Relating Ratios and Fractions

Relating Ratios and Fractions


Ratios can be written as a fraction: fractions may also be written as a ratio.

A ratio compares sizes of quantities that make up a total. A fraction compares a quantity against a total.

To turn a ratio into a fraction,add the two parts of the ratio together to make a total: this will become the denominator. A ratio of 3 : 5 can be turned into two fractions of `frac(3)(8)` and `frac(5)(8)`.


1. Write `frac(3)(16)` as a ratio.

Answer: 3 : 13

The first part of the ratio uses the numerator, 3.

Work out the second numberator as denominator - numerator.

16 - 3 gives the second part of the ratio as 13.

The answer is 3 : 13.

2. The colours of cars were noted in a car park. The ratio of red : white : blue was 3 : 4 : 5. What fraction of the number of cars were red?

Answer: `frac(1)(4)`

The total of the ratios is 3 + 4 + 5 = 12. This is the denominator.

The red ratio had a value of 3: this is the numerator.

This is a fraction of `frac(3)(12)` which simplifies to `frac(1)(4)`.