If the ratio of one length to another is 1 : 2, this means that the second length is twice as large as the first. If a boy has 5 sweets and a girl has 3, the ratio of the boy’s sweets to the girl’s sweets is 5 : 3 . The boy has 5/3 times more sweets as the girl, and the girl has 3/5 as many sweets as the boy. Ratios behave like fractions and can be simplified.

*Example*:

Simone made a scale model of a ‘hot rod’ car on a scale of 1 to 12.5 . The height of the model car is 10cm.

(a) Work out the height of the real car.

The ratio of the lengths is 1 : 12.5 . So for every 1 unit of length the small car is, the real car is 12.5 units. So if the small car is 10 units long, the real car is 125 units long. If the small car is 10cm high, the real car is __125cm__ high.

(b) The length of the real car is 500cm. Work out the length of the model car.

We know that model : real = 1 : 12.5 . However, the real car is 500cm, so 1 : 12.5 = x : 500 (the ratios have to remain the same). x is the length of the model car. To work out the answer, we convert the ratios into fractions:

__ 1 __ = __ x __

12.5 500

multiply both sides by 500:

500/12.5 = x

so x = __40cm__

*Example*:

Alix and Chloe divide £40 in the ratio 3 : 5. How much do they each get?

First, add up the two numbers in the ratio to get 8. Next divide the total amount by 8, i.e. divide £40 by 8 to get £5. £5 is the amount of each ‘unit’ in the ratio. To find out how much Alix gets, multiply £5 by 3 (‘units’) = £15. To find out how much Chloe gets, multiply £5 by 5 = £25.

**Map Scales**

If a map has a scale of 1 : 50 000, this means that 1 unit on the map is actually 50 000 units across the land. So 1cm on the map is 50 000cm along the ground (= 0.5km). So 1cm on the map is equivalent to half a kilometre in real life.

For 1 : 25 000, 1 unit on the map is the same as 25 000 units on the land. So 1 inch on the map is 25 000 inches across the land, or 1cm on the map is 25 000 cm in real life. You can manipulate these ratios if necessary.