abm matematik
-
Upload
gmin-jaimin -
Category
Documents
-
view
120 -
download
4
Transcript of abm matematik
ROUND OFF
Example: 83 495 83 000
(Nearest thousands)
Rules to remember for rounding off
0, 1, 2, 3, 4 retain the digit.
5, 6, 7, 8, 9 add by 1.
Rounding off to the nearest tens, hundreds or thousands.
Tens 10 One zero
Hundreds 100 Two zeros
Thousands 1 000 Three zeros
Tens (10) circle 1 digit from the right.
Hundreds (100) circle 2 digits from the right.
Thousands (1 000) circle 3 digits from the right.
Examples 1 : Round off 5 246 to the nearest tens (10).
5 24 6
5 25 0 (answer)
o If the 1st digit from the right 6 is larger than 5 (see diagram 1) add 1 to the
digit 4 and replace 1 zero at the end.
Examples 2: Round off 48 379 to the nearest hundreds (100).
48 3 7 9
48 4 0 0 (answer)
If the 2nd digit from the right 7 is larger than 5 (see diagram 1) add 1 to the digit 3 and replace 2 zeros at the end.
1
2
3
4 5
6
7
8
9
+1
0
+1
+1
PLACE VALUE
Ten Thousands
Thousands Hundreds Tens Ones
20 000 5 000 100 80 3
Example:
3 8 9 2 4 5
5 one
4 tens
2 hundreds
9 thousands
8 ten thousands
3 hundred thousands
Digit value
Place value
ADDITION
Example: Adding two numbers.
1
Step 1
Write the problem in the columns.
Step 2
Then, add the ones column.
8 ones + 4 ones.
= 12 ones.
Step 3
Next, add the tens column.
1 tens + 5 tens + 7 tens. = 13 tens = 1 hundreds 3 tens.
ADDITION
Thousands Hundreds Tens Ones
3 04
57
48+
Thousands Hundreds Tens Ones
3 04
57
48+
2
1
1
+
3 0 5 4
4 7 8
Thousands Hundreds Tens Ones
3 04
57
48+
3 2
1
1
1
Adding three numbers (without trading)
Example: (2 051 + 1 228 + 510 = )
Add the first two numbers (a).
Add the other number to this sum, as illustrated below (b).
Adding three numbers (with trading)
Example: (3 029 + 4 876 + 698 = )
Add the first two numbers (a).
Add the other number to this sum, as illustrated below (b).
SUBTRACT
Subtract two numbers (with trading)
Example :
2 0 5 1
1 2 2 8+
9723
9723
5 1 0+
9873
(a)
(b)
(a) (b)
3 0 2 9
4 8 7 6+
5097
5097
6 9 8+
3068
11 111
- 6 8 2 34 7 6 9
Step 1
Write the problem on the columns.
Step 2
First, subtract the ones.
Subtract the bottom ones place digit from the top ones place digit (3 – 9).
We do not know how to do this, so we need to rearrange the number to make the top
value larger.
Regroup 1 tens into 10 ones, make the 3 into 13.
13 ones – 9 ones = 4 ones.
The 4 is placed below the line in the ones place column.
Next, subtract the tens.
Thousands Hundreds Tens Ones
64
87
26
39
Thousands Hundreds Tens Ones
64
87
26
39
4
10 +1
Thousands Hundreds Tens Ones
64
87
26
39
5 4
7 10 + 1
The top tens place value becomes 1 after trading one tens from it.
Regroup 1 hundreds into 10 tens
10 tens + 1 tens = 11 tens.
11 tens – 6 tens = 5 tens.
Then, subtract the hundreds.
7 hundreds – 7 hundreds = 0 hundreds.
Finally, subtract the thousands.
6 thousands – 4 thousands = 2 thousands.
6 823 – 4 769 = 2 054
Subtract three numbers (without trading)
Example: (6 994 – 3 012 – 251 = )
Subtract the first two numbers (a).
Subtract the other number from this remainder, as illustrated below (b).
Subtract from right to left.
Thousands Hundreds Tens Ones
64
87
26
39
0 5 4
5
Thousands Hundreds Tens Ones
64
87
26
39
2 0 5 4
7 1
7 1
Subtract three numbers (with trading)
Example: ( 6 994 – 3 012 – 251 = )
Subtract the first two numbers (a).
Subtract the other number from this remainder, as illustrated below (b).
Subtract from right to left.
7 4 8 0
2 3 8 9-
1905
1905
4 6 1-
0364
173 10410
6 9 9 4
3 0 1 2-
2893
2893
2 5 1-
1373
(a) (b)
(a) (b)
MULTIPLY
Since it is multiply by 100, place the two zeros (00) to the right after product.
3 1 5
x 1 (00)
3 1 5 00 (answer)
Generalizing from the pattern, have pupils consider:
485 x 100 is:
485 x 1 = 485
485 x 1 hundreds = 485 hundreds
= 485 00 48 500 (answer)
9 312 x 10 is:
9 312 x 1 = 9 312
9 312 x 1 tens = 9312 tens
= 9312 0 93 120 (answer)
75 x 1 000 is:
75 x 1 = 75
75 x 1 thousands = 75 thousands
= 75 000 (answer)
Multiply any four-digit numbers with 10, two digit-numbers with 100 000 is the same
way as multiply three-digit numbers with 100.
Tips (DIVISION)
Points to note
Tens has one zero (0)
Hundreds has two zeros (00)
Thousands has three zeros (000)
(Divide four or five-digit number with two-digit)
Build related time-table.
Example: 42 252 ÷ 12 =
0 1 2 3 4 5 6 7 8 9
0 12 24 36 48 60 72 84 96 108
12
3 6–
6 2
6 0–
2 5
2 4–
1 2
1 2–
0 0
4 2 2 5 21
3 5 12
FRACTION
Notes:
A proper fraction is a fraction with the numerator smaller than the denominator, for example
and it is read as ‘two over three’ or two thirds.
a) Same denominators
bigger
**The bigger the numerator, the higher the value
b) Numerator of 1 and different denominators
bigger
**The smaller the denominator, the higher the value.
Notes:
1. To add fractions having the same denominator, add the numerators to get the
numerator of the sum and use the same denominator.
Example : + =
= simplest form
2. To add fractions with different denominators, change the fractions to its equivalent
fractions.
: Examples addition of fractions,
numerator
denominator
a) with same denominator
+ =
+ = = 1
b) with different denominator
+ = +
= +
=
+ = +
= +
=
= simplest form
DECIMAL
x 2
x 2
X 2
X 2
Place value:
Whole number part Decimal part
Hundreds Tens Ones Tenths Hundredths
1 7 3 8 9
100 70 3
1 digit numerator
2 digits numerator
= 0.4
= 0.9
= 0.08
= 0.24
●
Decimal
TIME
1 cm = 10 mm10 cm = 100 mm
1 m = 100 cm10 m = 1000 cm
1 Km = 1000 m1 m = 100 m1 cm = 10 mm
TABLE “AKU”
metre cm mm
1 0
TABLE “AKU”
metre cm
1 0 0
1 minute = 60 seconds 1 hour = 60 minutes
1 week = 7 days
1 month = 30 days
1 year = 12 months
1 day = 24 hours
1 year = 365 days
1 leap year = 366 days 1 decade = 10 years
MASS VOLUME OF LIQUID
‘Table Aku’:
kilogram
gram
1.0 1 000
0.9 900
0.8 800
0.7 700
0.6 600
0.5 500
0.4 400
0.3 300
0.2 200
0.1 100
Shape and Space
Rectangle 4 sides
The perimeter of a shape is the sum of the lengths of all its sides.
Example 1:
Perimeter = 6 cm + 3 cm + 6 cm + 3 cm Perimeter = 5 cm + 5 cm + 5 cm + 5 cm
= 18 cm = 20 cm
Example 1
Breadth
Length
Example 2
Triangle 3 sides
Square 4 sides
5 cm
6 cm
3 cm
Area = Length x Breadth
a) Length = 10 cm
b) Breadth = 5 cm
10 cm
5 cm
7 cm
3 cm
Area = Length x Breadth
= 7 cm x 3 cm
= 21 cm 2
NOTE : The Standard unit for area:
1. Square centimetre (cm²)
2. Square metre (m²)