year 8 maths

4B
Computation with fractions
205
■ Dividing fractions
Example:
3
3
4
w
Key ideas
1
4
4 shaded is one-half of
1
4
1
4
1
8
1
8
1
8
1
8
1
8
1
8
3
4 ÷ 1 is the same as ‘how many
4
quarters ( 1 4 ) are in 3
4 ?’
3
4 ÷ 1 4 = 3 4 × 4 1
= 3
3
8
3
4
3
4 ÷ 2 is the same as ‘one-half of 3 4 .’
3
4 ÷ 2 = 3 4 × 1 2
• Denominators do not need to be the same before you can proceed.
• Mixed numerals must be converted to improper fractions before you can proceed.
• To divide by a fraction multiply by its reciprocal.
• The reciprocal of a fraction is found by swapping the numerator and the denominator. This
is known as inverting the fraction.
Proceed as for multiplying fractions.
Example:
3
8 ÷ 5 4 = 3 8 × 4 5 = 12
40 = 3 10
Instead of ÷, × by the reciprocal fraction.
■ Checking your answer
• Final answers should be written in simplest form.
• It is common to write answers involving improper fractions as mixed numerals.
Summary
■ Adding and subtracting fractions
When the denominators are the same, simply add or subtract the numerators. The denominator
remains the same.
■ Multiplying fractions
Cancel where possible, then multiply the numerators together and multiply the denominators
together.
■ Dividing fractions
To divide by a fraction multiply by its reciprocal.
= 3 8
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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