Cambridge International Mathematics

16 Assumed Knowledge (Number)

EQUAL RATIOS

Ratios areequalif they can be expressed in the same simplest form.

For example, 6:4and 9:6are equal as they are both expressed in simplest form as 3:2.

Aproportionis a statement that two ratios are equal.

For example, 6:4=9:6is a proportion.

Sometimes we need to find one quantity given the ratio and the other quantity. To do this we use equal

ratios.

Example 22 Self Tutor

Findxif: a 3:5=6:x b 15 : 20 =x:16

a 3:5=6:x

) x=5£ 2

) x=10

b 15 : 20 = 15¥ 5 :20¥ 5

=3:4

) 3:4=x:16

) x=3£4=12

Example 23 Self Tutor

The ratio of walkers to guides on the Milford Track walk was9:2. How many

guides were needed if there were 27 walkers?

Let the number of guides bex. walkers:guides=27:x

) 9 : 2 = 27 :x

) x=2£ 3

) x=6

) 6 guides were needed.

1 Findxif:

a 2:3=8:x b 1:4=x:12 c 3 : 2 = 15 :x

d 4:3=x:21 e 5:7=25:x f 6 : 11 =x:77

g 5:12=40:x h 7 : 10 =x:80 i 4:5=x:45

2 Findxif:

a 4 : 5 = 12 :x b 3:9=x:18 c 2 : 3 = 10 :x

d 5 : 10 =x:18 e 16 : 4 = 12 :x f 21 : 28 = 12 :x

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