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?

Answer: 80%

Multiply the numerator and denominator of `frac(4)(5)` by 20 = `frac(80)(100)`. The numerator is the answer as a percentage.

2. The pass mark on a test was 55%. Alex scored 31/60. Did he pass the test?

Answer: No

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)`.
His percentage score was 31%.
(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.)