Page 143 - MAT KS3 Y8 Cambridge CheckPoint

14.1 Simplifying ratios

14.1 Simplifying ratios

A ratio is a way of comparing two or more quantities.
Pastry recipe
In this pastry recipe, the ratio of flour to butter is 500 : 250.
500 g flour
You can simplify this ratio by dividing the numbers by the highest
250 g butter
common factor. In this case the highest common factor is 250.
500 : 250 water to mix
Divide both numbers by 250 to simplify the ratio to 2 : 1. ÷ 250 ÷ 250
2 : 1
If you cannot work out the highest common factor of the numbers in a ratio, you can simplify the ratio
in stages. Divide the numbers in the ratio by common factors until you cannot divide any more.
In the example above you could start by:
r dividing by 10 500 : 250
÷ 10 ÷ 10 When you simplify a ratio you
r then by 5 50 : 25
r then by 5 again ÷ 5 ÷ 5 must make sure that all the
10 : 5
r giving you the same answer of 2 : 1. quantities are in the same units.
÷ 5 ÷ 5
2 : 1

Worked example 14.1
Simplify these ratios.
a 12 : 20 b 12 : 30 : 24 c 2 m : 50 cm

a 12 : 20 The highest common factor of 12 and 20 is 4,
÷ 4 ÷ 4 so divide both numbers by 4.
3 : 5

b 12 : 30 : 24 The highest common factor of 12, 30 and 24 is 6,

÷ 6 ÷ 6 ÷ 6 so divide all three numbers by 6.
2 : 5 : 4
c 2 m : 50 cm First, change 2 metres into 200 centimetres.
200 : 50 Once the units are the same you don’t need to write them down.

÷ 50 ÷ 50 The highest common factor of 200 and 50 is 50,
4 : 1 so divide both numbers by 50.

✦ Exercise 14.1

1 Simplify these ratios.
a 2 : 10 b 3 : 18 c 5 : 25 d 30 : 5 e 36 : 12 f 180 : 20
g 4 : 6 h 9 : 15 i 10 : 35 j 75 : 10 k 72 : 20 l 140 : 112

2 Simplify these ratios.
a 5 : 10 : 15 b 8 : 10 : 12 c 20 : 15 : 25
d 18 : 15 : 3 e 27 : 9 : 45 f 72 : 16 : 32

3 Simplify these ratios.
a 500 m : 1 km b 36 seconds : 1 minute c 800 ml : 2.4 l
d 1.6 kg : 800 g e 3 cm : 6 mm f 2 days : 18 hours
g 2 hours : 48 minutes h 8 months : 1 year i 4 days : 1 week

14 Ratio and proportion 141