Percentages as Multipliers

Percentages as Multipliers

GCSE(F),

An original amount is equivalent to 100%. An increase of 25% to that original amount gives a new amount that is 125% of the original amount.

Per cent means out of a hundred. Dividing the percentage by 100 gives a multiplier: the new amount is therefore frac(100 + 25)(100) = frac(125)(100), or 1.25, times bigger.

If the price of a coat was originally £80, and the price was subsequently increased by 20%, then the new price is 80 x frac(100+20)(100) or 80 x 1.2 = £96. The 1.2 is called the multiplier.

Similarly, if an amount is reduced by 15%, then the new amount is equal to 100-15 = 85% of the original price. In this instance the multiplier is frac(100 - 15)(100), or 0.85.

Examples

1. Rail fares are being increased by 4%. What would the percentage multiplier be?

frac(100 + 4)(100) = 1.04
The multiplier is frac(100 - 8)(100) = frac(92)(100) = 0.92. The new price is therefore £36 x 0.92 = £33.12.