè biÕt r»ng hai ph©n sè ®ã ®Òu cã mÉu sè lµ 8, c¸c tö sè cÇn t×m lµ hai sè tù nhiªn
liªn tiÕp vµ ph©n sè 5
3 n»m gi÷a hai ph©n sè ®ã.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 156: T×m hai ph©n sè biÕt r»ng hai ph©n sè ®ã ®Òu cã tö sè lµ 1, c¸c mÉu sè ph¶i t×m lµ hai sè tù nhiªn
liªn tiÕp vµ ph©n sè 84
13 n»m gi÷a hai ph©n sè ®ã.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
68
22/So s¸nh ph©n sè Bµi 1: So s¸nh c¸c ph©n sè sau b»ng c¸ch hîp lÝ nhÊt:
a) 17
12vµ
15
7 d)
1999
1998 vµ
2000
1999 PhÇn bï
b) 2001
1999 vµ
11
12 So s¸nh víi 1
c) 27
13vµ
41
27 PhÇn bï g)
47
23 vµ
45
24 ( Trung gian)
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
69
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 2: So s¸nh c¸c ph©n sè sau b»ng c¸ch hîp lÝ nhÊt:
a) 25
15 vµ
7
5 PhÇn bï d)
8
3 vµ
49
17 SS víi 15/49
b) 60
13 vµ
100
27 Trung gian26/120 e)
15
47 vµ
35
29 ( TS > MS)
c) 1995
1993 vµ
998
997 (997x2) SS phÇn bï g)
27
16 vµ
29
15SS 16/29
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
70
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 3: So s¸nh c¸c ph©n sè sau b»ng c¸ch hîp lÝ nhÊt:
a) 15
13vµ
25
23 (SS phÇn bï) c)
25
12vµ
49
25 SS 24/49
b) 28
23 vµ
27
24 SS Trung gian
.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
71
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 157: So s¸nh b»ng c¸ch hîp lÝ
a)7
3 vµ
77
33 ;
1414
1313 vµ
14
13 b)
11
22 vµ
5
11 c)
8
13 vµ
2
7 d)
2006
2007 vµ
2008
2006
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
72
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 158: Kh«ng quy ®ång mÉu sè h·y so s¸nh c¸c ph©n sè
a)2008
2007vµ
2009
2008 b)
3
2vµ
4
3 c)
13
2vµ
14
3 d)
14
5vµ
11
2 e)
6
5vµ
10
9 g)
78
77vµ
79
78
h)18
17vµ
19
18 i)
21
20vµ
22
21
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
73
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 159: So s¸nh b»ng c¸ch hîp lÝ
a)96
97vµ
95
96 b)
2006
2007vµ
2004
2005 c)
2006
2007vµ
2007
2008 d)
24
25vµ
23
24
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
74
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 160: Kh«ng quy ®ång mÉu sè h·y so s¸nh
a)9
4vµ
10
3 b)
19
11vµ
18
13 c)
97
45vµ
96
47 d)
31
20vµ
33
19 e)
46
45vµ
47
44
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
75
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 161: H·y chøng tá r»ng c¸c ph©n sè sau b»ng nhau
a)999
777
99
77
9
7 b)
127127
123123
127
123 c)
151515
131313
1515
1313
15
13
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 162: So s¸nh c¸c ph©n sè sau víi 1
a) 3533
3434
b)
19951995
19991991
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
76
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 163: So s¸nh c¸c ph©n sè sau (víi n lµ sè tù nhiªn)
a) 2
1
n
n vµ
4
3
n
n b)
3n
n vµ
4
1
n
n
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 164: So s¸nh c¸c ph©n sè sau(a lµ sè tù nhiªn kh¸c 0)
a) a
a 1 vµ
2
3
a
a b)
6a
a vµ
7
1
a
a
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
23/ TÌM PHÂN SỐ CỦA MỘT SỐ
Bài 165: Lớp 4A có 27 học sinh, trong đó số bạn nữ bằng 3
2 số học sinh cả lớp. Tìm số học sinh nam?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 166: Lớp 4B có 10 bạn nữ, số bạn nam bằng2
3 số bạn nữ. Tìm số bạn nam?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 167: Một sân trường hình chữ nhật có chiều rộng bằng 90m, chiều dài bằng 3
4 chiều rộng. Tính
diện tích sân trường đó. ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
77
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 168: Nam có 27 viên bi gồm hai màu vàng và đỏ, trong đó số bi màu vàng bằng 3
2tổng số bi. Tìm số
bi màu đỏ? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 169: An có 10 quyển vở, Bình có số vở bằng2
3 số vở của An. Bình có bao nhiêu quyển vở?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 170: Một sân trường hình chữ nhật có chiều dài bằng 90m, chiều rộng bằng 3
2 chiều dài. Tính diện
tích sân trường đó. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 171: C¶ 3 ngêi thî lµm c«ng ®îc 270 000 ®ång. Ngêi thø nhÊt ®îc 2
1 sè tiÒn, ngêi thø hai ®îc
5
2 sè tiÒn. TÝnh tiÒn cña ngêi thø ba.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 17 2: Hai ngêi chia nhau 720 000 ®ång. Ngêi thø nhÊt ®îc 6
1 sè tiÒn, ngêi thø hai ®îc
8
1 sè
tiÒn, sè tiÒn cßn l¹i lµ cña ngêi thø ba. Hái ngêi thø ba ®îc bao nhiªu tiÒn? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
78
Bµi 1: C¶ ba ngêi thî lµm c«ng ®îc 270000 ®ång. Ngêi thø nhÊt ®îc 3
1 sè tiÒn. Ngêi thø hai ®îc
5
2 sè tiÒn. TÝnh sè tiÒn cña ngêi thø ba.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 2: Hai ngêi chia nhau 720000 ®ång. Ngêi thø nhÊt ®îc 6
1sè tiÒn. Ngêi thø hai ®îc
8
1 sè tiÒn.
Sè tiÒn cßn l¹i lµ cña ngêi thø ba. Hái ngêi thø ba ®îc chia bao nhiªu tiÒn? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 3: Ba b¹n chia nhau 30 qu¶ cam. Nam lÊy 5
2 sè cam, Phîng lÊy sè cam b»ng
5
4 sè cam cña Mai.
Hái mçi b¹n ®îc bao nhiªu qu¶ cam? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 4: Hai anh em cã tÊt c¶ 40 viªn bi, biÕt 3
1sè bi cña em b»ng
5
1 sè bi cña anh. TÝnh sè bi cña mçi
ngêi. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 5: HiÖn nay mÑ h¬n con 24 tuæi, biÕt3
1tuæi cña con b»ng
11
1 tuæi cña mÑ.TÝnh tuæi cña mçi ngêi.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
79
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 6: Líp 5A cã 2
1sè häc sinh n÷ b»ng
5
1 sè häc sinh nam. BiÕt sè häc sinh n÷ kÐm sè häc sinh nam lµ
15 b¹n. TÝnh sè häc sinh n÷ vµ sè häc sinh nam. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 7: Líp 5A cã 35 häc sinh, biÕt 5
1 sè häc sinh nam b»ng
2
1sè häc sinh n÷. TÝnh sè häc sinh nam vµ
häc sinh n÷. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 8: Ba khu vùc A, B, C cã tæng sè d©n lµ 12000 ngêi. TÝnh sè d©n mçi khu vùc, biÕt 3
2 sè d©n khu
vùc A b»ng 10
5 sè d©n khu vùc B vµ b»ng
10
4 sè d©n khu vùc C.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 9: Hai anh em ®i mua s¸ch hÕt 112000 ®ång. BiÕt 5
3sè tiÒn s¸ch cña em b»ng
3
1 sè tiÒn cña anh. Hái
mçi ngêi mua hÕt bao nhiªu tiÒn s¸ch? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
80
24/ t×m sè khi biÕt gi¸ trÞ mét ph©n sè cña
nã
Bµi 1: Mét xe m¸y ngµy thø nhÊt ®i ®îc 5
2 qu·ng ®êng, ngµy thø hai ®i
®îc 3
1 qu·ng ®êng, ngµy thø ba ®i thªm 40km n÷a th× võa hÕt qu·ng ®êng. Hái qu·ng ®êng
xe m¸y ®i trong ba ngµy lµ bao nhiªu ki-l«-mÐt? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 2: Mét ngêi b¸n hµng v¶i, lÇn thø nhÊt b¸n 2
1 sè v¶i, lÇn thø hai b¸n
3
1 sè v¶i th× cßn l¹i 7m. Hái
tÊm v¶i ®ã dµi bao nhiªn mÐt? ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
81
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 3: Mét bÇy ong ®i t×m mËt, 2
1 sè ong bay ®Õn vên nh·n,
3
1 sè ong bay ®Õn vên hång, cßn l¹i 5 con
®ang bay ®Õn vên xoµi. Hái bÇy ong ®ã cã bao nhiªu con? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 4: Tæng sè tuæi cña ba cha con lµ 85 tuæi. Tuæi con g¸i b»ng 5
2 tuæi bè, tuæi cña con trai b»ng
4
3tuæi
cña con g¸i. TÝnh tuæi cña mçi ngêi. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 5: Ba thïng ®ùng 52 lÝt x¨ng. Thïng thø nhÊt ®ùng b»ng 2
1thïng thø ba, thïng thø hai ®ùng b»ng
3
2
thïng thø ba. TÝnh xem mçi thïng ®ùng bao nhiªu lÝt x¨ng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 6: Mét cöa hµng b¸n tÊm v¶i lµm ba lÇn. LÇn thø nhÊt b¸n 3
1 tÊm v¶i vµ 5m, lÇn thø hai b¸n
7
3 sè v¶i
cßn l¹i vµ 3m, lÇn thø ba b¸n 17m v¶i th× võa hÕt. Hái lÇn mét, lÇn hai mçi lÇn b¸n bao nhiªu mÐt? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
LuyÖn tËp
Bµi 2: Mét ngêi b¸n hµng, lÇn mét b¸n 5
1sè trøng , lÇn thø hai b¸n
8
3 sè trøng th× cßn l¹i 17 qu¶. Hái
ngêi ®ã ®em b¸n bao nhiªu qu¶ trng vµ mçi lÇn b¸n bao nhiªu qu¶?
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
82
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 3: Mét gi¸ s¸ch cã 3 ng¨n, biÕt sè s¸ch ë ng¨n thø nhÊt b»ng 3
2sè s¸ch ë ng¨n thø ba, sè s¸ch ë ng¨n
thø hai b»ng 4
3sè s¸ch ë ng¨n thø nhÊt. BiÕt ng¨n thø thø ba nhiÒu h¬n ng¨n thø hai lµ 45 quyÓn.
TÝnh sè s¸ch ë mçi ng¨n. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 4: Nhãm thî gÆt thø nhÊt gÆt ®îc8
3diÖn tÝch thöa ruéng. Nhãm thî gÆt thø hai gÆt ®îc
5
2diÖn tÝch
thöa ruéng. Nhãm hai gÆt nhiÒu h¬n nhãm mét lµ 100m2. TÝnh diÖn tÝch mçi nhãm gÆt ®îc. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 5: Ba ®µn gµ, ®µn gµ thø nhÊt b»ng 3
4®µn gµ thø hai. §µn gµ thø ba b»ng
6
4®µn gµ thø hai. §µn thø
nhÊt nhiÒu h¬n ®µn gµ thø ba 24 con. Hái mçi ®µn cã bao nhiªu con? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 6: Mét « t« ®i trong 2 ngµy ®îc 14
13 qu·ng ®êng. Ngµy thø 2 ®i ®îc
7
5 qu·ng ®êng vµ ®i nhiÒu
h¬n ngµy thø nhÊt 35km. Hái mçi ngµy « t« ®i ®îc bao nhiªu ki-l«-mÐt? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
83
Bµi 7: Mai vµ Hång ®i mua s¸ch. Sau khi mua mai mua hÕt 4
3 sè tiÒn mang ®i, Hång tiªu hÕt
3
2 sè tiÒn
Hång mang ®i th× c¶ hai cßn l¹i 20600®ång, Trong ®ã Mai cßn nhiÒu h¬n Hång 600®ång. Hái mçi b¹n mang ®i bao nhiªu tiÒn?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 8: ChÞ T mang ®i chî mét ræ cam. LÇn ®Çu chÞ b¸n ®îc 5
2 sè cam, lÇn sau chÞ b¸n ®îc
4
3 sè cam
cßn l¹i. Sau hai lÇn b¸n chÞ cßn l¹i 21 qu¶ cam. Hái ræ cam ban ®Çu cã bao nhiªu qu¶? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 9: Ngêi l¸i xe tríc khi ®i thÊy chØ cßn 5
3 thïng x¨ng, sî kh«ng ®ñ ngêi ®ã mua thªm 15 lÝt x¨ng
n÷a. Khi vÒ tíi nhµ anh thÊy chØ cßn 10
3 thïng x¨ng vµ tÝnh ra xe tiªu thô hÕt 30 lÝt x¨ng trong
chuyÕn ®i ®ã. Hái thïng x¨ng chøa bao nhiªu lÝt x¨ng? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 10: Ba anh em Nam, H¶i, TÊn ®îc mÑ cho mét sè tiÒn . Nam ®îc 4
1 sè tiÒn, H¶i ®îc
5
2 sè tiÒn, sè
tiÒn cßn l¹i lµ cña TÊn. Hái mçi ngêi ®îc mÑ cho bao nhiªu tiÒn, biÕt sè tiÒn mÑ cho TÊn h¬n Nam 6000®ång?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 12: §Çu xu©n Êt DËu gia ®×nh b¸c An nu«i 268 con gµ gåm 3 lo¹i: gµ vµng, gµ tr¾ng, gµ khoang. BiÕt
sè gµ tr¾ng b»ng 6
5 sè gµ vµng, sè gµ khoang b»ng
9
7 sè gµ tr¾ng. TÝnh sè gµ mçi lo¹i.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
84
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 13: Ba xe chë g¹o lªn nói 4
1 sè g¹o chë trªn xe thø nhÊt b»ng
3
1 sè g¹o chë trªn xe
thø 2 vµ b»ng 5
1 sè g¹o chë trªn xe thø 3. Xe thø 3 chë nhiÒu h¬n xe thø 2 lµ 6 tÊn. Hái mçi xe
chë bao nhiªu tÊn g¹o? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 14: Cóc võa ®îc thëng mét sè tiÒn. Cóc lÊy 5
3 sè tiÒn ®em ®i chî, Cóc ®· mua hÕt
3
2sè tiÒn mang
®i. Sè tiÒn cßn l¹i Cóc ®em vÒ 27 000 ®ång. Hái sè tiÒn Cóc ®îc thëng lµ bao nhiªu? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 15: Mét to¸n c«ng nh©n nhËn lµm mét ®o¹n ®êng trong 3 tuÇn. TuÇn ®Çu lµm ®îc 5
2
®o¹n ®êng. TuÇn thø 2 lµm ®îc ®o¹n ®êng b»ng 3
2 tuÇn ®Çu. TuÇn thø 3 lµm ®îc 450m th×
hÕt ®o¹n ®êng. Hái: a) §o¹n ®êng dµi bao nhiªu mÐt? b) Hai tuÇn ®Çu, mçi tuÇn lµm ®îc bao nhiªu mÐt?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
85
25. T×m hai sè khi biÕt tæng vµ tØ sè cña hai
sè ®ã Bµi 1: MÑ em tr¶ hÕt tÊt c¶ 84600 ®ång ®Ó mua mét sè tr¸i c©y gåm cam, t¸o vµ lª. T¸o gi¸ 2100 ®ång 1
qu¶, cam gi¸ 1600 ®ång 1 qu¶ vµ lª gi¸ 3500 ®ång mét qu¶. BiÕt mÑ em ®· mua sè cam b»ng 2 lÇn sè t¸o vµ sè t¸o b»ng 2 lÇn sè lª. T×m sè qu¶ mçi lo¹i mÑ em ®· mua.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 2: Mét cöa hµng rau qu¶ cã 185,5kg chanh vµ cam. Sau khi b¸n, ngêi b¸n hµng thÊy r»ng: lîng
chanh ®· b¸n b»ng 4
1 lîng cam ®· b¸n vµ lîng chanh cßn l¹i nhiÒu h¬n lîng cam cßn l¹i
17,5kg. Hái cöa hµng ®ã ®· b¸n ®îc bao nhiªu ki - l« - gam mçi lo¹i, biÕt r»ng ban ®Çu sè chanh
b»ng 3
2 sè cam?
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
86
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 3: Mét cöa hµng cã 215,5kg g¹o tÎ vµ g¹o nÕp. Lîng g¹o nÕp ®· b¸n b»ng 4
1 lîng g¹o tÎ ®· b¸n.
Sau khi b¸n, lîng g¹o nÕp cßn l¹i h¬n lîng g¹o tÎ cßn l¹i lµ 25,9kg. Hái cöa hµng ®· b¸n bao
nhiªu ki - l« - gam mçi lo¹i, biÕt r»ng ban ®Çu g¹o nÕp b»ng 3
2 g¹o tÎ?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 4: Mét cöa hµng rau qu¶ cã hai ræ ®ùng cam vµ chanh. Sau khi b¸n, 7
4 sè cam vµ
9
5 sè chanh th×
ngêi b¸n hµng thÊy cßn l¹i 160 qu¶ hai lo¹i. Trong ®ã sè cam b»ng 5
3 sè chanh. Hái lóc ®Çu cöa
hµng cã bao nhiªu qu¶ mçi lo¹i? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 5: Ba líp cïng gãp b¸nh ®Ó liªn hoan cuèi n¨m. Líp A gãp 5kg b¸nh, líp B gãp 3kg
b¸nh cïng lo¹i. Sè b¸nh ®ã ®ñ dïng cho c¶ 3 líp nªn líp C kh«ng ph¶i mua b¸nh mµ ph¶i tr¶ cho 2 líp kia lµ 24000 ®ång. Hái mçi líp A, B nhËn ®îc bao nhiªu tiÒn? (Mçi líp gãp sè tiÒn nh nhau).
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 6: Tuæi vµ th¬ gãp b¸nh ¨n chung, Tuæi gãp 3 chiÕc, Th¬ gãp 5 chiÕc. Võa lóc ®ã, To¸n ®i tíi. Tuæi
vµ Th¬ mêi To¸n ¨n cïng. ¡n xong To¸n tr¶ l¹i cho 2 b¹n 8000 ®ång. Hái Tuæi vµ Th¬ mçi ngêi nhËn ®îc bao nhiªu tiÒn?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
87
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 7: Trong thóng cã 150 qu¶ trøng gµ vµ trøng vÞt. MÑ ®· b¸n mçi lo¹i 15 qu¶. TÝnh ra sè trøng gµ cßn
l¹i b»ng 5
2 sè trøng vÞt cßn l¹i. Hái lóc ®Çu trong thóng cã bao nhiªu trøng gµ, bao nhiªu trøng
vÞt? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 8: Trong thóng cã 210 qu¶ quýt vµ cam. MÑ ®· b¸n 60 qu¶ quýt. Lóc nµy, trong thóng cã sè quýt cßn
l¹i b»ng 3
2 sè cam. Hái lóc ®Çu sè cam b»ng bao nhiªu phÇn sè quýt?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 9: B¹n B×nh cã 22 viªn bi gåm bi ®á vµ bi xanh. B×nh cho em 3 viªn bi ®á vµ 2 viªn bi xanh. B¹n An
l¹i cho B×nh thªm 7 viªn bi ®á n÷a. Lóc nµy, B×nh cã sè bi ®á gÊp ®«i sè bi xanh. Hái lóc ®Çu B×nh cã bao nhiªu viªn bi ®á, bao nhiªu viªn bi xanh?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 10: Trong mét khu vên, ngêi ta trång tæng céng 120 c©y gåm 3 lo¹i: cam, chanh vµ xoµi. BiÕt sè
cam b»ng 3
2 tæng sè chanh vµ xoµi, sè xoµi b»ng
5
1 tæng sè chanh vµ sè cam. Hái mçi l¹i cã bao
nhiªu c©y? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 11: Dòng cã 48 viªn bi gåm 3 lo¹i: bi xanh, bi ®á vµ bi vµng. Sè bi xanh b»ng tæng sè bi ®á vµ bi
vµng, sè bi xanh céng sè bi ®á gÊp 5 lÇn sè bi vµng. Hái mçi lo¹i cã bao nhiªu viªn bi? ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
88
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 14: Ngµy xu©n 3 b¹n: HuÖ, H»ng, Mai ®i trång c©y. BiÕt r»ng tæng sè c©y cña 3 b¹n trång ®îc lµ 17
c©y. Sè c©y cña 2 b¹n HuÖ vµ H»ng trång ®îc nhiÒu h¬n Mai trång lµ 3 c©y. Sè c©y cña HuÖ trång
®îc b»ng 3
2 sè c©y cña H»ng. Em h·y tÝnh xem mçi b¹n trång ®îc bao nhiªu c©y?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 173: T×m hai sè cã tæng b»ng 80. BiÕt sè bÐ b»ng 3
2 sè lín
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 174: T×m hai sè cã trung b×nh céng b»ng 108, biÕt th¬ng cña hai sè ®ã b»ng 5.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 175: T×m hai sè cã trung b×nh céng b»ng 231, biÕt r»ng nÕu thªm mét ch÷ sè 0 vµo bªn ph¶i sè bÐ th×
®îc sè lín. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 176: Hai thïng dÇu cã tæng céng 126 lÝt, biÕt sè dÇu ë thïng thø nhÊt b»ng 2
5 sè dÇu ë thïng thø hai.
Hái mçi thïng cã bao nhiªu lÝt dÇu? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 177: Dòng vµ Minh cã tæng céng 55 viªn bi, biÕt r»ng nÕu Dòng cho Minh 5 viªn bi th× sè bi cña
Minh sÏ b»ng 7
4 sè bi cña Dòng. Hái mçi b¹n cã bao nhiªu viªn bi?
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
89
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 178: Hång vµ Lan cã tæng céng 40 quyÓn vë. 3 lÇn sè vë cña Hång th× b»ng 2 lÇn sè vë cña Lan. Hái
mçi b¹n cã bao nhiªu vë? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 179: Hép bi gåm hai lo¹i xanh vµ ®á, cã tæng céng 49 viªn bi, biÕt r»ng 3
1 sè bi xanh b»ng
4
1 sè bi
®á. Hái mçi lo¹i cã bao nhiªu viªn bi. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 180: Mét trang tr¹ingêi ta nu«i mét sè ®µn gia sóc cã 104 con gåm hai lo¹i tr©u vµ bß, biÕt r»ng 3
lÇn sè tr©u th× b»ng 5 lÇn sè bß. Hái trang tr¹i ®ã cã bao nhiªu con tr©u, bao nhiªu con bß? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 181: T×m hai sè cã tæng b»ng 295, biÕt r»ng nÕu lÊy sè lín chia cho sè bÐ th× ®îc th¬ng lµ 8 vµ sè d lµ 7. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 182: Tæng sè tuæi cña hai «ng ch¸u lµ 65 tuæi, biÕt tuæi ch¸u bao nhiªu th¸ng th× tuæi «ng bÊy nhiªu n¨m. Hái «ng bao nhiªu tuæi, ch¸u bao nhiªu tuæi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 183: HiÖn nay tuæi bè gÊp 4 lÇn tuæi con,biÕt r»ng 5 n¨m n÷a th× tæng sè tuæi cña hai bè con lµ 55 tuæi. Hái hiÖn nay bè bao nhiªu tuæi? con bao nhiªu tuæi? ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
90
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 184: Tríc ®©y lóc tuæi anh b»ng tuæi em hiÖn nay th× tuæi anh gÊp ®«i tuæi em, hiÖn nay tæng sè tuæi cña hai anh em lµ 20 tuæi. Hái hiÖn nay anh bao nhiªu tuæi, em bao nhiªu tuæi. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
26. T×m hai sè khi biÕt hiÖu vµ tØ sè cña hai
sè ®ã Bµi 1: N¨m nay con 25 tuæi, nÕu tÝnh sang n¨m th× tuæi cha gÊp 2 lÇn tuæi con hiÖn nay. Hái lóc cha bao
nhiªu tuæi th× tuæi con b»ng 4
1 tuæi cha?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
91
Bµi 2: Mét líp cã 3
1 sè häc sinh nam b»ng
5
1 sè häc sinh n÷. Sè häc sinh nam Ýt h¬n sè häc sinh n÷ 12
b¹n. TÝnh sè häc sinh nam, sè häc sinh n÷ cña líp ®ã. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 3: Cho mét ph©n sè cã tæng cña tö sè vµ mÉu sè lµ 4013 vµ mÉu sè lín h¬n tö sè lµ 1.
a) H·y t×m ph©n sè ®ã. b) NÕu céng thªm 4455332 vµo tö sè th× ph¶i céng thªm vµo mÉu sè bao nhiªu ®Ó gi¸ trÞ cña ph©n sè kh«ng thay ®æi.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 4: Khi anh t«i 9 tuæi th× mÑ míi sinh ra t«i. Tríc ®©y, lóc mµ tuæi anh t«i b»ng tuæi t«i hiÖn nay th×
t«i chØ b»ng 5
2 tuæi anh t«i. §è b¹n tÝnh ®îc tuæi cña anh t«i hiÖn nay.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 5: Mét cöa hµng cã sè bót ch× xanh gÊp 3 lÇn sè bót ch× ®á. Sau khi cöa hµng b¸n ®i 12
bót ch× xanh vµ 7 bót ch× ®á th× phÇn cßn l¹i sè bót ch× xanh h¬n sè bót ch× ®á lµ 51 c©y. Hái tríc khi b¸n mçi lo¹i bót ch× cã bao nhiªu chiÕc?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 6: Lõa vµ Ngùa cïng chë hµng. Ngùa nãi: “NÕu anh chë gióp t«i 2 bao hµng th× 2 chóng ta chë b»ng
nhau”. Lõa nãi l¹i víi Ngùa: “Cßn nÕu anh chë gióp t«i 2 bao hµng th× anh sÏ chë gÊp 5 lÇn t«i”. Hái mçi con chë bao nhiªu bao hµng?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
92
Bµi 7: BiÕt 2
1tuæi An c¸ch ®©y 6 n¨m b»ng
5
1 tuæi An 6 n¨m tíi. Hái hiÖn nay An bao nhiªu tuæi?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 8: Cho mét sè tù nhiªn. NÕu thªm 28 ®¬n vÞ vµo 4
1 sè ®ã ta ®îc sè míi gÊp 2 lÇn sè cÇn t×m. T×m sè
tù nhiªn ®ã. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 9: T×m hai sè cã hiÖu b»ng 252, biÕt sè bÐ b»ng 4
1tæng 2 sè ®ã.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 10: T×m 2 sè cã hiÖu b»ng 310, biÕt 3
2 sè thø hai gÊp 4 lÇn sè thø nhÊt.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 11: T×m sè A, biÕt 4 lÇn sè A h¬n 4
1sè A lµ 2025 ®¬n vÞ.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 184: T×m hai sè cã hiÖu b»ng 516, biÕt r»ng nÕu lÊy sè lín chia cho sè bÐ th× ®îc th¬ng b»ng 4.
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
93
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 185:T×m hai sè biÕt tØ sè cña chóng b»ng 7
4 vµ nÕu lÊy sè lín trõ ®i sè bÐ th× ®îc kÕt qu¶ b»ng 360.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 186:T×m hai sè cã hiÖu b»ng 333, biÕt r»ng nÕu viÕt thªm mét ch÷ sè 0 vµo bªn ph¶i sè bÐ th× ®îc sè
lín. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 187: T×m hai sè cã tØ sè lµ 9
1, biÕt r»ng sè lín lµ sè cã ba ch÷ sè vµ nÕu xãa ch÷ sè 4 ë hµng tr¨m cña
sè lín th× ®îc sè bÐ. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 188: T×m hai sè cã hiÖu b»ng 165, biÕt r»ng nÕu lÊy sè lín chia cho sè bÐ th× ®îc th¬ng lµ 7 vµ cã
sè d lµ 3. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 189: HiÖn nay bè 32 tuæi, em 5 tuæi. Hái bao nhiªu n¨m n÷a tuæi cña bè gÊp 5 lÇn tuæi cña con.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 190 : T×m hai sè cã hiÖu b»ng 216, biÕt r»ng nÕu thªm mét ch÷ sè 0 vµo bªn ph¶i sè bÐ th× ®îc sè lín. ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
94
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 191: HiÖu cña hai sè b»ng 393, biÕt r»ng nÕu xo¸ ch÷ sè cuèi cña sè lín th× ®îc sè bÐ. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 192: HiÖn nay bè 31 tuæi, con 4 tuæi. Hái bao nhiªu n¨m n÷a tuæi bè gÊp 4 lÇn tuæi con? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 193: BiÕt 2
1 tuæi Thanh håi 6 n¨m tríc b»ng
5
1 tuæi cña Thanh 6 n¨m tíi. Hái hiÖn Thanh bao nhiªu
tuæi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 194: HiÖn nay tæng sè tuæi cña hai bµ ch¸u lµ 72 tuæi, tuæi bµ gÊp 5 lÇn tuæi ch¸u. Hái c¸ch nay mÊy n¨m tuæi bµ gÊp 9 lÇn tuæi ch¸u? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 195: HiÖn nay tuæi mÑ gÊp 4 lÇn tuæi con, tríc ®©y 6 n¨m tuæi mÑ gÊp 13 lÇn tuæi con. Hái hiÖn nay mÑ bao nhiªu tuæi? Con bao nhiªu tuæi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
27. t×m mét sè khi biÕt “Hai tØ sè”
Bµi 1: Mét gi¸ s¸ch cã hai ng¨n, sè s¸ch ë ng¨n díi b»ng 6
5 sè s¸ch ë ng¨n trªn. NÕu ng¨n díi bít ®i
11 quyÓn th× sè s¸ch ng¨n díi b»ng 7
4 sè s¸ch ë ng¨n trªn. Hái trªn gi¸ cã bao nhiªu quyÓn
s¸ch?
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
95
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 2: Líp 5A cã sè häc sinh b»ng 3
1 sè häc sinh cña líp. NÕu líp 5A bít ®i 2 b¹n n÷ th× sè häc sinh n÷
b»ng 4
1 sè häc sinh c¶ líp. Hái líp 5A cã bao nhiªu häc sinh?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 3: Líp 5A cã sè häc sinh n÷ b»ng 3
2 sè häc sinh nam. NÕu hai b¹n n÷ chuyÓn ®i vµ thay vµo ®ã lµ
hai b¹n nam th× sè häc sinh n÷ b»ng 7
4 sè häc sinh nam. T×m sè häc sinh líp 5A.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 4: Mét gi¸ s¸ch gåm hai ng¨n. Sè s¸ch ë ng¨n díi b»ng 5
6 sè s¸ch ë ng¨n trªn. NÕu thªm 15 cuèn
s¸ch vµo ng¨n trªn th× sè s¸ch ë ng¨n trªn b»ng 12
11 sè s¸ch ë ng¨n díi. Hái gi¸ s¸ch cã bao
nhiªu quyÓn? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 5: Giê ra ch¬i, líp 5A cã sè häc sinh trong líp b»ng 4
1 sè häc sinh ngoµi
s©n. NÕu cã hai b¹n tõ trong líp ra s©n th× sè häc sinh trong líp b»ng 5
1 sè häc sinh ngoµi s©n.
TÝnh sè häc sinh líp 5A? ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
96
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 6: Giê ra ch¬i, líp 5A cã sè häc sinh trong líp b»ng 3
1 sè häc sinh ngoµi s©n. NÕu sè häc sinh trong
líp bít ®i 2 em vµ sè häc sinh ngoµi s©n gi÷ nguyªn th× sè häc sinh trong líp b»ng 4
1 sè häc sinh
ngoµi s©n. TÝnh sè häc sinh líp 5A? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 7: Giê ra ch¬i, líp 5B cã sè häc sinh trong líp b»ng 3
1 sè häc sinh ngoµi s©n. NÕu sè
häc sinh ngoµi s©n ®îc t¨ng 12 em vµ gi÷ nguyªn sè häc sinh trong líp th× sè häc sinh trong líp
b»ng 4
1 sè häc sinh ngoµi s©n. TÝnh sè häc sinh líp 5B?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 8: Giê ra ch¬i, líp 5B cã sè häc sinh trong líp b»ng 4
1 sè häc sinh c¶ líp. NÕu sè häc
sinh trong líp bít ®i 2 em vµ gi÷ nguyªn sè häc sinh ngoµi s©n th× sè häc sinh trong líp b»ng 5
1
sè häc sinh c¶ líp. TÝnh sè häc sinh líp 5B? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 9: §Çu n¨m häc, sè ®éi viªn trêng em b»ng 3
1 sè häc sinh cßn l¹i cña trêng. §Õn cuèi häc k× I
trêng kÕt n¹p thªm 210 häc sinh vµo ®éi nªn sè häc sinh cßn l¹i cña trêng b»ng 3
2 sè ®éi viªn
cña trêng. Hái ®Õn cuèi häc k× I, sè ®éi viªn cña trêng lµ bao nhiªu em? BiÕt sè häc sinh cña trêng kh«ng thay ®æi.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
97
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 10: Mét ngêi b¸n mét tÊm v¶i ®îc l·i 5
1 gi¸ mua. NÕu ngêi ®ã b¸n tÊm v¶i cao h¬n 40 000 ®ång
n÷a th× sè tiÒn l·i b»ng 5
1 gi¸ b¸n. Hái tÊm v¶i ®ã ®îc b¸n víi gi¸ bao nhiªu tiÒn?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 11: HiÖn nay, tuæi con b»ng 4
1 tuæi cha. Sau 15 n¨m n÷a th× tuæi con b»ng
5
2 tuæi cha. TÝnh tuæi cña
mçi ngêi hiÖn nay? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 12: HiÖn nay tuæi mÑ gÊp 4 lÇn tuæi con. N¨m n¨m sau tuæi mÑ gÊp 3 lÇn tuæi con. TÝnh tuæi hiÖn nay
cña mçi ngêi? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
28. Ph©n sè - tØ sè phÇn tr¨m
Bµi 1: ViÕt tÊt c¶ c¸c ph©n sè b»ng ph©n sè 100
75 mµ mÉu sè lµ sè trßn chôc vµ cã 2 ch÷ sè.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
98
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 2: ViÕt tÊt c¶ c¸c ph©n sè b»ng ph©n sè 39
21 mµ mÉu sè cã 2 ch÷ sè vµ chia hÕt cho 2 vµ 3.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 3: ViÕt mçi ph©n sè sau thµnh tæng 3 ph©n sè cã tö sè lµ 1 nhng cã mÉu sè kh¸c nhau: ;8
7
3
2;
8
3
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 4: ViÕt mçi ph©n sè sau thµnh tæng 2 ph©n sè tèi gi¶n cã mÉu sè kh¸c nhau.
a) 12
7 b)
27
13
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 5:
a) ViÕt 5 p/s cã tö sè b»ng nhau mµ mçi ph©n sè ®Òu lín h¬n 5
4 nhng bÐ h¬n 1
b) ViÕt 5 p/s cã mÉu sè b»ng nhau vµ mçi p/s ®Òu bÐ h¬n 2
1
c) ViiÐt 3 p/s cã tö sè b»ng 1 mµ mçi p/s ®Òu lín h¬n 6
1 nhng bÐ h¬n
3
2
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 6: H·y viÕt mçi ph©n sè sau thµnh tæng c¸c ph©n sè cã tö sè b»ng 1 vµ mÉu sè kh¸c nhau.
.27
25;
16
15;
12
31
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
99
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 7: H·y viÕt tÊt c¶ c¸c ph©n sè cã tæng cña tö sè vµ mÉu sè b»ng 10.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
.......................................................................................................................................................................... Bµi 8: T×m:
a) 2
1 cña 6m
b) 7
1cña 21kg
c) 10
1cña
5
1
d) 9
8cña
4
3
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 9: BiÕt 2
1sè häc sinh cña líp 3A b»ng
3
1sè häc sinh cña líp 3B. H·y t×m tØ sè gi÷a sè häc sinh líp 3A
vµ häc sinh líp 3B. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 10: T×m sè häc sinh cña khèi líp 4, biÕt 3
1sè häc sinh cña khèi líp 4 lµ 50 em.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
29. CÁC BÀI TOÁN VỀ CẤU TẠO SỐ Bµi 2. Rót gän c¸c ph©n sè sau:
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
100
a) 95...999
9...199(100 ch÷ sè 9 ë tö sè vµ 100 ch÷ sè 9 ë mÉu sè)
b) 414141
373737.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
101
30.CÁC DẠNG TOÁN LIÊN QUAN ĐẾN PHÂN SỐ
THÊM BỚT TỬ SỐ MẪU SỐ ,CẢ TỬ SỐ VÀ MẪU SỐ
* TÌM PHÂN SỐ BIẾT TỔNG VÀ HIỆU CỦA TỬ SỐ VÀ
MẪU SỐ.
VD1:Cho phân số có tổng của tử số và mấu số là 68 Tìm phân số đó biết nếu chuyển 6 đơn vị từ mẫu số
lên tử số thì phân số có giá trị bằng 1.
* Tìm số tự nhiên a sao cho khi bớt cả tử số và mẫu số đi a đơn vị thì ta được phân số mới . (Hiệu sẽ
không thay đổi dựa vào hiệu để giải) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
VD2: Cho phân số 35/45 .Tìm số tự nhiên a sao cho khi ta bớt cả tử số và mẫu số di a đơn vị thì ta đợc
phân số 2/3.
*Tìm số tự nhiên a sao cho khi thêm cả tử số và mẫu số a đơn vị thì ta đợc phân số mới .( Hiệu sẽ không
thây đổi dựa vào hiệu để giải) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
VD3: Cho phân số 17/25 .Tìm số tự nhiên a sao cho khi ta bớt cả tử số và mẫu số di a đơn vị thì ta đợc
phân số 2/3.
-Tìm số tự nhiên a sao cho khi thêm (hoặc bớt) tử số đi a đơn vị ta được phân số mới .(Mẫu số không đổi
cần dựa vào mẫu số để giải) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
VD 4: Cho phân số 34/90 .Hỏi phải bớt tử số bao nhiêu đơn vị để đợc phân số có giá trị bằng 1/5
*Tìm số tự nhiên a sao cho khi thêm hoặc bớt mẫu số a đơn vị ta được phân số mới. (Tử số không đổi cần
dựa vào tử số để giải ) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
102
BÀI TÂP
1. Cho phân số 35/54 Hỏi phải bớt tử số đi bao nhiêu đơn vị để đợc phân số 5/9. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
2.Cho phân số 15/54 Hỏi phải bớt mẫu số đi bao nhiêu đơn vị để được phân số 3/10.
* Chuyển từ tử số xuống mẫu số a đơn vị (hoặc mẫu số lên tử số a đơn vị thì phân số có giá trị...) Tổng
của tử số và mẫu số không thay đổi dựa vào tổng để giải . .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Ví dụ : Cho phân số 13 /47 Hỏi phải chuyển bao nhiêu đơn vị từ tử số xuống mẫu số để được phân số 1/5.
CHÚ Ý: Dạng bài này cần xác định hiệu của tử số và mẫu số (Lưu ý khi có cụm từ phân số bằng 1 nghĩa
là tử số bằng mẫu số) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 1: Cho phân số có tổng của tử số và mấu số là 68 Tìm phân số đó biết nếu chuyển 6 đơn vị từ mẫu số
lên tử số thì phân số có giá trị bằng 1. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 2. Cho phân số 35/54 Hỏi phải bớt tử số đi bao nhiêu đơn vị để đợc phân số 5/9. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 3. Cho phân số 26/45. Hãy tìm số tự nhiên c sao cho thêm c vào tử số và giữ nguyên mẫu số , ta được
phân số mới có giá trị bằng 2/3. ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
103
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 4. Cho phân số 25/37 . Hãy tìm số tự nhiên c sao cho đem mẫu số của phân số đã cho trừ đi c và giữ
nguyên tử số ta được phân số mới có giá trị bằng 5/6. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 5. Cho phân số a/b có b-a = 21. Phân số a/b sau khi rút gọn thì được phân số 16/23. Tìm phân số a/b. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 6. Cho phân số 33/21. Hỏi cùng phải bớt đi ở cả tử số và mẫu số một số là bao nhiêu đê được một
phân số mới có giá trị bằng 5/3. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 7. Cho phân số 37/128. Hãy tìm số tự nhiên a sao cho khi bớt a ở tử số và thêm a vào mẫu số ta được
phân số mới có giá trị bằng 2/9. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 8. Cho phân số 39/69. Hãy tìm số tự nhiên m, sao cho thêm m vào cả tử số và mẫu số thì được phân
số mới có giá trị bằng 3/5. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 9. Cho phân số 234/369. Hỏi phải cùng bớt ở tử số và mẫu số bao nhiêu đơn vị để được phân số mới
và rút gọn phân số mới đó, ta được phân số 5/8. ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
104
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 10. Cho phân số a/b có a + b = 136. Rút gọn phân số a/b thì được phân số 3/5. Tìm phân số đã cho. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 11. Cho phân số a/b có hiệu giũa mẫu số và tử số là 18. Sau khi rút gọn phân số a/b ta được phân số
5/7. Tìm phân số a/b. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 12. Cho phân số m/n có giá trị bằng phân số 6/7. Nếu giảm tử số đi 12 đơn vị thì được phân số mới có
giá trị bằng phân số 36/49. Tìm phân số m/n đã cho. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 13. Hãy tìm 6 phân số tối giản ở giữa 1/5 và 3/8. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 12. a, Viết các phân số sau theo thứ tự tăng dần: 3/4; 5/6; 7/8
b, Hãy tím 5 phân số có tử số chia hết cho 5 và nằm giữa 9/10 và 11/13. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 14. Viết các phân số sau thàh tổng của các phân có mẫu số khác nhau và có tử số đều bằng 1: a, 31/32
; b, 25/27. ..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
105
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bài 15.: Hãy phân tích các phân số sau đây thành tổng của 3 phân số tối giản có cùng mẫu số:
a, 13/36 b, 31/60 .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bài 16. Tìm tổng của các phân số có tử số là 3, lớn hơn 1/6 nhưng bé hơn 1/5
(Tham khảo thêm Đề thi và phần Bài tập mở rộng) .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
106
31.CÁC PHÂN SỐ NẰM GIỮA HAI SỐ Bài 1 : Hãy viết 5 phân số nằm giữa 2 phân số 2002/2003 và 2003/2004. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 2 : Viết các phân số nằm giữa 1 và 2 mà tử số là 5. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bài 3 : Có bao nhiêu phân số nằm giữa 2003 và 2004 có mẫu lớn hơn 50?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
107
32. c¸c bµi to¸n gi¶i b»ng ph¬ng ph¸p s¬ ®å
®o¹n th¼ng
Bµi 1: Mét hiÖu s¸ch ®em vÒ mét sè s¸ch TiÕng ViÖt líp 5. ChÞ b¸n hµng ®· ®em ra 5
1sè s¸ch ®ã ®Ó bµy
b¸n. Sau khi b¸n ®îc 4 cuèn chÞ b¸n hµng nhËn thÊy r¾ng sè s¸ch bµy ra b¸n lóc nµy b»ng 5
1 sè
s¸ch ë trong kho. Hái chÞ b¸n hµng nhËn vÒ bao nhiªu cuèn s¸ch TiÕng ViÖt líp 5? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 2: Mét hiÖu s¸ch ®em vÒ mét sè s¸ch TiÕng ViÖt líp 5. ChÞ b¸n hµng ®· ®em ra 5
1sè s¸ch ®ã ®Ó bµy
b¸n. Sau khi b¸n ®îc 4 cuèn chÞ b¸n hµng nhËn thÊy r¾ng sè s¸ch bµy ra b¸n lóc nµy b»ng 6
1 sè
s¸ch ë trong kho. Hái chÞ b¸n hµng nhËn vÒ bao nhiªu cuèn s¸ch TiÕng ViÖt líp 5? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 3: Tæng sè tuæi cña 2 anh em hiÖn nay lµ 24, tÝnh tuæi cña mçi ngêi, biÕt r»ng khi tuæi anh b»ng tuæi
em hiªn nay th× tuæi em b»ng 5
3 tuæi anh hiÖn nay.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
108
Bµi 4: Bèn tæ häc sinh trång ®îc tÊt c¶ 950m2 rau. BiÕt tæ 1 trång kÐm tæ 3 lµ 20m2, tæ 2 trång kÐm h¬n
tæ 4 lµ 70m2, tæ 4 trång kÐm h¬n tæ 3 lµ 10m2. Hái mçi tæ trång ®îc bao nhiªu mÐt vu«ng rau? .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 5: ThÇy gi¸o ®iÒu 36 häc sinh líp 5B ®i lao ®éng vµ ®îc chia lµm 3 tæ. Trong ®ã tæ 1 nhiÒu h¬n tæ 2
lµ 4 häc sinh. Lóc sau thÇy l¹i chuyÓn 2 häc sinh tõ tæ 2 sang tæ 3 th× sè lîng häc sinh lóc nµy cña 2 tæ b»ng nhau. Hái lóc ®Çu mçi tæ cã bao nhiªu häc sinh?
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 6: Mét phÐp chia cã th¬ng lµ 4 vµ sè d lµ 2. Tæng cña sè bÞ chia, sè chia vµ sè d lµ 29. T×m sè bÞ
chia, sè chia trong phÐp chia ®ã. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. ....................................................................................................................................................................................................................................................................................................................................................
Bµi 7: HiÖu cña 2 sè lµ 1217. NÕu gÊp sè trõ lªn 4 lÇn th× ®îc sè míi lín h¬n sè bÞ trõ lµ 376. T×m sè bÞ
trõ vµ sè trõ. .................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................................................................................................................... Bµi 8: HiÖu cña 2 sè lµ 4. NÕu gÊp mét sè lªn 3 lÇn vµ gi÷ nguyªn sè kia th× ®îc hiÖu lµ 60. T×m 2 sè ®ã.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 9: Tæng cña 2 sè lµ 38570. Chia sè lín cho sè bÐ ®îc th¬ng lµ 3 d 922. T×m hai sè ®ã.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
109
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 10: HiÖu cña 2 sè lµ 8210. Chia sè lín cho sè bÐ ®îc th¬ng lµ 206 d 10. T×m 2 sè ®ã.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 1: Cho ph©n sè 369
234. Hái ph¶i cïng bít ë tö sè vµ mÉu sè bao nhiªu ®¬n vÞ ®Ó ®îc ph©n sè míi, rót
gän ph©n sè míi ta ®îc ph©n sè 8
5.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 2: Cho ph©n sè b
a cã a + b = 136. Rót gän ph©n sè
b
a ta ®îc ph©n sè
5
3. T×m ph©n sè
b
a.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 3: Cho ph©n sè b
a cã a + b = 108, khi rót gän ph©n sè
b
a ta ®îc ph©n sè
7
5. T×m ph©n sè
b
a.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 4: Cho ph©n sè b
a cã b - a = 18, khi rót gän ph©n sè
b
a ta ®îc ph©n sè
7
5. T×m ph©n sè
b
a.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Gia Sư Tài Năng Việt https://giasudaykem.com.vn/
110
Bµi 5: Cho ph©n sè 36
54. H·y t×m sè tù nhiªn a sao cho khi bít a ë tö, thªm a vµo mÉu cña
ph©n sè ta ®îc ph©n sè míi. Rót gän ph©n sè míi ta ®îc 5
4.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 6: Cho ph©n sè 45
26. H·y t×m sè tù nhiªn a sao khi thªm a ë tö sè vµ gi÷ nguyªn mÉu sè ta ®îc ph©n
sè míi cã gi¸ trÞ lµ 3
2.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 7: Cho ph©n sè 37
25. H·y t×m sè tù nhiªn a sao cho khi ®em mÉu sè trõ ®i a vµ gi÷ nguyªn tö sè ta
®îc ph©n sè míi cã gi¸ trÞ lµ 6
5.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
Bµi 8: Cho ph©n sè 58
43. H·y t×m sè tù nhiªn m sao cho khi lÊy c¶ tö sè vµ mÉu sè cña ph©n sè ®· cho trõ
®i sè tù nhiªn m ta ®îc ph©n sè míi. Rót gän ph©n sè míi nµy ta ®îc ph©n sè lµ 4
1.
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................
..........................................................................................................................................................................