# GCSE Maths – Ratios A ratio is a way of comparing the sizes of two (or more) quantities. Colons are used when expressing ratios, so that the values of A and B being in the ratio 2 to 5 would be written as A : B = 2 : 5.

NB: In some older text books, :: is used here, i.e. A : B :: 2 : 5.

If you multiply/divide one side of a ratio then you must multiply/divide the other side of the ratio by the same amount.

To divide a total in a given ratio you must first add the separate parts of the ratio to get the total amount, which is divided into each part of the ratio to get a fraction of the total amount.

Example

Express the ratio 9:21 in its simplest form, and divide a total length of 50m in this ratio.

9 and 21 both have a common factor of 3, so 9 : 21 = 9/3 : 21/3 = 3 : 7

3 + 7 = 10, so the total 50m is split into two pieces of 3/10 x 50m = 15m and 7/10 x 50m = 35m

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