A ratio compares how much there is of a specific thing in comparison to another. Ratios are two or more numbers separated with a colon ‘:’ e.g. 3:5:7.

For example, if someone has two red sweets and 4 red sweets, then the ratio of red sweets to blue sweets is 2:4.


If I have a mixture consisting of cement, sand and gravel and it is split as follows: 3 ‘pieces’ of cement, 5 ‘pieces’ of sand and 7 ‘pieces’ of gravel. To put this as a ratio, as it is split across 15 pieces, the ratio is as above 3:5:7.

Ratios can be simplified if tall the numbers included have a common factor i.e. 12:18 is the same as (6\times2):(6\times3), cancelling the 6 on both sides gives 2:3.

Ratios can be converted into fractions and therefore percentages. To change a ratio into a fraction, we take every number in the ratio and add them together i.e. if the ratio is a:b:c, then we do a+b+c.

Then each component as a fraction will be \frac { a }{ a+b+c }, \frac { b }{ a+b+c } and \frac { c }{ a+b+c }.


Taking the ratio from above, 3:5:7, we start by adding these numbers together as follows 3+5+7=15.

We then do each part of the ratio divided by the total: \frac { 3 }{ 15 }, \frac { 5 }{ 15 } and \frac { 7 }{ 15 }, to give the fraction of each segment.


Adam has £50 to share between his three children: Bill, Claire and Diana, in the ratio 4:5:1. How much does each child receive?

Bill =\dfrac{4}{10}\times £50=£20

Claire =\dfrac{5}{10}\times £50=£25

Diana =\dfrac{1}{10}\times £50=£5