How it works

Percentage change compares the change in a value to its original value, expressed as a percentage. To increase or decrease by a percentage, use a multiplier (e.g. +15% means x1.15, -20% means x0.8). Reverse percentage problems give you the result after a change and ask for the original amount, so you divide by the multiplier instead of multiplying.

The method

1. 1.Identify whether it is an increase or a decreaseRead the question carefully
2. 2.Convert the percentage to a multiplier (100% ± change)/100
3. 3.Multiply the original value by the multiplierOr divide for reverse percentage problems
4. 4.Check the answer is sensible (increase should be bigger, decrease smaller)

Worked example

A jacket costs £60 before a 15% increase. Find the new price.

1. Multiplier = 1 + 0.15 = 1.15
2. New price = 60 x 1.15 = £69

Worked example

After a 20% decrease, a price is £48. Find the original price.

1. Multiplier = 1 - 0.20 = 0.8
2. Original = 48 ÷ 0.8 = £60

Common mistakes

• Finding the percentage of the new amount instead of the original amount
• Adding or subtracting the percentage value instead of using a multiplier
• Dividing by the wrong multiplier in reverse percentage questions