Fractions

1

Fractions

1 3

2

3 4

1 5

Equivalent Fractions look different but hold the same value 1Â whole

1 2

1 2

1 5 1 6

1 10 1 12

1 4

1 4

1 4

1 8

1 3

1 3

1 3

1 5

1 5

1 6

1 6

1 8

1 8

1 8 1 1 1 1 10 10 10 10 1 1 1 1 1 12 12 12 12 12

1 4

1 5

1 5

1 1 1 6 6 6 1 1 1 1 8 8 8 8 1 1 1 1 1 10 10 10 10 10 1 1 1 1 1 1 12 12 12 12 12 12

1

1 3

2

Fractions

1 5

3 4

Equivalent Fractions look different but hold the same value

A

B

1 2

4 8

What is the fraction shaded red in each case?

1

2

1 3

Fractions

1 5

3 4

Equivalent Fractions look different but hold the same value

A What fraction of rectangle A is shaded?

2 3

B What fraction of rectangle B is shaded?

6 9

1

1 3

2

Fractions

1 5

3 4

Equivalent Fractions look different but hold the same value

A

3 6

B

2 8

Do rectangles A and B show equivalent fractions?

1

2

1 3

Fractions

1 5

3 4

Equivalent Fractions look different but hold the same value

How can I find an equivalent fraction to the one below?

1 3 1 3 1 3

x2

= x2

x3

= x3

x4

= x4

2 6

3 9

4 12

Whatever you do to the top you must do to the bottom and vice versa!

1

2

1 3

Fractions

1 5

3 4

Equivalent Fractions look different but hold the same value

Try these.

2 3 3 5

x4

= x4

x7

= x7

8 12

6 10

÷2

21

32 40

÷8

35

= ÷2

= ÷8

3 5 4 5

12

÷4

16

÷4

=

48

÷16

64

÷16

=

3 4 3 4

1

1 3

2

Fractions

1 5

3 4

Which fraction is bigger?

1 4

1 7

This seems obvious with a picture but how do we do it without a picture?

1

2

1 3

Fractions

1 5

3 4

Which fraction is bigger?

4 7

or

3 5

Numerator Denominator

The denominator tells us how many pieces the whole has been split into

If I can find a common denominator I can compare the fractions

3 4

is bigger than

2 4

Common Denominators

1

2

1 3

Fractions

1 5

3 4

Finding a common denominator

4 7

and

3 5

4 = 20 7 35

Easiest way is to multiply denominators

21 3 = 5 35

1

2

1 3

Fractions

1 5

3 4

Finding a common denominator

2 3

and

3 5

2 = 10 3 15

Easiest way is to multiply denominators

9 3 = 5 15

1

2

1 3

Fractions

1 5

3 4

Adding and Subtracting They must have a common denominator

1+ 3 = 4 7 7 7

4- 3 1 = 5 5 5

=

+ -

=

1

2

1 3

Fractions

1 5

3 4

Adding and Subtracting

+

What if they have different denominators

A common mistake is shown below

1+ 1 = 2 2 3 5

+

=

This doesn't make any sense!!

1

1 3

2

Fractions

1 5

3 4

Adding and Subtracting They must have a common denominator

1+ 1

2

3

+

=

= 6+ 6

Find common denominator by multiplying 2 by 3

= 3+ 2 6 6

Find equivalent fractions with denominator of 6

5 = 6

1

2

Fractions

1 3

1 5

3 4

Adding and Subtracting

= =

2+ 1 3 5 10 + 3

15

13

15

15

3- 2 4 3

= =

9- 8 12 12 1 12

1

2

1 3

Fractions

1 5

3 4

Adding and Subtracting

2+ 3 = 4+ 6 = 7 6 1 =1 6

1 2 3 6

Sometimes you end up with a bigger number on the top.

We can write this another way.

=

1

2

Fractions

1 3

1 5

3 4

Adding and Subtracting

3

1 + 3

2

1 + 6 +

=

5

=

+

1

1 3

2

5 6 =

2 3 Its sometimes easier to visualise fractions with pictures

=

4

1

2

Fractions

1 3

1 5

Adding and Subtracting

3

4 + 5

2

3 5

+

3

3 5 -

-

=

5

7 5 =

=

2

1 5

=

= =

6

1

2 5

2 5

3 4

1

2

1 3

Fractions

1 5

Multiplying Fractions

1 1 What is 2 of 4 ?

3 4

1

2

1 3

Fractions

1 5

3 4

Multiplying Fractions

1 1 What is 2 of 4 ?

1 What is 2 x

1 4 ?

Is there a difference between these questions?

From our work with areas of triangles

9m

Area =

1 2

x b x h

Area =

1 2

x 12 x 9

Area = 6 x 9

12m

Area = 54m2

Therefore 1 of 12 means 2

1 x 12 and vice versa 2

1

2

1 3

Fractions

1 5

3 4

Multiplying Fractions

We can see visually

1 1 1 2 of 4 = 8

or

One eighth

1 1 1 2 x 4 = 8 But can we do this without drawing a picture?

Rule

Multiply the numerators Multiply the denominators

1

2

1 3

Fractions

1 5

3 4

Multiplying Fractions

1 1 1 3 x 5 = 15 One Fifth

Solution 6 2 3 4 x 3 = 12 One Third

Solution

1

2

1 3

Fractions

3 4

1 5

Dividing Fractions

If we look firstly at

6รท 2

We interpret this as how many 2's are in 6 If we now look at

1 1 2 รท 4 =

2

1

2

1 3

Fractions

1 5

3 4

Dividing Fractions

Imagining the diagrams can become complex though

2 3 รท 8 5 =

?

We need a better way!

Often mathematical rules are about spotting patterns

1 10 รท 2 = 20

2 10 x 1 = 20

1 9 รท 3 = 27

3 9 x 1 = 27

1 3 รท 4 = 12

4 3 x 1 = 12

Dividing is the same as multiplying by the inverse

1

2

1 3

Fractions

1 5

3 4

Dividing Fractions

Can we now solve this calculation without a diagram?

2 3 8 รท 5 =

2 3 8 รท 5 5 3 = 8 x 2 = 15 16

1 4 7 รท 3 3 4 = 7 x 1 = 12 = 1 75 7

?

5 3 รท 4 6 6 3 = 4 x 5 = 18 = 9 10 20

1

2

1 3

Fractions

1 5

3 4

Fractions of time

1 hour

=

60 mins

1 hour 4

=

15 mins

1 hour 2

=

30 mins

3 hour 4

=

45 mins

What fraction of an hour would 12 mins be?

1

2

1 3

Fractions

1 5

3 4

Fractions of time Changing minutes into a fraction of an hour

30mins =

12mins =

36mins =

30 60

÷ 10

=

÷ 10

12 60

÷6

36 60

÷6

=

÷6

=

÷6

3 6

÷3

=3 ÷

2 10

÷2

6 10

÷2

= ÷2

= ÷2

1 2 1 5

3 5

Always simplify as much as you are able to

1

2

1 3

Fractions

1 5

3 4

Fractions of time Changing fractions of an hour into minutes

1 hr = 60mins รท 5 = 12mins 5

1 hr = 60mins รท 3 = 20mins 3

5 hr = 60mins รท 12 x 5 = 25mins 12