year 8 maths

1E
Adding and subtracting algebraic fractions
25
Example 9d
9 Simplify the following expressions, giving your final answer as an algebraic fraction.
4x
(Hint: 4x is the same as
1 .)
a 4x + x b 3x + x a
c
3
2
5 + 2a
8p
d
3 − 2p e 10u
3 + 3v
7y
f
10
10 − 2x
5
g 2t + 7p x
h
2
3 − y i 5 − 2x
7
PROBLEM-SOLVING AND REASONING
10, 13a,b 10, 11, 13
11–14
10 Cedric earns an unknown amount $x every week. He spends 1 3 of his income on rent and 1 4 on
groceries.
a Write an algebraic fraction for the amount of money he spends on rent.
b Write an algebraic fraction for the amount of money he spends on groceries.
c Write a simplified algebraic fraction for the total amount of money he spends on rent and
groceries.
11 Egan fills the bathtub so it is a quarter full and then adds half a bucket of water. A full bathtub can
contain T litres and a bucket contains B litres.
a Write the total amount of water in the bathtub as the sum of two algebraic fractions.
b Simplify the expression in part a to get a single algebraic fraction.
c If a full bathtub contains 1000 litres and the bucket contains 2 litres, how many litres of water
are in the bathtub?
12 Afshin’s bank account is halved in value and then $20 is removed. If it initially had $A in it, write
an algebraic fraction for the amount left.
x
13 a Demonstrate that
2 + x 3
b Demonstrate that
c
Is
is equivalent to
5x
6
x
4 + x 2x
is not equivalent to
5 9 .
x
2 + x 5 equivalent to x − x ? Explain why or why not.
3
by substituting at least three different values for x .
14 a Simplify:
x
i
2 − x x
ii
3
3 − x 4
b What patterns did you notice in the results above?
c
iii
x
4 − x 5
Write a difference of two algebraic fractions that simplifies to
x
110 .
iv
x
5 − x 6
ENRICHMENT
– –
15
Equivalent sums and differences
15 For each of the following expressions, find a single equivalent algebraic fraction.
z
a
4 + z 3 + z
2x
b
12
5 + x 2 − x 7u
c
5
2 + 3u 4 − 5u d
8
p
e
4 + p 2 − 3 f u
3 + u 4 + u g
5
8k
3 + k 6 − 5k
12
5j
12 − j 3 + 2 h 7t
5 − t 3 + 2r
15
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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