← Percentages
Percentages · Learn

Four lessons, about three minutes each

One idea runs through all of them: the multiplier. Learn it once and every percentage question gets easier.

Lesson 1

Multipliers

THE BIG IDEA

Any percentage change is one multiplication. Start from 100%, add or take away the change, then write it as a decimal.

ChangeWorkingMultiplier
20% more100% + 20% = 120%1.2
15% less100% − 15% = 85%0.85
3% more100% + 3% = 103%1.03
7.5% less100% − 7.5% = 92.5%0.925
COMMON MISTAKE

15% less is not 0.15. That's the 15% being taken off. You want what's left: 0.85.

Exam tip: always write the multiplier down. On WJEC papers it often earns a mark on its own.

Lesson 2

Percentage increase and decrease

THE BIG IDEA

You know the starting amount, so go forwards: starting amount × multiplier.

WORKED EXAMPLE

A jacket costs £80. It is reduced by 15% in a sale. Work out the sale price.

  1. 15% off leaves 85%, so the multiplier is 0.85
  2. £80 × 0.85 = £68.00
Practise this
Lesson 3

Reverse percentages

THE BIG IDEA

You know the amount after the change and want the original. Work backwards: new amount ÷ multiplier.

WORKED EXAMPLE

In a sale, a jacket costs £36 after 20% off. Work out the original price.

  1. 20% off leaves 80%, so £36 is 80% of the original. The multiplier is 0.8
  2. £36 ÷ 0.8 = £45.00
  3. Check: £45 × 0.8 = £36 ✓
COMMON MISTAKE

Adding 20% of £36 back on gives £43.20. That's wrong, because the 20% was taken off the original price, not off £36.

How to spot one: the question gives you the price after a change and asks for the price before.

Practise this
Lesson 4 · A* level

Repeated changes, compound interest and depreciation

THE BIG IDEA

When there's more than one change, multiply the multipliers. Never add or subtract the percentages.

TWO DIFFERENT CHANGES

A price goes up 20%, then down 15%.

  1. Multipliers: 1.2 and 0.85
  2. Combined multiplier: 1.2 × 0.85 = 1.02, so overall the price rises 2%
THE SAME CHANGE, YEAR AFTER YEAR

A car loses 10% of its value every year for 3 years.

  1. One year's multiplier: 0.9
  2. Three years: 0.9 × 0.9 × 0.9 = 0.9³ = 0.729

Compound interest works the same way: 4% a year for 2 years is 1.04² = 1.0816.

WORKED EXAMPLE: WORKING BACKWARDS

A car loses 10% of its value each year. After 3 years it is worth £5,832. Work out its value when new.

  1. Combined multiplier: 0.9³ = 0.729
  2. Work backwards: £5,832 ÷ 0.729 = £8,000.00
TWO CLASSIC TRAPS

Up 20% then down 20% does not cancel out: 1.2 × 0.8 = 0.96, a 4% drop overall.

Three years of 10% is not 30%: each year's 10% comes off a smaller value, so it's 0.9³, not 0.7.

Typing tip: in the working box you can write products and powers, like 1.2 × 0.85 or 0.9^3.

Try A* stretch questions