A ratio describes the relationship between parts of an amount.

A sum of money - £100 - is split into two sums of £30 and £70, then the sum has been split into a ratio of 30:70. Note that in describing the ratio, there is a colon : between the two amounts, and that the order of the numbers is important.

Ratios can be simplified. The ratio 30:70 is simplified by dividing both sides by 10; a ratio of 30:70 is the same as a ratio of 3:7. Ratios are fully simplified when both numbers are integers, and have been reduced in value as much as possible.


1. A bag contains 40 red and blue balls. there are 10 red balls. What is the ratio of red to blue balls?

Answer: 1:3

The number of blue balls is 40 - 10 = 30. Therefore there are 10 red balls and 30 blue balls, or 10:30. This simplifies to 1:3. Note that the order of numbers is important.

2. An amount of money is split into £50 and £200. Write this as a ratio in its simplest form.

Answer: 1:4

The ratio is written as 50:200. Divide both sides by 10 for 5:20, then divide both sides by 5 for 1:4.