Percentages
A percentage is a fraction out of 100, using the symbol %. Percentages are used to find part of an amount, describe increases and decreases, and compare proportions.
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Method
- To find a percentage of an amount without a calculator, find 10% by dividing by 10, then scale that up or down to build the percentage you need - 5% is half of 10%, 30% is three lots of 10%, and so on.
- With a calculator, convert the percentage to a decimal by dividing by 100, then multiply by the amount.
- To increase or decrease an amount by a percentage, add or subtract the amount found from the original - or use a single multiplier, e.g. a 15% increase means multiplying by 1.15.
- To find one amount as a percentage of another, divide the first amount by the second and multiply by 100.
- For repeated percentage change over several time periods, such as compound interest, raise the multiplier to the power of the number of periods.
Worked example
A jacket costs 80 pounds before a 15% sale discount. Find the sale price.
- Convert 15% to a decimal: 15 divided by 100 = 0.15.
- Find 15% of 80: 0.15 x 80 = 12.
- This means the discount is 12 pounds.
- Subtract the discount from the original price: 80 - 12 = 68.
- Alternatively, use a single multiplier: a 15% decrease means multiplying by (1 - 0.15) = 0.85, and 80 x 0.85 = 68.
- The sale price is 68 pounds.
Practice questions
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Exam-style questions
Written in the style of a GCSE exam paper, with a full mark scheme.
A laptop's price is reduced from 600 pounds to 510 pounds in a sale. Work out the percentage decrease.
3000 pounds is invested for 2 years at 4% compound interest per year. Work out the total value of the investment after 2 years.
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