year 8 maths

5D
Scale drawings
293
Example 9
Converting scale distance to actual distance
A map has a scale of 1 : 20 000 .
Find the actual distance for each scaled distance.
a 2 cm b 5 mm c 14.3 cm
SOLUTION
a Actual distance = 2 cm × 20000
= 40000 cm
= 400 m (or 0.4 km)
b Actual distance = 5 mm × 20000
= 100000 mm
= 100 m
c Actual distance = 14.3 cm × 20000
= 286000 cm
= 2.86 km
EXPLANATION
Scale factor = 20000
Multiply scaled distance by scale factor.
Convert answer into sensible units.
Multiply scaled distance by scale factor.
Convert answer into sensible units.
Multiply scaled distance by scale factor.
Shortcut: × 2 , then × 10 000 .
Convert answer into sensible units.
Example 10
Converting actual distance to scaled distance
A model boat has a scale of 1 : 500 .
Find the scaled length for each of these actual lengths.
a 50 m b 75 cm c 4550 mm
SOLUTION
a Scaled distance = 50 m ÷ 500
= 5000 cm ÷ 500
= 10 cm (0.1 m)
b Scaled distance = 75 cm ÷ 500
= 750 mm ÷ 500
= 1.5 mm
c Scaled distance = 4550 mm ÷ 500
= 45.5 mm ÷ 5
= 9.1 mm
EXPLANATION
Scale factor = 500
Convert metres to centimetres.
Divide actual distance by scale factor.
Convert answer into sensible units.
Convert centimetres to millimetres.
Divide actual distance by scale factor.
Divide actual distance by scale factor.
Shortcut: ÷ 100 , then ÷ 5 (or vice versa) .
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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