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FRACTION


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Without renaming

Adding and subtracting fractions

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

He received $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

He had 44 stamps left.

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.

He had 44 stamps 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!