Fractions Re-cap2

Mathematics

Which is bigger or ?38

512

To compare two fractions convert them to fractions with the same denominator.

First we need to find the lowest common multiple of 8 and 12.

The lowest common multiple of 8 and 12 is 24.

Now, write and as equivalent fractions over 24. 38

512

38

=24

×3

×3

9and

512

=24

×2

×2

10so,

38

512

<

Using equivalent fractions

Ordering fractions

Multiplying a fraction by a fraction

To multiply two fractions together, multiply the numerators together and multiply the denominators together:

38

What is × ?25

38

45

× =1240

3

10

=310

We could also cancel at

this step.

56

What is × ?12255

Start by writing the calculation with any mixed numbers as improper fractions.

To make the calculation easier, cancel any numerators with any denominators.

1225

356

× =

7

5

2

1

145

= 2 45

Multiplying a fraction by a fraction

Using cancellation to simplify calculations

712

What is 16 × ?

We can write 16 × as:712

161

×712

4

3=

283

=139

45

What is ÷ ?23

To divide by a fraction we flip the second fraction and multiply.

45

23

÷ can be written as54

23

×

Swap the numerator and the denominator and multiply.

54

23

× =1012

=56

Dividing a fraction by a fraction

This is the reciprocal of .45

67

What is ÷ ?353

Start by writing as an improper fraction. 353

185

353 =

185

÷67

=185

×76

3

1

=215

=154

Dividing a fraction by a fraction

Dividing fractions

When fractions have the same denominator it is quite easy to add them together and to subtract them.

For example,

3

5+

1

5=

3 + 1

5=

4

5

We can show this calculation in a diagram:

+ =

Adding and subtracting fractions

7

8–

3

8=

7 – 3

8=

4

8

Fractions should always be cancelled down to their lowest terms.

1

2 =1

2

We can show this calculation in a diagram:

– =

Adding and subtracting fractions

Fractions with different denominatorsFractions with different denominators are more difficult to add and subtract.

For example,

What is 56

–29

?

–

1518

–418

=

=15 – 4

18=

1118

Using a common denominator

1) Write any mixed numbers as improper fractions.

1 34

= 74

2) Find the lowest common multiple of 4, 9 and 12.

The multiples of 12 are: 12, 24, 36 . . .

36 is the lowest common denominator.

What is +19

?134

+512

3) Write each fraction over the lowest common denominator.

74

=36

×9

×9

63 19

=36

×4

×4

4 512

=36

×3

×3

15

4) Add the fractions together.

3663

+364

+3615

=36

63 + 4 + 15=

3682

= 2 3610

= 2 185

What is +19

?134

+512

Using a common denominator