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.

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

Answer: 1.04

`frac(100 + 4)(100)` = 1.04

2. A pair of shoes is being discounted by 8%. If the shoes originally cost £36, what is the new price? Use a multiplier in the calculation.

Answer: £33.12

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

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