Percentage change

To increase or decrease by a percentage, use a multiplier: a 15% increase means multiply by 1.15; a 15% decrease means multiply by 0.85. To find the percentage change, divide the change by the original and multiply by 100.

Key facts

  • Increase by r%: multiply by 1 + r/100.
  • Decrease by r%: multiply by 1 − r/100.
  • Percentage change = change ÷ original × 100.
  • Reverse percentages: divide by the multiplier to get back to the original.

Worked examples

Example 1

A £40 game goes up by 15%. What is the new price?

  1. A 15% increase is a multiplier of 1.15. 40 × 1.15 = 46
  2. The new price is £46.

Answer: £46

Example 2

A bike is £240 in a sale after 20% off. What was the price before the sale?

  1. After 20% off, 80% is left: multiplier 0.8. original × 0.8 = 240
  2. Divide to undo. 240 ÷ 0.8 = 300

Answer: £300

Example 3

A plant grows from 25 cm to 32 cm. What is the percentage increase?

  1. Find the change. 32 − 25 = 7
  2. Divide by the original and × 100. 7 ÷ 25 × 100 = 28%

Answer: 28%