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
A table costs £300 after 20% VAT has been added. What did it cost before VAT?
The multiplier was 1 + 0.20 = 1.20 or 1.2
Answer is £300 ÷ 1.2 = £250
A tennis racket costs £76.50 in a 15% sale. What did it cost before the discount was applied?
The multiplier was 1 - 0.15 = 0.85
Answer is £76.50 ÷ 0.85 = £90