Percentage Increase and Decrease

Percentage Increase and Decrease

GCSE(F),

100% of an amount is the same value as the original amount.

103% is `frac(103)(100)` = 1.03 times larger than the original amount.

The number 1.03 is known as a multiplier.

To calculate a multiplier increase, divide the percentage by 100 (to make it a decimal), then add it to 1. Multiply this against the original amount:

Increase 80 by 5%

Multiplier = 1 + `frac(5)(100)` = 1.05

Calculation = 80 x 1.05 = 84

To calculate a multiplier decrease, divide the percentage by 100 and subtract from 1:

Reduce 92 by 4%

Multiplier = 1 - `frac(4)(100)` = 0.96

Calculation = 92 x 0.96 = 88.32

Examples

1. A brand of washing powder is being sold on a special offer. The offer states that there is an additional 30% (by weight) compared to the normal box. If the normal weight is 3200g, what weight is sold in the special offer box?

Answer: 4160g

The multiplier is 1 + `frac(30)(100)` = 1.3

The new amount is 3200 x 1.3

= 4160g

2. In a sale, a jacket has been reduced by 15%. If the original price of the jacket was £140, what is the sale price?

Answer: £119

The multiplier is 1 - `frac(15)(100)` = 0.85 (it is a decrease)

= 140 x 0.85

= 119