Percentages to Fractions

## Percentages to Fractions

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 a percentage into a fraction, create a fraction by setting the numerator to the percentage and the denominator to 100, then simplify that fraction.

Turn a fraction into a percentage by obtaining an equivalent fraction where the denominator is 100. The numerator represents the percentage.

## Example 1

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

Make the denominator of the fraction a 100:

Multiply the numerator and denominator by 20 = frac(80)(100).

The numerator is the answer as a percentage.

## Example 2

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

First change the denominator to be 100:

Multiply top and bottom by 10 = 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.)