abm matematik

24
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 1 st 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. 1 2 3 4 5 6 7 8 9 + 1 0 +1

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Page 1: 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

Page 2: abm matematik

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

Page 3: abm matematik

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

Page 4: abm matematik

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

Page 5: abm matematik

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

Page 6: abm matematik

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

Page 7: abm matematik

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)

Page 8: abm matematik

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)

Page 9: abm matematik

(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

Page 10: abm matematik

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

Page 11: abm matematik

a) with same denominator

+ =

+ = = 1

b) with different denominator

+ = +

= +

=

+ = +

= +

=

= simplest form

DECIMAL

x 2

x 2

X 2

X 2

Page 12: abm matematik

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

Page 13: abm matematik

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

Page 14: abm matematik

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

Page 15: abm matematik
Page 16: abm matematik
Page 17: abm matematik

Shape and Space

Rectangle 4 sides

Page 18: abm matematik

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

Page 19: abm matematik

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)