year 8 maths

4B
Computation with fractions
207
Example 5
Multiplying fractions
Evaluate:
2
a
5 × 3 7
b
8
5 × 7 4
c 3 1 3 × 2 2 5
SOLUTION
2
a
5 × 3 7 = 2 × 3
5 × 7
= 6 35
EXPLANATION
Multiply the numerators together.
Multiply the denominators together.
The answer is in simplest form.
b
2
8
5 × 7
4 = 2 × 7
5 × 1
1
= 14 5 = 2 4 5
Cancel first. Then multiply numerators together and
denominators together.
Write the answer as an improper fraction.
c 3 1 3 × 2 2 5 = 2 10
3 × 4 12
5
Convert to improper fractions first.
1 1 Simplify fractions by cancelling.
= 2 × 4
Multiply ‘cancelled’ numerators and ‘cancelled’
1 × 1
denominators together.
= 8 1 = 8 Write the answer in simplest form.
Example 6
Dividing fractions
Evaluate:
2
a
5 ÷ 3 7
b
5
8 ÷ 15
16
c 2 1 4 ÷ 1 1 3
SOLUTION
2
a
5 ÷ 3 7 = 2 5 × 7 3
= 14
15
5
b
8 ÷ 15
16 = 1 5
8 × 16 2
15
1 3
EXPLANATION
Change ÷sign to a × sign and invert the divisor (the second fraction).
Proceed as for multiplication.
Multiply numerators together and multiply denominators together.
Change ÷sign to a × sign and invert the divisor (the second fraction).
Proceed as for multiplication.
= 1 1 × 2 3
= 2 3
c 2 1 4 ÷ 1 1 3 = 9 4 ÷ 4 3
= 9 4 × 3 4
= 27
16 = 1 11
16
Convert mixed numerals to improper fractions.
Change ÷ sign to × sign and invert the divisor (the second
fraction).
Proceed as for multiplication .
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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