year 8 maths

26 Chapter 1 Algebraic techniques 2 and indices
1 F Multiplying and dividing algebraic fractions EXTENSION
As with fractions, it is generally easier to multiply and divide algebraic fractions than it is to add or
subtract them.
3
5 × 2 7 = 6 35
Fractions
3 × 2
5 × 7
4x
7 × 2y
11 = 8xy
77
Algebraic fractions
Dividing is done by multiplying by the reciprocal of the second fraction.
4
5 ÷ 1 3 = 4 5 × 3 1
= 12 5
Fractions
2x
5 ÷ 3y
7 = 2x
5 × 7 3y
= 14x
15y
Algebraic fractions
Let’s start: Always the same
One of these four expressions always gives the same answer, no matter what the value of x is.
x
2 + x x
3
2 − x x
3
2 × x x
3
2 ÷ x 3
• Which of the four expressions always has the same value?
• Can you explain why this is the case?
• Try to find an expression involving two algebraic fractions that is equivalent to 3 8 .
Key ideas
■ To multiply two algebraic fractions, multiply the numerators and the denominators
separately. Then cancel any common factors in the numerator and the denominator.
For example:
2x
5 × 10y
3 = 4
20xy
15 3
= 4xy
3
■ The reciprocal of an algebraic fraction is formed by swapping the numerator and denominator.
For example, the reciprocal of
3b
4 is 4
3b .
■ To divide one fraction by another, multiply the first fraction by the reciprocal of the second
fraction. For example:
2a
5 ÷ 3b 4 = 2a 5 × 4 3b
= 8a
15b
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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