Percentages to Fractions

# Percentages to Fractions

GCSE(F)

A percentage is really a division by a 100. Changing a percentage to a fraction means setting the denominator of the percentage to 100.

To turn 48% into a fraction, create a fraction by setting the numerator to 48 and the denominator to 100: frac(48)(100); and then simplify to frac(12)(25).

Turn a fraction into a percentage by setting the denominator of a fraction to 100: then the numerator represents the percentage. For example, frac(3)(20) has an equivalent fraction (multiplying top and bottom by 5) of frac(15)(100); the numerator gives the percentage value of 15%.

## Examples

1. Four-fifths of cars leaving a car park paid for parking for three hours or more. What is this in percentage terms?

Multiply the numerator and denominator of frac(4)(5) by 20 = frac(80)(100). The numerator is the answer as a percentage.
Turn the score into a percentage by multiplying top and bottom by 10 (to get frac(310)(600)).
Then divide by 6 to set the denominator to 100: frac(31)(100).
(You could also answer this question by changing the pass percentage into a fraction frac(55)(100) and setting the denominator to 60 = frac(33)(60), and checking his score against the pass mark.)