Ratio

Reverse percentages

Undo a percentage multiplier to find the original.

Predict, test and explain

Step 1 of 3

Predict

An amount is £80 after a 20% reduction. What was the original?

80=\text{original}\times 0.8

Scroll the diagram sideways to see every label.

The multiplier acts on the original amount. Divide the final amount by that multiplier to undo the change. Subtracting the same percentage from the final amount does not reverse an increase.

Check the working

Quantity	Value
Percentage change	-20%
Multiplier	0.8
Original amount (£)	$100$
Forward check	$100\times 0.8=80$

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Predict

Try it in the simulation. Change one thing at a time.

Explain

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Hints, self-check and connections

Try a self-check

Fixed values, separate from the diagram controls.

A jacket costs £72 after a 20% reduction. What was its original price?

Hint

The sale price is 80% of the original. Divide by 0.80.

Reveal answer

£90. Check: 80% of £90 is £72.

$72\div0.80=90$

Build an explanation

Hint 1

Convert the percentage change to a multiplier: a 20% increase uses 1.20 and a 20% decrease uses 0.80.

Hint 2

The relationship is final amount = original amount × multiplier.

Hint 3

Reverse the change by dividing: original amount = final amount ÷ multiplier. The multiplier must be positive.

Worked example

This example uses fixed values, separate from the diagram controls.

A price is £84 after a 20% increase. What was the original price?

A 20% increase gives a multiplier of 1 + 20/100 = 1.20.
Original price = £84 ÷ 1.20 = £70.
Check: 20% of £70 is £14, and £70 + £14 = £84.

Answer: £70

Connect this idea

Watch out: Subtracting 20% of £84 does not undo a 20% increase. The increase was calculated from the original amount.