# GCSE Maths – Percentages A percentage is a standardised form for a fraction, in which it is quoted as a fraction of 100. To change a percentage into a decimal or a fraction we divide it by 100%; to change a decimal or a fraction into a percentage we multiply it by 100%.

Examples To get a percentage of a number, multiply the number by the percentage expressed as a fraction or a decimal.

Examples To express one number as a percentage of another, write the two numbers as a fraction and multiply by 100%.

Example

Express 117 as a percentage of 500: To calculate a percentage change (either increase or decrease) use the formula

Percentage change = [NB: A very common mistake is to use the new value instead of the original value]

Example

A company had expected sales of £15,000 last month, but when the actual sales for the month were totalled they came to £17,280. By what percentage did the actual sales exceed the expected?

Increase = £17,280 – £15,000 = £2,280, so percentage increase = × 100% = 15.2%

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