Percentages
A percentage is a way of expressing a number as a fraction out of 100, using the % sign, so 25% means 25 out of every 100. 11+ papers test finding percentages of amounts, percentage increase and decrease, and converting between fractions, decimals and percentages, all without a calculator.
Method
- Find 10% of an amount by dividing by 10, then use this to build other percentages by adding or halving: 5% is half of 10%, 20% is double 10%, and so on.
- To find a percentage of an amount directly, convert the percentage to a fraction or decimal and multiply, for example 15% of 40 = 0.15 x 40.
- For a percentage increase, either add the increase to the original amount or multiply by the single multiplier, so a 20% increase means multiplying by 1.20.
- For a percentage decrease, either subtract the decrease from the original amount or multiply by the single multiplier, so a 20% decrease means multiplying by 0.80.
- To express one amount as a percentage of another, write it as a fraction of the total, then convert that fraction to a percentage.
- For reverse percentage problems that ask for the original amount, identify what percentage the given amount represents, find 1%, then scale up to 100%.
Worked example
A jacket priced at 65 pounds is reduced by 20% in a sale. Work out the sale price.
- Find 10% of 65 pounds by dividing by 10: 6.50 pounds.
- Double this to find 20%: 6.50 x 2 = 13.00 pounds.
- Subtract the 20% reduction from the original price: 65.00 - 13.00.
- Work out the subtraction: 65.00 - 13.00 = 52.00.
Practice questions
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Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
Find 35% of 60 minutes, showing your method.
A shop reduces all its prices by 20% in a sale. A pair of trainers now costs 44 pounds in the sale. Calculate the original price of the trainers before the sale.
A laptop priced at 500 pounds is first reduced by 15%. A loyalty-card discount of a further 10% is then applied to the reduced price. (a) Calculate the final price of the laptop. (b) A shop assistant claims that a 15% discount followed by a 10% discount is the same as a single 25% discount. Show that the assistant is wrong, and find the single percentage discount that is equivalent to the two discounts combined.
Free printable worksheet
Want more practice on paper? Download the percentages worksheet pack - 12 pages of exam-style questions with a full mark scheme. No sign-up, no email wall - just the PDF, free for personal and classroom use.
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