year 8 maths

24 Chapter 1 Algebraic techniques 2 and indices
Exercise 1E
EXTENSION
UNDERSTANDING AND FLUENCY
1–6, 7–8(½) 3–6, 7–9(½)
6, 7–9(½)
1 Complete these sentences.
2
a For the fraction the numerator is 2 and the denominator is _____.
7
4
b For the numerator is _____ and the denominator is _____.
9
c
The expression
12x
5
d The denominator of
is an example of an __________ fraction.
5x + 3
7
is _____.
2 Find the lowest common denominator (LCD) of the following pairs of fractions.
1
a
3 and 2
1
b
5
4 and 1
3
c
5
7 and 5
d
6
2
3 and 1
6
3 Find the missing numerator to make the following equations true.
a
2
3 = □ 6
b
4
7 = □ 21
c
1
3 = □ 12
d
6
11 = □ 55
4 Evaluate the following, by first converting to the lowest common denominator.
a
1
4 + 1 3
b
2
7 + 1 5
c
1
10 + 1 5
d
2
5 − 1 4
Example 8a
5 Find the LCD of the following pairs of algebraic fractions.
x
a
3 and 2y
3x
b
5
10 and 21y
x
c
20
4 and y
5
d
x
12 and y
6
Example 8b
6 Copy and complete the following, to make each equation true.
a
x
5 = □ 10
b
2a
7 = □ 21
c
4z
5 = □ 20
d
3k
10 = □ 50
Example 9a,b
7 Simplify the following sums.
x
a
4 + 2x
5a
b
4
3 + 2a 3
a
e
2 + a a
f
3
4 + a 5
i
2k
5 + 3k
7
j
2m
5 + 2m 3
c
g
k
2b
5 + b 5
p
2 + p 5
7p
6 + 2p 5
d
h
l
4k
3 + k 3
q
4 + q 2
x
4 + 3x
8
Example 9c
8 Simplify the following differences.
3y
a
5 − y 7p
b
5
13 − 2p
13
p
e
2 − p 2t
f
3
5 − t 3
i
r
3 − r 2
j
6u
7 − 7u 6
c
g
k
10r
7 − 2r
7
9u
11 − u 2
9u
1 − 3u 4
d
h
l
8q
5 − 2q 5
8y
3 − 5y
6
5p
12 − 7p
11
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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