Maths · Common misconception
Why doesn’t a 20% decrease undo a 20% increase?
Change the starting amount and watch why the same percentage gives a different change.
The short answer
A percentage is always a percentage of something. After an increase, the amount used as the base for a decrease is larger. Equal percentage increases and decreases therefore do not usually cancel.
Conceptual illustration. Colours distinguish parts of the model.
TRY A SMALL CHANGE
Predict first. Then move the control.
Where the confusion starts
The percentages look symmetrical, but the amounts being compared are different. Always identify the base before calculating a percentage change. A percentage point change is also different from a percentage change.
WORK IT THROUGH
A £100 price rises by 20%, then falls by 20%.
- Increase: £100 × 1.20 = £120.
- Decrease: £120 × 0.80 = £96. The reduction is £24, not £20.
- Combined multiplier: 1.20 × 0.80 = 0.96. The final amount is 4% below the original.
CHECK YOUR UNDERSTANDING
A £50 item rises by 10% and then falls by 10%. What is its final price?
Make a prediction or write an answer before opening the explanation.
Reveal the explanation
£49.50. £50 × 1.10 = £55; £55 × 0.90 = £49.50. The second change uses £55 as its base.
SEE IT. CHANGE IT. EXPLAIN IT.
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Use the visual explanation in the lesson, then choose Practice to test the idea with another question.
Spotted something unclear? Send feedback. These are original teaching explanations, not predictions of future exam questions.