Deriving Ratios

Deriving Ratios


A ratio shows the relationships between amounts that make up a total quantity.

400 people work at a communications company. 300 are technical, and 100 are office staff. The ratio of technical staff to office staff is written as 300:100. The ratio is simplified by dividing both sides by 100, such that 300:100 becomes 3:1 - for each 3 technicians, there is 1 office staff.

A ratio is written in the form part : part - both numbers in the ratio are part of the whole.

Ratios may consist of more than 2 numbers. £120 is split into a sum of £24, a sum of £36 and a sum of £60. This ratio is written as 24:36:60, and simplified to 2:3:5.


1. A packet of sweets contains two flavours: there are strawberry sweets and banana sweets. If there are 64 sweets in the packet, and 40 of the sweets are banana flavour, what is the ratio of strawberry to banana sweets?

Answer: 3:5

Number of strawberry sweet = 64 - 40 = 24

The ratio is 24:40.

This simplifies to 3:5 (divide both parts by 8).

Note that the numbers have to be in that order.

2. A mix of concrete weights 48kg. It is known that 12kg is cement and that the rest was sand. What is the cement - sand ratio?

Answer: 1:3

The amount of sand was 48 - 12 = 36kg.

The mix was therefore 12:36, which simplifies to 1:3.