Increasing and decreasing an amount by a percentage
To increase or decrease an amount by a percentage, first calculate the percentage of the amount and then either add this answer on to increase the quantity, or subtract this answer to decrease the quantity. There is more than one way to find the percentage of an amount.
Examples
Increase £50 by 8%.
Using the multiplying method, first find 8% of £50:
\(\frac{8}{100} \times 50 = \frac{8}{100} \times \frac{50}{1} = \frac{400}{100} = 4\)
8% of £50 is £4, so to increase £50 by 8%, add the £4 onto the £50, which is £54.
Decrease 72 kg by 40%.
Using the 10% method, first find 40% of 72 kg:
10% = \(72 \div 10 = 7.2\)
10% = 7.2, so 40% = \(7.2 \times 4 = 28.8\)
40% of 72 kg is 28.8 kg, so to decrease 72 kg by 40%, subtract 28.8 from 72, which is 43.2 kg.
You can also use the multiplier method. This type of calculation is most convenient when used with a calculator but it is vital to use it when dealing with compound interest questions.
Firstly, consider what the overall percentage would be after the figure has had its percentage increase or decrease added or subtracted. Then convert this amount to a decimal, before finally multiplying by the number in question.
Examples
What is the multiplierAn amount that each number or numbers will be multiplied by. for a 15% increase?
A 15% increase would mean that the overall percentage would be:\(100 \% + 15 \% = 115 \%\)
115% as a decimal = \(115 \div 100 = 1.15\)
What is the multiplier for a 33% decrease?
A 33% increase would mean that the overall percentage would be \(100\% - 33\% = 67\%\)
67% as a decimal = \(67 \div 100 = 0.67\)
Question
Increase £50 by 8%.
The multiplier for an 8% increase is 1.08.
\(50 \times 1.08 = 54\)
Question
Decrease 72 kg by 40%.
The multiplier for a 40% decrease is 0.6.
\(72 \times 0.6 = 43.2~\text{kg}\)