Page 82 - MAT KS3 Y8 Cambridge CheckPoint

7.8 Multiplying and dividing fractions

7.8 Multiplying and dividing fractions

When you need to multiply and divide simple fractions mentally, follow these rules.
When you multiply fractions, multiply the numerators together and multiply the denominators
together.
×
Example: 1 × 5 = 15 = 5
×
3 7 37 21
When you divide fractions, start by turning the second fraction upside down, then multiply the
fractions as usual.
×
Example: 2 ÷ 5 = 2 × 11 = 2 11 = 22 = 1 7
×
3 11 3 5 3 5 15 15
This is quite a lot of work to do mentally. It is simpler to think of it as multiplying the diagonal pairs of
numbers together like this.

×
2 ÷ 5 = 2 11 = 22
×
3 11 3 5 15
The answer, 22 , is an improper fraction, so change it to a mixed number. 22 = 1 7
15 15 15
Whether you are multiplying or dividing, once you have worked out the answer, cancel it to its simplest
form when possible. If the answer is an improper fraction, turn it into a mixed number.

Worked example 7.8
5 2 3 5
Work these out. a × b ÷
6 3 4 12
×
52 10
a = Multiply the numerators together and multiply the denominators together.
×
63 18
10 5
= 10 and 18 can both be divided by 2, so cancel the answer to its simplest form.
18 9
×
312 36
b = Multiply the diagonal pairs of numbers.
×
45 20
36 16
= 1 The answer is an improper fraction, so changed to a mixed number.
20 20
4
1 16 = 1 16 and 20 can both be divided by 4, so cancel the answer to its simplest form.
20 5
✦ Exercise 7.8
1 Work these out mentally.
3
1
2
1
1
a 1 × b 3 × c 2 × d 4 × e 3 × f 7 × 2
4 2 4 4 3 5 5 5 7 4 9 3
2 Work out mentally.
Cancel each answer to its simplest form.
2
8
5
3
3
a 3 × b 2 × c 4 × d 1 × e 3 × f 6 × 1
4 5 3 4 5 8 6 9 10 6 11 3

80 7 Fractions