Percentage multipliers are useful as a quick way to work out percentage increases and decreases.

They can also be used to work out the original quantity after a percentage increase or decrease. Here we divide by the percentage multiplier to find the original amount.

**To find the orginal amount:**

**after a percentage increase**

Divide by 1 + percentage as a decimal

A 5% increase is the equivalent of a percentage multiplier of 1.05

**after a percentage decrease**

Divide by 1 - percentage as a decimal

A 5% decrease is the equivalent of a percentage multiplier of 0.95

**Example 1**

A table costs £300 after 20% VAT has been added. What did it cost before VAT?

**Answer**

The multiplier was 1 + 0.20 = 1.20 or 1.2

Answer is £300 ÷ 1.2 = **£250**

**Example 2**

A tennis racket costs £76.50 in a 15% sale. What did it cost before the discount was applied?

**Answer**

The multiplier was 1 - 0.15 = 0.85

Answer is £76.50 ÷ 0.85 = **£90**