Unit one The mixed numbers · 2015-02-09 · 1): ( ) ….) ….) ….)...

1

Unit one

The mixed numbers

1) Look to the shapes ,count the parts then complete:

2) Change the following improper fractions into mixed numbers:

…

4 = 1

…

4

…

6 = 2

…

6

3

2 =

7

5 =

15

7 = ……… ……… ………

9

8 =

17

9 =

16

5 = ……… ……… ………

7

3 =

16

3 =

29

10 = ……… ……… ………

13

12 =

57

15 =

45

19 = ……… ……… ………

50

23 =

50

25 =

76

35 = ……… ……… ………

2

3) Change the following mixed numbers into improper fractions:

1

2 = ……… 1

1

3 = 2

3

4 = ……… 6

2

3 = ……… 6

1

10 = ……… 9

4

9 = ……… 5

21

23 = ……… 1

7

8 = ……… 6

5

6 = ……… 3

10

11 = ……… 9

9

11 = ……… 6

4

5 = ……… 7

5

6 = ……… 7

9

10 = ……… 8

23

25 = ……… 3

8

9 = ……… 11

5

6 = ……… 20

2

3 = ……… 12

………

3

The Decimals

1) change the following into decimal form:

- Remarks:

- Decimal is normal fractions its denominators are 10 , 100 , 1000 , 10000……ect.

7

10 = 2) ………

3

10 = 1) ………

85

100 = 4) ………

79

100 = 3) ………

235

100 = 5) ………

965

100 = 6) ………

789

100 = 7) ………

311

100 = 8) ………

2

100 = 9) ………

195

100 = 10) ………

55

1000 = 11)

11

……… 165

1000 = 12) ………

585

1000 = 13) ………

9635

1000 = 14) ………

5555

1000 = 15) ………

7214

1000 = 16) ………

9365

1000 = 17) ………

5241

10 = 18) ………

4

2) Write the following in numeral form:

1) Four tenths = …………

2) Sixty thousands = ………………..

3) Twenty eight hundredths = …………

4) Four hundreds, forty five thousandths = …………

5) Sixty one thousandths = …………

6) Forty-eight and seven tenths = …………

7) Sixty three and Nine hundreds, thirty one thousandths = …………

8) Twenty one hundredths = ………………….

9) Sixty one and three hundredths = ………………….

10) Seven thousands and six hundreds forty nine thousandths = …………

11) Nine hundreds twenty five and seven hundredths = …………

12) One thousand six hundreds forty five and nine hundreds fifty four thousandths = …..

3) Read the following decimals: (as the first example):

1) 0.4 = Four tenths

2) 0.7 = …………………………………………………………………………

3) 0.54 = …………………………………………………………………………

4) 0.036 = …………………………………………………………………………

5) 0.085 = …………………………………………………………………………

6) 2.4 = …………………………………………………………………………

7) 16.35 = …………………………………………………………………………

8) 73.02 = …………………………………………………………………………

9) 63.054 = …………………………………………………………………………

…………………………………………………………

5

10) 125.69 = …………………………………………………………………………

11) 6325.124 = …………………………………………………………………………

4) Change the following into decimal form:

- Remarks (Use the following multiplication problems in answer the following):

1) 2 x 5 = 10 2) 4 x 25 = 100 3) 8 x 125 = 1000

3

2 = 2) ………

1

2 = 1) ………

11

5 = 4) ………

3

5 = 3) ………

5) 6) 1

2 = ……… 1

3

5 = 5 ………

7) 8) 4

5 = ……… 11

1

2 = ……… 20

1

4 = 10) ………

3

4 = 9) ………

11

25 = 12) ………

1

25 = 11) ………

7

25 = 14) ………

3

25 = 13) ………

15) 16) 3

4 = ……… 1

1

4 = 7 ………

6

Change the following decimals number into mixed number :

a) 10.6 = ………… b) 9.4 = ………… c) 3.7 = …………

d) 63.8 = ………… e) 5.7 = ………… f) 5.1 = …………

g) 52.25 = ………… h) 36.16 = ………… i) 35.44 = …………

j) 30.52 = ………… k) 55.93 = ………… l) 9.57 = …………

m) 24.55 = ………… n) 63.33 = ………… o) 7.12 = …………

5) Colour the parts represents the following numbers:

a) = = 0.9

b) = = 0.7

c) = = 1.2

17) 18) 13

25 = ……… 17

19

25 = ……… 2

11

125 = 20) ………

3

125 = 19) ………

21) 22) 1

8 = ……… 1

3

8 = 5 ………

…

…

…

…

7

The place value:

1) Complete the following table:

Number The digit lies in:

Tens Units Tenths Hundredths Thousands

15.325 ………… ………… ………… ………… …………

32.569 ………… ………… ………… ………… …………

72.154 ………… ………… ………… ………… …………

17.981 ………… ………… ………… ………… …………

………… 9 7 0 7 8

………… 7 6 0 8 4

………… 8 1 5 3 9

2) Determine the place value of encircled digits (three forms):

a) 256. 8 1 = …………

b) 31.05 2 = …………

c) 9 2 .705 = …………

d) 3.4 5 = …………

e) 36.78 9 = …………

f) 2 . 635 = …………

g) 458. 6 89 = …………

h) 1 35.741 = …………

i) 365.9 3 2 = …………

8

j) The Expanded & Compact forms:

1) Complete the following:

a) 63.729 = …… Ts + …… Us + …… Tth + …… Hth + …… Thth

b) 9.567 = …… Us + ………Ts + …… Hth +…… Thth

c) 45.635 = …… Ts +…… Us + +…… Tth + …… Hth + …… Thth

d) 6.328 = …… Us + …… Tth …… Hth +…… Thth

e) 12.635 = …… Ts + …… Us + …… Tth + …… Hth +…… Thth

f) ……… = 8 Ts + 9 Us +5 Tth + 7 Hth + 1 Thth

g) ……… = 7 Us +3 Tth + 1 Hth + 8 Thth

h) ……… = 4 Us +1 Tth + 7 Hth + 6 Thth

i) ……… = 8 Us + 4 Ts + 1 Tth + 6 Hth + 9 Thth

j) ……… = 9 Ts +8 Us +1 Tth + 3 Hth +7 Thth

k) ……… =3 Ts + 7 Us + 8 Hth + 6 Thth

l) ……… = 3 Ts +8 Us + 5 Tth + 1 Hth

m) ……… =5 Hs + 3 Ts + 7 Us + 2 Hth + 7 Thth

n) ……… = 9 Us + 5 Hth + 8 Tth

o) ……… = 1 U + 8 Ts + 6 Tth + 9 Thth

9


a) 6.52 = …… + 0.5 + ……

b) 75.48 = …… +…… + 0.4 + ……

c) 63.524 = …… + …… + …… + ……

d) 59.257 = …… + 0.2 + …… + ……

e) 8.325 = …… + …… + …… + ……

f) 99.9 = …… + ……

g) 16.325 = 16 + …… + …… + ……

h) 127.965 = 127 + …… + …… + ……

i) 632.635 = 632 + 0.6 + …… + ……

j) 925.124 = 925+ …… + …… + ……..

k) ……… = 6 + 0.5

l) ……… = 0.08 + 0.2 + 7

m) ……… = 3 + 0.1 + 0.05

n) ……… = 0.9 + 0.08

o) ……… = 7 + 0.2 + 0.09

p) ……… = 8 + 0.05 + 0.8

q) ……… = 30 + 0.04 + 0.1

r) ……… = 80 + 0.9 + 0.07

s) ……… = 30 + 0.5 + 0.02

10

Decimals comparison:

1) Put (>) or (<) or (=):

a) 0.3 0.4 m) 9.5 9.1

b) 5.8 5.9 n) 0.6 0.9

c) 4.82 9.17 o) 6.52 3.19

d) 8.77 6.59 p) 9.81 10.23

e) 7.45 7.49 q) 9.83 9.38

f) 2.99 21.89 r) 6.58 16.85

g) 7.42 74.24 s) 4.25 42.50

h) 4.85 48.5 t) 8.41 14.8

i) 4.58 45.8 u) 63.5 0.635

j) 7.42 7.63 v) 15.9 1.59

k) 1.02 10 w) 8.591 8.99

l) 7.5 x) 8.5

1

2 7

1

5 8

11

2) Arrange the following in ascending order:

a) 1.34 , 9.97 , 4.45 , 7.51 , 5.63 , 5.32

The order : …………………………………………………………………

b) 5.63 , 8.65 , 7.95 , 4.52 , 7.84 , 33.42

The order : …………………………………………………………………

c) 9.36 , 5.98 , 1.54 , 5.32 , 7.85 , 9.68

The order : …………………………………………………………………

d) 5.3 , 8.69 , 6.9 , 8.6 , 5.39 , 5.21

The order : …………………………………………………………………

e) 3.4 , 3.04 , 0.34 , 4.03 , 0.43

The order : …………………………………………………………………

f) 5.58 , 5.5 , 5.85 , 5.7

The order : …………………………………………………………………

g) 0.804 , 0.84 , 0.85 , 0.084

The order : …………………………………………………………………

h) 4.8 , 8.4 , 4.08 , 4.85 , 0.48

The order : …………………………………………………………………

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3) Arrange the following in descending order:

a) 0.35 , 0.235 , 0.336 , 0.3 , 0.365

The order : …………………………………………………………………

b) 44.2 , 4.64 , 4.351 , 4.53 , 4.31 , 4.138

The order : …………………………………………………………………

c) 3.5 , 5.3 , 35.3 , 53.3 , 0.35 , 0.53

The order : …………………………………………………………………

d) 5.5 , 55.1 , 5.51 , 5.05 , 1.55 , 5.15

The order : …………………………………………………………………

e) 2.6 , 2.59 , 2.509 , 2.591 , 2.601

The order : …………………………………………………………………

f) 12.87 , 12.78 , 12.71 , 12.17

The order : …………………………………………………………………

g) 0.365 , 3.605 , 6.305 , 5.306

The order : …………………………………………………………………

h) 8.752 , 9.52 , 7.53 , 5.73 , 2.875

The order : …………………………………………………………………

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4) Write decimal number lies between the following:

a) 6.3 < ……… < 6.9 h) 0.45 < ……… < 0.51

b) 2.3 < ……… < 2.6 i) 1.58 < ……… < 1.61

c) 7.25 < ……… < 7.29 j) 2.52 < ……… < 2.54

d) 5.35 < ……… < 5.37 k) 8.2 < ……… < 8.3

e) 0.7 < ……… < 0.8 l) 1.5 < ……… < 1.6

f) 6.3 < ……… < 6.4 m) 9.3 < ……… < 9.31

g) 1 < ……… < 1.2 n) 2 < ……… < 2.2

o) 5 < ……… < 6 t) 8 < ……… < 9

p) 11 < ……… < 12 u) 10 < ……… < 11

q) 7 < ……… < 8 v) 2 < ……… < 3

r) 8 < ……… < 8.1 w) 9 < ……… < 9.1

s) 6 < ……… < 6.2 x) 7 < ……… < 7.2

14

Adding Decimals

1) Find the answer of the following:

a) 0.3 + 0.6 = …………… b) 0.5 + 0.4 = ……………

c) 1.2 + 1.5 = …………… d) 2.5 + 2.9 = ……………

e) 3.8 + 2.9 = …………… f) 12.5 + 3.9 = ……………

g) 3.7 + 7.9 = …………… h) 4.9 + 6.35 = ……………

i) 8.45 + 9.6 = …………… j) 6.412 + 9.65 = ……………

k) 10 + 0.01 = …………… l) 5.247 + 5.6 + 1.52 = ……………

m) 3.254 + 9.2 + 6 = …………… n) 6.52 + 7 + 6.52 = ……………

o) 5.241 + 9.254 + 6.3 = …………… p) 5.24 + 3.6 + 4.852 = ……………

15

Subtracting Decimals

a)0.8 – 0.2 = …………… b) 0.5 – 0.4 = ……………

c) 2.2 – 1.5 = …………… d) 7.5 – 2.9 = ……………

e) 3.8 – 2.9 = …………… f) 12.5 – 3.9 = ……………

g) 9.7 – 7.9 = …………… h) 4.29 – 3.35 = ……………

i) 10.45 – 9.6 = …………… j) 6.532 – 4.65 = ……………

k) 9.25 – 3.001 = …………… l) 13 – 7.36 = ……………

m) 10 – 3.52 = …………… n) 9 – 6.325 = ……………

o) 0.9 – 0.111 = …………… p) 100 – 63.852 = ……………

16

The missing numbers for addition and

subtraction

a. Complete the following:

a) …………… + 3.25 = 9.5 b) …………… + 6.25 = 6.9

c) …………… + 6.52 = 8 d) …………… + 1.002 = 7.63

e) 9.36 + …………… = 10.5 f) 6.52 + …………… = 9.5

g) 6.309 + …………… = 14.21 h) 4.52 + …………… = 6

i) …………… – 3.6 = 2.51 j) …………… – 8.62 = 10.52

k) …………… – 7.52 = 13.52 l) …………… – 5.2 = 63.5

m) 9.63 – …………… = 1.523 n) 6.52 – …………… = 5.329

o) 9 – …………… = 2.325 p) 6 – …………… = 3.25

17

Dividing by (10 , 100 , 1000 ,…… ect.)

2) Find the answer of the following:

a)3 10 = …………… b) 4 10 = ……………

c)32 10 = …………… d) 25 10 = ……………

e)99 10 = …………… f) 65 10 = ……………

g) 26 100 = …………… h) 19 100 = ……………

i) 81 100 = …………… j) 52 100 = ……………

k) 8 100 = …………… l) 7 100 = ……………

m) 3 100 = …………… n) 4 100 = ……………

o) 883 100 = …………… p) 157 100 = ……………

q) 638 100 = …………… r) 675 100 = ……………

s) 254 1000 = …………… t) 109 1000 = ……………

u) 375 1000 = …………… v) 452 1000 = ……………

w) 76 1000 = …………… x) 635 1000 = ……………

y) 6 1000 = …………… z) 9 1000 = ……………

aa) 7 1000 = …………… bb) 1 1000 = ……………

cc) 8242 1000 = …………… dd) 9635 1000 = ……………

ee) 1247 1000 = …………… ff) 12475 1000 = ……………

18

Story problems

1) Ahmed bought a toy car for 25.63 pounds; toy train for 95.26 pounds, Find

the total money paid?

Total money paid: ……………………………………………………………

2) Ali bought a book for 62.5 piasters. If he had one pound, find the money left

with him?

The money left : …………………………………………………

3) Mona bought a pen for L.E. 6.32 and a rubber for L.E. 5.28 and a ruler for L.E.

5.85 ; find the total money paid?

Total money paid : ………………………………………………………………

4) Baher bought a T-shirt for L.E 56.75 , a training suit for L.E 75.25 and a pair

of shoes for L.E 65.65 ; How much did he pay?

He paid : …………………………………………………………………………

5) Karim had 10.5 pounds ; he bought a jam jar for L.E. 5.35 And bar of

chocolate for L.E. 3.55 ; find the remaining money?

Total money paid : ………………………………………………………………

The remaining money : …………………………………………………………

6) Marwa had 100 pounds ; she bought a kilogram of banana for L.E. 2.55 and a

kilogram of apple for L.E. 25.5 and a kilogram of mango for L.E. 35.25 ; find

the remaining money?

Total money paid : …………………………………………………………………

The remaining money : ……………………………………………………………

19

Approximation

1) Approximate the following to nearest ten:

a) 64 ≈ …………… b) 94 ≈ ……………

c) 325 ≈ …………… d) 855 ≈ ……………

e) 294 ≈ …………… f) 298 ≈ ……………

g) 2 472 ≈ …………… h) 1 979 ≈ ……………

i) 5 103 ≈ …………… j) 8 089 ≈ ……………

k) 5 693 ≈ …………… l) 7 358 ≈ ……………

m) 69 987 ≈ …………… n) 12 996 ≈ ……………

o) 19 974 ≈ …………… p) 69 935 ≈ ……………

q) 52 649 ≈ …………… r) 11 111 ≈ ……………

s) 87 635 ≈ …………… t) 65 234 ≈ ……………

u) 63 254 ≈ ……………

v) 52 415 ≈ ……………

w) 99 999 ≈ ……………

x) 88 888 ≈ ……………

y) 6 325.8 ≈ …………… z) 5 234.9 ≈ ……………

aa) 684.55 ≈ …………… bb) 963.25 ≈ ……………

20

2) Approximate the following to nearest hundred:

a) 564 ≈

…………… b) 427 ≈ ……………

c) 373 ≈ …………… d) 852 ≈ ……………

e) 3 498 ≈ …………… f) 3 758 ≈ ……………

g) 9 939 ≈ …………… h) 4 000 ≈ ……………

i) 2 470 ≈ …………… j) 6 489 ≈ ……………

k) 29 637 ≈ …………… l) 98 760 ≈ ……………

m) 55 475 ≈ …………… n) 342 74 ≈ ……………

o) 3 490.9 ≈ …………… p) 3 758.3 ≈ ……………

q) 2 799.39 ≈ …………… r) 4 096.97 ≈ ……………

s) 70 ≈ …………… t) 96 ≈ ……………

u) 63 ≈ …………… v) 85 ≈ ……………

w) 54 ≈ …………… x) 15 ≈ ……………

y) 859 ≈ …………… z) 899 ≈ ……………

aa) 748 ≈ …………… bb) 996 ≈ ……………

cc) 68455 ≈ …………… dd) 963.25 ≈ ……………

21

3) Approximate the following to nearest thousand:

a) 8 384 ≈ …………… b) 9 190 ≈ ……………

c) 2 100 ≈ …………… d) 1 009 ≈ ……………

e) 12 394 ≈ …………… f) 89 999 ≈ ……………

g) 99 992 ≈ …………… h) 52 486 ≈ ……………

i) 29 976 ≈ …………… j) 12 274 ≈ ……………

k) 63 254 ≈ …………… l) 99 888 ≈ ……………

m) 524 361 ≈ …………… n) 632 589 ≈ ……………

o) 745 369 ≈ …………… p) 111 111 ≈ ……………

q) 9351.35 ≈ …………… r) 6352.95 ≈ ……………

s) 6352.961≈ …………… t) 8524.36 ≈ ……………

u) 5234.63 ≈ …………… v) 4521.63 ≈ ……………

w) 523.325 ≈ …………… x) 8524.63 ≈ ……………

y) 8888.99 ≈ …………… z) 9658.42 ≈ ……………

aa) 999.999 ≈ …………… bb) 8524.99 ≈ ……………

cc) 888.999 ≈ …………… dd) 9789.62 ≈ ……………

22

4) Approximate the following to nearest ten thousand:

a) 28 384 ≈ …………… b) 12 149 ≈ ……………

c) 95 254 ≈ …………… d) 63 563 ≈ ……………

e) 825 365 ≈ …………… f) 888 888 ≈ ……………

g) 425 632 ≈ …………… h) 111 1111 ≈ ……………

i) 7 325 ≈ …………… j) 7 824 ≈ ……………

k) 2 524 ≈ …………… l) 3 526 ≈ ……………

5) Approximate the following to nearest hundred thousand:

a) 52 639 ≈ …………… b) 78 635 ≈ ……………

c) 42 125 ≈ …………… d) 25 635 ≈ ……………

e) 125 635 ≈ …………… f) 741 256 ≈ ……………

g) 325 635 ≈ …………… h) 253 666 ≈ ……………

i) 999 999 ≈ …………… j) 888 777 ≈ ……………

k) 524 635 ≈ …………… l) 988 812 ≈ ……………

23

6) Approximate to the nearest unit (Whole number):

a) 4.6 ≈ …………… b) 3.6 ≈ ……………

c) 9.5 ≈ …………… d) 4.4 ≈ ……………

e) 16.5 ≈ …………… f) 68.5 ≈ ……………

g) 14.69 ≈ …………… h) 85.39 ≈ ……………

i) 71.38 ≈ …………… j) 89.89 ≈ ……………

k) 97.38 ≈ …………… l) 84.73 ≈ ……………

m) 58.897 ≈ …………… n) 84.187 ≈ ……………

o) 742.327 ≈ …………… p) 1848.245 ≈ ……………

q) 894.847 ≈ …………… r) 452.424 ≈ ……………

s) 96.3225 ≈ …………… t) 999.89 ≈ ……………

u) 89.6742 ≈ …………… v) 69.45 ≈ ……………

w) 99.288 ≈ …………… x) 389.249 ≈ ……………

y) 699.89 ≈ …………… z) 354.659 ≈ ……………

aa) 5999 10

7 ≈ …………… bb) 5999 10

9 ≈ ……………

cc) 523 2

1 ≈ …………… dd) 253 5

1 ≈ ……………

24

7) Approximate the following to nearest tenths (1 Decimal Place):

a) 3.65 ≈ …………… b) 52.69 ≈ ……………

c) 8.99 ≈ …………… d) 8.98 ≈ ……………

e) 58.63 ≈ …………… f) 5.99 ≈ ……………

g) 89.9999 ≈ …………… h) 85.999 ≈ ……………

i) 9.1111 ≈ …………… j) 96.525 ≈ ……………

k) 4.888 ≈ …………… l) 78.635 ≈ ……………

m) 99 100

9 ≈ …………… n) 99 100

99 ≈ ……………

o) 542 100

8 ≈ …………… p) 854 1000

8 ≈ ……………

q) 852 100

98 ≈ …………… r) 35 1000

999 ≈ ……………

s) 2 1000

88 ≈ …………… t) 95 1000

777 ≈ ……………

u) 99 1000

999 ≈ …………… v) 989 100

98 ≈ ……………

w) 89 4

3 ≈ …………… x) 6 25

9 ≈ ……………

y) 8 4

1 ≈ …………… z) 122 25

2 ≈ ……………

aa) 36 25

7 ≈ …………… bb) 325 8

3 ≈ ……………

25

8) Find the answer of the following and then approximate the

answer to required approximation degrees:

a) 3.6 + 8.36 = ………… ≈ ………… ( To nearest Tenth)

b) 1.7 + 1.9 = ………… ≈ ………… ( To nearest Units)

c) 3.55 + 2.47 = ………… ≈ ………… ( To nearest Tenth)

d) 524 + 494 + 7784 = ………… ≈ ………… ( To nearest Hundred)

e) 3.5 + 4.2 +1.288 = ………… ≈ ………… ( To nearest Tenth)

f) 0.8 – 0.5 = ………… ≈ ………… ( To nearest Unit)

g) 7.9 – 5.3 = ………… ≈ ………… ( To nearest Unit)

h) 4.8 – 2.4 = ………… ≈ ………… ( To nearest Tenth)

i) 525.7 – 125.9 = ………… ≈ ………… ( To nearest Ten)

j) 4 525 – 2 365 = ………… ≈ ………… ( To nearest Thousand)

k) 8 524 – 3001 = ………… ≈ ………… ( To nearest Thousand)

l) 3 10 = ………… ≈ ………… ( To nearest Unit)

m) 882 10 = ………… ≈ ………… ( To nearest Ten)

n) 85 962 100 = ………… ≈ ………… ( To nearest Hundred)

o) 852 398 1000 = ………… ≈ ………… ( To nearest Hundred)

p) 8254 1000 = ………… ≈ ………… ( To nearest Tenth)

26

9) Complete the following by suitable number:

a) …………… ≈ 2000 ( To nearest Thousand)

b) …………… ≈ 600 ( To nearest Hundred)

c) …………… ≈ 6.3 ( To nearest Tenth)

d) …………… ≈ 83 ( To nearest Units )

e) …………… ≈ 900 ( To nearest Hundred)

f) …………… ≈ 0.3 ( To nearest Tenth)

g) …………… ≈ 52 ( To nearest Unit)

h) …………… ≈ 60 ( To nearest Ten)

i) …………… ≈ 3 000 ( To nearest Thousand)

j) …………… ≈ 1 000 ( To nearest Hundred)

k) …………… ≈ 0.8 ( To nearest Tenth)

l) …………… ≈ 800 ( To nearest Hundred)

m) …………… ≈ 30 ( To nearest Ten)

n) …………… ≈ 3 500 ( To nearest Hundred)

o) …………… ≈ 630 ( To nearest Tenth)

p) …………… ≈ 78 000 ( To nearest Hundred)

q) …………… ≈ 10 000 ( To nearest Thousand)

27

10) State the degree of approximation in the following:

a) 3524 ≈ 4000 ( To nearest …………)

b) 8524 ≈ 8520 ( To nearest …………)

c) 63.2 ≈ 63 ( To nearest …………)

d) 61 ≈ 100 ( To nearest …………)

e) 523.51 ≈ 523.5 ( To nearest …………)

f) 635.9 ≈ 635.92 ( To nearest …………)

g) 92509 ≈ 92510 ( To nearest …………)

h) 485.695 ≈ 485.7 ( To nearest …………)

i) 625 ≈ 600 ( To nearest …………)

j) 8 526 ≈ 9000 ( To nearest …………)

k) 5 241 ≈ 5200 ( To nearest …………)

l) 14 578 ≈ 15 000 ( To nearest …………)

m) 635 248 ≈ 635 250 ( To nearest …………)

n) 985 324 ≈ 985 300 ( To nearest …………)

o) 985 324 ≈ 985 000 ( To nearest …………)

p) 985 324 ≈ 990 000 ( To nearest …………)

q) 0.2 ≈ 0 ( To nearest …………)

82

11) Story Problems:

1) If Farida had L.E. 256 and her sister had L.E. 325 find the total money both of them had,

and then approximate the money both of them had to nearest pound?

Total money both of them had : ………………………………………………………

Total money to nearest pound : ………………………………………………………

2) Mahmoud bought a new car for L.E. 85 365 and a new apartment for L.E. 125

365, Find the total money paid, and then approximate the total money paid to nearest

hundreds thousand?

Total money paid : ………………………………………………………………………

Total money paid to nearest hundreds thousand pounds: ………………………

3) Yousef had L.E. 20 ; He bought a bar of chocolate for L.E. 2.35 and a packet of biscuit

for L.E. 3.75 , Find the money left for him to nearest pound?

Total money paid : ……………………………………………………………………

The remaining money : ………………………………………………………………

Total money left to nearest pound: ………………………………………………

82

Congruency

1) Put (√) for right statements and (X) for the wrong statements:

a) A square of side length 10 Cm can be be congruent with another one of side length 10

Cm ( )

b) A recatngle of length = 7 Cm & width = 3 Cm can be congurent with another of width =

3 Cm and length = 7 Cm ( )

c) A triangle of sides lengths 7 Cm , 3 Cm , 6 Cm is congurent to another of sides lengths

3 Cm , 6 Cm , 7 Cm ( )

d) An equilateral triangle of side length 5 Cm is congurent to another of side length 5 Cm

( )

e) The scalene triangle is congruent to the isosceles triangle ( )

Lines of symmetry

- Remarks:

- Two squares are congruent if the two sides' lengths of the two squares are equal.

- Two rectangles are congruent if the length & width in one of them are equal in

length to the other one.

- Two triangles are congruent if their corresponding sides are equal in length.

* If ∆ ABC ≡ ∆ XYZ , then m( A) = m( ….), m( ….) = m( Y),

m( C) = m( ….) , and

AB = …... , BC = ……. , AC =……

03

The following figure shows the axes (lines) of symmetry of some

geometric figures:

The Triangles:

The Quadrilaterals:

The Parallelograms:

1) Put (√) for right statements and (X) for the wrong statements:

Three lines of symmetry

The Equilateral Triangle

One line of symmetry

The Isosceles Triangle

No lines of symmetry

The Scalene Triangle

Two lines of symmetry

The Rhombus

Four lines of symmetry

The Square

Two lines of symmetry

The Rectangle

No lines of symmetry

The Parallelogram

One line of symmetry

The Isosceles Trapezium

03

a) The isosceles triangle has four lines of symmetry ( )

b) The equilateral triangle has 3 lines of symmetry ( )

c) The parallelogram has infinite number of lines of symmetry ( )

d) The quadrilateral which has 4 lines of symmetry is recatngle ( )

e) The quadrilateral which has no lines of symmetry is parallelogram ( )

f) The trapezium has no lines of symmetry ( )


a) Number of lines of symmetry for triangle which has sides

lengths are 5 cm , 9 cm , 10 cm is ……………

b) Number of lines of symmetry for triangle which has sides length 6 cm , 6

cm , 6 cm is ……………

c) Number of lines of symmetry for triangle which has sides lengths are 7

cm , 6 cm & 7 cm is ………………

Two dimensional coordinates

(Ordered Pairs)

- Remarks:

- The ordered pair ( 2 , 5 ) ≠ ( 5 , 2 )

08

1) Use the following lattice to answer and complete the following:


1) The coordinate of point (A) is ( … , … ) so the first coordinate of point (A) is

…… while the second coordinate of point (A) is ……

2) The coordinate of point (C) is ( … , … ) so the first coordinate of point (C) is

…… while the second coordinate of point (C) is ……

3) The coordinate of point (K) is ( … , … ) so the first coordinate of point (K) is

…… while the second coordinate of point (K) is ……

2

3

4

5

6

7

8

9

1

10

1 3 5 7 9 11 13 2 4 6 8 10 12

A

B

D C

L M

N

K

Y Z

W

X

00

4) The coordinate of point (M) is ( … , … ) so the first coordinate of point (M) is

…… while the second coordinate of point (M) is ……

5) The coordinate of point (W) is ( … , … ) so the first coordinate of point (W) is

…… while the second coordinate of point (W) is ……

6) The coordinate of point (Y) is ( … , … ) so the first coordinate of point (Y) is

…… while the second coordinate of point (Y) is ……

3) Join the points (ABCD) and then complete the following:

The name of the figure (ABCD) is ………… & it has number of lines of symmetry

equal …………

4) Join the points (KLMN) and then complete the following:

The name of the figure (KLMN) is ………… & it has number of lines of symmetry

equal …………

5) Join the points (WXYZ) and then complete the following:

The name of the figure (WXYZ) is ………… & it has number of lines of symmetry

equal …………

6) Use the previous lattice to draw a figure congruent to the shape

(KLMN).

1) Use the following lattice to draw and answer the following:

03

Draw the figure (ABCD) where A ( 1 , 3 ) ; B ( 4 , 5 ) ; C ( 4 , 7 ) ; D ( 1 , 5 )

1) Name of the produced figure: ……………..

2) Number of its lines of symmetry: …………

Draw the figure (WXYZ) where W ( 9 , 1 ) ; X ( 8 , 4 ) ; Y ( 9 , 7 ) ; Z ( 10 , 4 )

3) Name of the produced figure.

4) Number of its lines of symmetry.

2) Use the following lattice to draw and answer the following:

2

3

4

5

6

7

8

9

1

10

1 3 5 7 9 11 13 2 4 6 8 10 12

7

8

9

10

03

a) Draw the triangle (ABC) where A ( 1 , 3 ) ; B ( 1 , 6 ) ; C ( 4 , 3 )

5) Type of the triangle according to sides lengths.

6) Type of the triangle according to angles measures.

b) Draw the figure (XYZ) where X ( 5 , 2 ) ; Y ( 9 , 2 ) ; Z ( 7 , 6 )



c) Draw the figure (KLM) where K ( 5 , 5 ) ; L ( 7 , 4 ) ; M ( 6 , 10 )



Measuring capacity:

Units of measuring capacity:

03

1) Complete the following by suitable units:

a) The amount of water for filling big water reservoir is measured by …………

b) The amount of fuel for car refueling is measured by …………

c) The amount of water for washing your car is measured by …………

d) The amount of perfume used by you everyday is measured by …………

e) The amount of alcohol for sterilization your hurt is measured by …………

f) The amount of blood in your body is measured by …………

2) Complete the following by suitable numbers:

a) 2000 milliliters = ………… liters e) 254 milliliters = ………… liters

b) 7695 milliliters = ………… liters f) 63254 milliliters = ………… liters

c) 25 liters = ………… milliliters g) 36 liters = ………… milliliters

d) 125 liters = ………… milliliters h) 524 liters = ………… milliliters

3) Arrange the following in ascending order: 3 liters , 3 500 milliliters , 2 liters , 757 milliliters , 4 535 militaries , 32 milliliters The order : …………………………………………………………………

Liter Milliliter

X

dm3 1000 cm3

÷

03

Measuring weight

Units of measuring weight:


a) The weight of loaded truck is measured by …………

b) The weight of necklace is measured by …………

c) The weight of patient is measured by …………

d) The weight of your rubber is measured by …………

e) The weight of an airplane is measured by …………


a) 52000 grams = ………… kilograms f) 85 kilograms = ………… grams

b) 6352 grams = ………… kilograms g) 80352 grams = ………… kilograms

c) 67 tons = ………… grams h) 852 kilograms = ………… tons

d) 8524635 grams = ………… tons i) 8 tons = ………… kilograms

e) 8524 kilograms = ………… tons j) 74 tons = ………… grams


3 tons , 4 635 kilograms , 8 tons , 8 632 585 grams , 35 kilograms , 3 grams

The order : …………………………………………………………………

Kilogram Gram

X

Ton 1000 Kgm 1000 gm

÷

X

÷

02

Measuring Time:

Units of measuring time:


a) Time taken to travel to Alexandria by car is measured by …………

b) Time taken for watching football match is measured by …………

c) Time taken for reading newspaper every day is measured by …………

d) Time taken for washing your face at the morning is measured by …………

e) Time taken for sleeping every day is measured by …………

f) Time of your week end is measured by …………


a) 1 day = …… x …… hours ● 3 hours = …… x …… minutes

b) 9 minutes = …… x …… seconds ● 48 hours = …… x …… days

c) 7 days = …… x …… hours = …… x …… minutes

d) 5 hours = …… x …… minutes = …… x …… seconds

e) 10 days = …… x …… hours = …… x …… minutes

f) 3 hours = …… x …… minutes = …… x …… seconds

g) 6 days = …… x …… hours = …… x …… minutes

Day 24 hours 60 minute 60 second

X X X

÷ ÷ ÷

02

3) Arrange the following in ascending order:

h) 1 day , 5 hours , 585 minutes , 36 hours , 9880 minutes

i) The order : …………………………………………………………………

j) 8 hours , 600 seconds , 420 minutes ,68000 seconds , 120 minutes

k) The order : …………………………………………………………………


1)72 hours , 4 days , 8000 minutes , 2 days , 45 hours , 10 minutes

The order : …………………………………………………………………

2) 245 minutes , 3 hours , 1500 seconds , 7500 seconds , 30 minutes

The order : …………………………………………………………………

Measuring temperature:

- Remarks:

- Unit for measuring temperature is degree centigrade and has a symbol (°C)

- The device used for measuring temperature is (thermometer)

- Normal room temperature is (25°C)

- Healthy person temperature is (37°C)

- Light cloths for temperatures more than (25°C) ( Hot Weather)

- Heavy cloths for temperatures less than (25°C) ( Cold Weather)

- Boiling point of water ( 100°C)

- Freezing point of water ( 0°C)

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Histogram:

1) The following table represents number of students participated in different

activities in the summer school time:

Activity Tally Number of students

Music …………………

Art …………………

Swimming …………………

Football …………………

Volleyball …………………

Tennis …………………

Use the following lattice to represent the previous data by histogram

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2) The following table represents classification of students in according to their

grades in Mathematics :

Activity Tally Number of students

Excellent …………………

Very Good …………………

Good …………………

Pass …………………


How many students in the class ?

Which grade obtained by greatest number of students ?

Find the sum of students who obtained grades excellent and good ?

38

3) The following table shows the quantities of sugar (in kilograms) consumed

by one family during five months:

Month March April May June July

Sugar consumed 5 4 8 9 10


In which month was the greatest quantity of sugar consumed ?

In which month was the smallest quantity of sugar consumed ?

Find the sum of quantities of sugar consumed May and June ?

Find the difference between quantities of sugar consumed in March and July ?

Did the quantity of sugar consumed by this family increase or decrease ?

30

Double bars graph:

1) The following graph shows the temperature in Cairo & Alex. through one week.

Day

City Sat. Sun. Mon. Tues. Wed. Thu. Fri.

Cairo …… …… …… …… …… …… ……

Alexandria …… …… …… …… …… …… ……

In which day was the temperature the highest in Cairo ? ………………

In which day was the temperature the Lowest in Cairo ? ……………….

In which day was the temperature the highest in Alexandria ? ………………

In which day was the temperature the Lowest in Alexandrina ? ………………..

In which day was the temperatures in Cairo and Alexandria equal ? …………………

In which day was the difference in temperatures in Cairo and Alexandria maximum?

Sat. Sun. Mon.

Tues. Wed. Thurs. Fri.

29

30

31

32

33

34

35

36

28

37 Cairo

Alexandria

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2) The following table shows money saved by Hossam and Alya in pounds

in four successive weeks:

Week

Name 1st week 2nd Week 3rd Week 4th week

Hossam 5 4 8 9

Alya 3 4 7 3

Represent these data by double bars

Find the sum saved by Hossam and Alya in 3 rd week?

Name the week in which saving of Hossam and Those for Alya were equal ?

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3) The following table shows the production of two factories of cement (In

Tons) in five consecutive days:

Day

Factory Sat. Sun. Mon. Tues. Wed.

Factory (A) 8 10 7 4 7

Factory (B) 6 7 8 7 6

Represent these data by double bars

Find the sum of two factories production in Monday?

Name the month in which production of factory (A) was minimum?

Name the month in which production of factory (B) was maximum?

Find the difference between productions of two factories in Sunday?

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Probability:

1) For tossing coin experiment find the probability of the following:

a) Getting tail = …… c) Getting head = …..

b) Getting head or tail = ……

2) For tossing dice experiment find the probability of the following:

a) Getting upper face of number (One) = …..

b) Getting upper face of number (Six) = ……

c) Getting upper face of number (Seven) = ……

d) Getting upper face of even numbers = …….

e) Getting upper face of number more than 6 = …….

f) Getting upper face of number less than 7 = …….

* Remarks:

- Probability of impossible event = Zero

- Probability of sure (certain) event = One

- Probability of possible event = proper fraction or decimal between 0 and 1

- The sum of probabilities of all possible events = 1

* Calculating probability: (Probability of an event A)

The number of ways event A can occur

The total number of possible outcomes

P ( A ) =

http://st-takla.org/Gallery/Gallery-index_.html

http://st-takla.org/Gallery/Gallery-index_.html

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3) A box contains 4 red balls and 3 blue balls and 2 green balls, if you

blindly draw one ball.Find the probability of each of the following:

a) Drawn ball is red = …..

b) Drawn ball is green = …..

c) Drawn ball is blue = ……

d) Drawn ball is red or blue = ……. Total = 9 balls

e) Drawn ball is red or green = ……..

f) Drawn ball is red or green or blue = …..

g) Drawn ball is black = …….

h) Drawn ball is not green nor red = ……

4) A card from the following cards is chosen randomly:

Calculate the probability of getting a number :

a. A number less than 8 = …………..

b. A number more than 5 = …………

c. A number between 2 and 7 = ……………

d. A number divisible by 3 = ……………….

e. A number divisible by 2 = ……………….

f. A number divisible by 5 = ………………..

red blue green

1 2 3 5 6 7 8 9 4

Unit one The mixed numbers · 2015-02-09 · 1): ( ) ….) ….) ….)...

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