# tambah&tolak pecahan

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FRACTION

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Without renaming

Fractions with the same denominator are known as like fractions.

Look at this pizza. It is cut into 8 equal

slices. 1 slice is of the pizza.1

8

I take 2 slicesof the pizza.

I take 1 sliceof the pizza.

+ =2

8

3

8

1

8

of the pizza is given away altogether.3

8

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Lets look at this strip of paper. Ithas been divided into 9 equal parts.

of the paperis

coloured blue.

4

9

of the paper iscoloured orange.

3

9

What fraction of the paper is coloured?

What fraction of the paper is not coloured?Try these.

+ =3

9 9

4

9

- =9 9

9

9

7

7 2

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Related fractions

Related fractions have 1 denominator that is a factor of the other.

and arerelated fractionsas 3 is a factor of 6.

1

6

2

3

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Let us add the 2 fractions, and .1

6

2

3

4

6

2

3=

X 2

X 2

2

3

1

6

4

6

1

6

6

16

23

+

1

6

4

6= +

5=

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How do we subtract from ?7

10

2

5

Here is of an apple pie.

Now, lets take away of the pie.

7

10

25

4

10

2

5 =

X 2

X 2

is the same as .4

10

2

5

I take away of the pie.

4

10

10

25

710

-

4

10

7

10= -

3=

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Mixed numbers

I have 3 mooncakes.I have of a mooncake.

1

2

1

23

1

23 + =

1

23

There are 3 mooncakes altogether.1

2

whole number part

fractional part

12

3

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Look at the mooncakes below.

23

1 + = 23

1

whole number part

fractional part

2

31

There are 1 mooncakes altogether.23

2

3

1

Numbers like 3 and 1 are mixed numbers. A mixed number has a

whole number part and a fractional part.

2

3

1

2

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Improper fractions

or5

51

or65

15

1

or7

5

2

5

1

or8

5

3

51

1

5

2

5

3

5

4

5

Look at the fractions below.

There are 6one-fifths in .

1

51

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An improper fraction can be expressed as a whole number or a mixed number.

, , and are improper fractions.6

5

7

5

5

5

8

5

In an improper fraction, the numerator is

greater than or equal to the denominator.

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Changing mixed numbers to improper fractions

Change into an improper fraction.2

33

2

3

3

11

3

Here isanother way.

There are 11 thirds in .

2

33

3

2

33= +

11=

2

33

23= +93

1

32

2

32

1

332

33

11

3

10

3

9

3

8

3

7

3

6

3

2 3

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Changing improper fractions to mixed numbers

Express as a mixed number.9

4

Here isanother way.

There are 9 quarters in .

1

42

1

412

413

411

42

9

4

8

4

7

4

6

4

5

4

4

4

1 2

9

4

1

4

2

1

4= +

=

9

4

1

4= +2

8

4

1

42

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Look at the diagram below.

Try these.

11

31

2

31

1

32

7

3

6

3

5

3

4

3

3

3

2

30

2

1

3

3

3=

4

3= 2

31 =

1

32 =

1

311

5

3

7

3

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We have divided these 9 sweets into 3 equal groups.

Each group is of 9.13

What is of 9?2

3

is 2 groups out of 3 groups.23

of 9 is 6.2

3

1

3of 9

1

3of 9

1

3of 9

Fraction of a set

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Look at the 12 candies below. It has been divided into

4 equal groups. Each group is of 12.1

4

What is of 12?34

is 3 groups out of 4 groups.34

of 12 is 9.3

4

1

4of 12

1

4of 12

1

4of 12

1

4of 12

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Product of a fraction and a whole number

123

4x

36

4

3 x 12

4= =

9=

1. Find the value of x 12.4

3

So, x 12 is the same as of 12.4

3

4

3

Recall

4

3 of 12 is 9.

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2. What is of 5?4

3

53

4x

15

4

3 x 5

4= =

3=3

4

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3. What is 5 x ?4

3

53

4x

15

4

5 x 3

4= =

3=3

4

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Word problems

3

9

1

3 =

X 3

X 3

2. The mass of Box A is kg. The mass of Box B is kg.3

1

9

5

(a) What is the total mass of the 2 boxes?

(b) How much heavier is Box B than Box A?

The total mass of the 2 boxes is kg.9

8

1

3(a) + = +

=

5

9

3

9

5

9

8

9

Box B is kg heavier than Box A.9

2

5

9(b) - = -

=

1

3

5

9

3

9

2

9

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4. Mrs Jones made 50 burgers. 30 of them were fish burgers and the rest werechicken burgers. Express the number of chicken burgers as a fraction of thenumber of burgers made.

2

5

20

50 =

10

10

50 30 = 20

52 of the burgers were chicken burgers.

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1202

3x

2 x 120

3=

80=

7. Mr Samson had 120 teddy bears in his toy store. He sold of them

at \$12 each. How much money did he receive?

2

3

Step 1 Find the number of teddy bears sold.

He sold 80 teddy bears.

Step 2Find how much money he received.

80 x 12 = 960

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8. My brother had 55 stamps in his stamp collection. He gave of

his stamps away. How many stamps did he have left?

1

5

Step 1Find the number of stamps given away.

My brother gave away 11 stamps.

Step 2Find the number of stamps he had left.

55 11 = 44

Hereisoneway.

551

5x

1 x 55

5=

11=

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Step 1Find the fraction of stamps that he had left.

Step 2Find the number of stamps he had left.

Lets tryanother

way.

5He had of his stamps left.

4

11

5

- = -

=

5

5

1

54

5

5545 x 4 x 555=

44=

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We can add or subtract fractions with the same denominators.Example:

3

7+ = ,

4

7

1

7

3

10+ = + ,

=

4

10

3

107

10

2

5

2

8-

3

8

5

8=

1

3- = -

=

8

9

3

95

9

8

9

A mixed number has a whole number part and a fractional part.Example: 2 and 3 are mixed numbers.

1

4

1

2

In an improper fraction, the numerator is greater than or equal tothe denominator.

Example: , and are improper fractions.3

3

7

5

11

10

Wrap-Up!

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1

10

A mixed number can be expressed as an improper fraction. An improperfraction can be expressed as a whole number or a mixed number.

Example: 2 = , = 3, = 13

5

13

5

12

4

11

10

72

5

x2 x 7

5

=

=

When we find the product of a fraction and a whole number, we

multiply the whole number to the numerator. We then write the

product over the denominator.

Example:

14

5

= 24

5

Wrap-Up!