year 8 maths

30 Chapter 1 Algebraic techniques 2 and indices
12 Recall that any value x can be thought of as the fraction x 1 .
a Simplify x × 1 x .
b Simplify x ÷ 1 x .
c
Show that x ÷ 3 is equivalent to 1 × x by writing them both as algebraic fractions.
3
d Simplify
a
b ÷ c .
e Simplify a ÷ b c .
13 a Simplify each of the following expressions.
x
i
5 + x x
ii
6
5 − x x
iii
6
5 × x x
iv
6
5 ÷ x 6
b Which one of the expressions above will always have the same value regardless of x ?
14 Assume that a and b are any two whole numbers.
a Prove that 1 ÷ a b is the same as the reciprocal of the fraction a b .
b Find the reciprocal of the reciprocal of a b by evaluating 1 ÷ ( 1 ÷ a b) .
ENRICHMENT
– –
15
Irrational squares
15 Consider a square with side length x .
x
a Write an expression for the area of the square.
b The length of each side is now halved. Give an expression for the area of the new square.
c If each side of the original square is multiplied by 3 , show that the resulting area is less than
5
half the original area.
d If each side of the original square is multiplied by 0.7 , find an expression for the area of the
square. Recall that 0.7 = 7 10 .
e
Each side of the square is multiplied by some amount, which results in the square’s area being
halved. Try to find the amount by which they were multiplied, correct to three decimal places.
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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