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Percentages

Years 5 to 11

A percentage is a number out of 100, and it links to fractions and decimals.

35 out of 100 = 35% = 0.35
A hundred square with 35 squares shaded: 35% = 35/100 = 0.35.

For learners

Per cent means out of 100. 35% means 35 out of every 100.

Colour in 35 squares of a hundred square, and you have shown 35%. It is also the fraction and the decimal 0.35.

10% is easy: divide by 10. To find 35% of something, find 10% three times and 5% once.

A worked example

Find 35% of £60.

  1. 10% of £60 = £6.
  2. 30% = 3 × £6 = £18.
  3. 5% = £3 (half of 10%).
  4. 35% = £18 + £3 = £21.

For grown-ups

Percentages, fractions and decimals are three ways to write the same amount. Learn the common ones: 50% = ½, 25% = ¼, 10% = ⅒, 20% = ⅕, 75% = ¾.

Common mistakes

  • Working out the change but forgetting to add it to (or take it from) the original price.
  • Taking a percentage increase and decrease as if they cancel. +20% then −20% is not back to the start.
  • Using the new value instead of the original value for percentage change.

Why it matters

Shops, interest, tax, test scores and statistics all use percentages.

Topics in quarter that use this

  • Percentages of amounts
  • Percentage increase and decrease
  • Fractions, decimals and percentages
  • Profit and loss
  • Simple interest
  • VAT, tax and wages
  • Growth and decay

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