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7.4 Dividing fractions

7.4 Dividing fractions

In Stage 8 you learned how to divide an integer by a fraction and also a fraction by a fraction.
In both cases you start by turning the fraction you are dividing by upside down, and then multiplying
instead.
!is is called invert and multiply. Remember to cancel common factors before you multiply, and write
each answer in its simplest form and as a mixed number when appropriate.

Worked example 7.4
5
4
6
2
Work out: a 18 ÷ b 26 ÷ 3 c 5 ÷ d 1 7 ÷ 21 e 4 ÷ 25
3
9
5
4
7
a 18 ÷ 2 = 18 × 3 Start by turning the fraction upside down and multiplying.
3
2
9 18 × 3 = 9 × 3 2 divides into 2 and 18, so the 2 cancels to 1 and the 18 cancels to 9.
2 1 1
= 9 × 3 = 27 3 is the same as 3, so just work out 9 × 3.
1
3 4
b 26 ÷ 4 = 26 × 3 Start by turning the fraction upside down and multiplying.
= 26 3 × 4 = 104 There are no common factors to cancel, so multiply 26 by 4.
3
2
= 34 Change 104 to a mixed number.
3
3
5 4 5 9 4
c 7 ÷ 9 = 7 × 4 Start by turning upside down and multiplying.
9
45
= 5 × 9 = 28 There are no common factors to cancel, so multiply 5 by 9 and 7 by 4.
× 4
7
17 45
= 1 Change to a mixed number.
28 28
d 1 ÷ 5 = 1 × 21 Start by turning 5 upside down and multiplying.
7 21 7 5 21
1 × 21 3 = 1 × 3 7 divides into 7 and 21, so the 7 cancels to 1 and the 21 cancels to 3.
5
1
5
1 7
= 1 1 × 3 = 3 Multiply 1 by 3 and 1 by 5. The answer is a proper fraction, so leave it as it is.
× 5
5
6
6
e 4 ÷ 25 = 4 × 25 Start by turning 25 upside down and multiplying.
5
5
6
2 4 25 5
×
5 × = 2 5 2 divides into 4 and 6 to give 2 and 3. 5 divides into 5 and 25 to give 1 and 5.
3
1
1 6 3
× 5
= 2 × 3 = 10 Multiply 2 by 5 and 1 by 3.
3
1
1
= 3 Change 10 to a mixed number.
3
3
) Exercise 7.4
1 Work out these divisions.
Write each answer in its simplest form and as a mixed number when appropriate.
4
2
2
3
a 16÷ b 21÷ c 14÷ d 8÷ 4 e 22÷ f 25÷ 5
7 5 9 11 3 8
4
4
6
g 18÷ h 26÷ i 6÷ j 25÷ 10 k 32÷ 6 l 42÷ 4
5 7 9 11 13 7
70 7 Fractions