year 8 maths

282 Chapter 5 Ratios and rates
Example 5
Changing quantities to the same units
First change the quantities to the same unit, and then express each pair of quantities as a ratio in
simplest form.
a 4 mm to 2 cm b 25 minutes to 2 hours
SOLUTION
a 4 mm to 2 cm = 4 mm to 20 mm
= 4 : 20
= 1 : 5
b 25 minutes to 2 hours
= 25 minutes to 120 minutes
= 25 : 120
= 5 : 24
EXPLANATION
2 cm = 20 mm
Once in same unit, write as a ratio.
Simplify ratio by dividing by HCF of 4 .
2 hours = 120 minutes
Once in same unit, write as a ratio.
Simplify ratio by dividing by HCF of 5 .
Exercise 5B
UNDERSTANDING AND FLUENCY
1–4, 5–7(½), 9(½) 3, 4, 5–9(½)
5–9(½)
1 Write down the ratio of shaded parts to unshaded parts for each of the following, in simplest form.
a
b
Example 3
Example 4a
2 To express the ratio 4 : 16 in simplest form, you would:
A multiply both quantities by 2
B subtract 4 from both quantities
C divide both quantities by 2 D divide both quantities by 4
3 Decide which of the following ratios is not written in simplest form.
A 1 : 5 B 3 : 9 C 2 : 5 D 11 : 17
4 Decide which of the following ratios is written in simplest form.
A 2 : 28 B 15 : 75 C 14 : 45 D 13 : 39
5 Simplify the following ratios.
a 2 : 8 b 10 : 50 c 4 : 24 d 6 : 18
e 8 : 10 f 25 : 40 g 21 : 28 h 24 : 80
i 18 : 14 j 26 : 13 k 45 : 35 l 81 : 27
m 51 : 17 n 20 : 180 o 300 : 550 p 150 : 75
q 1200 : 100 r 70 : 420 s 200 : 125 t 90 : 75
6 Simplify the following ratios.
a 2 : 4 : 6 b 12 : 21 : 33 c 42 : 60 : 12 d 85 : 35 : 15
e 12 : 24 : 36 f 100 : 300 : 250 g 270 : 420 : 60 h 24 : 48 : 84
7 Simplify the following ratios.
1
1
2
2
a
b
c
d
e
3 : 1
2
3
8 : 1
4
f
4 : 1
5
7
10 : 4
5
g
5 : 3
4
11
10 : 2
15
h
7 : 1
5
9
8 : 7
12
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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