year 8 maths

1F
Multiplying and dividing algebraic fractions
27
Example 10
Multiplying algebraic fractions
Simplify the following products.
2a
a
5 × 3b 7
b
4x
15 × 3y
2
SOLUTION
2a
a
5 × 3b 7 = 6ab
35
b Method 1:
4x
15 × 3y
2 = 12xy
30
= 2xy
5
Method 2:
2
4x 1
5
15 × 3y
2 = 2xy
1 5
EXPLANATION
2a × 3b = 6ab and 5 × 7 = 35 .
4x × 3y = 12xy
15 × 2 = 30
Divide by a common factor of 6 to simplify.
First divide by any common factors in the
numerators and denominators: 4x and 2 have
a common factor of 2 . Also 3y and 15 have a
common factor of 3 .
Example 11
Dividing algebraic fractions
Simplify the following divisions.
3a
a
8 ÷ b 5
b
u
4 ÷ 15p
2
SOLUTION
3a
a
8 ÷ b 5 = 3a 8 × 5 b
= 15a
8b
u
b
4 ÷ 15p
2 = u 4 × 2
15p
= 2u
60p
= u
30p
EXPLANATION
Take the reciprocal of b 5 , which is 5
b .
Multiply as before: 3a × 5 = 15a, 8 × b = 8b .
Take the reciprocal of 15p
2 , which is 2
15p .
Multiply as before: u × 2 = 2u and
4 × 15p = 60p .
Cancel the common factor of 2 .
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.