GCSE Maths · Number

Percentages

Percentage change, reverse percentages, and compound interest.

200 GCSE-style practice questions

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Percentages, explained point by point

Everything the GCSE specification expects you to be able to do, and how to actually do it - the same lesson a signed-in student studies from.

  1. Convert between fractions, decimals and percentages

    A percentage is just a fraction out of 100, so 45% = 45100 = 0.45. To turn a fraction into a percentage, divide top by bottom and multiply by 100: 38 = 0.375 = 37.5%. Knowing the common ones by heart - 12 = 50%, 14 = 25%, 15 = 20% - saves time in every paper.

  2. Find a percentage of an amount, with and without a calculator

    Without a calculator, build the percentage from easy pieces: 10% of £60 is £6, so 35% is £6 × 3 + £3 = £21. With a calculator, convert to a decimal and multiply: 35% of 60 is 0.35 × 60. Both routes should give exactly the same answer - a good self-check.

  3. Increase or decrease an amount by a percentage using a multiplier

    A 12% increase means you end with 112% of the original, so multiply by 1.12; a 12% decrease leaves 88%, so multiply by 0.88. One multiplication does the whole job: £250 increased by 12% is 250 × 1.12 = £280. Multipliers also chain neatly for repeated changes.

  4. Write one quantity as a percentage of another

    Divide the part by the whole and multiply by 100: scoring 34 out of 40 is 34 ÷ 40 × 100 = 85%. Make sure both quantities are in the same units first - 30p out of £2 is 30200, which is 15%.

  5. Calculate percentage change - profit, loss and simple interest

    Percentage change is the change divided by the ORIGINAL value, times 100. A bike bought for £80 and sold for £92 makes 1280 × 100 = 15% profit. Simple interest adds the same amount each year: £400 at 3% simple interest earns £12 every year.

  6. Work backwards from a percentage change to find the original amount (reverse percentages)

    If a price AFTER a 20% increase is £54, then £54 is 120% of the original - so divide by the multiplier: 54 ÷ 1.2 = £45. The trap is taking 20% off the new price instead; dividing by the multiplier always undoes the change exactly.

Practice

Try a Percentages question

A GCSE-style original question from this topic. Have a go before you open the working - deciding on an answer first is what makes the working stick.

The price of a phone drops from £250 to £210. Work out the percentage decrease.

  1. 19%
  2. 84%
  3. 40%
  4. 16%
Show the answer and the working

Answer: 16%

The decrease is £40, and 40250 × 100 = 16%.

  1. Find the actual decrease: 250 − 210 = 40.
  2. Divide by the original price: 40 ÷ 250 = 0.16.
  3. Multiply by 100: 0.16 × 100 = 16%.

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