Recover an original value by undoing its multiplier

By UK GCSE Mathematics · independent study · myAudience

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Recover an original value by undoing its multiplier

If a changed value equals the original multiplied by m, the original equals the changed value divided by m, provided m is nonzero. Recovering a price after a 25% increase requires division by 1.25, not a 25% decrease.

Identify which amount represents 100%. A final price after a 20% discount represents 80% of the original, so dividing it by 0.8 recovers the original. A percentage difference relative to a different reference cannot be substituted into the same formula.

Check the recovered amount by applying the original change again. This check also helps detect whether a question describes a markup, a discount or a percentage of a total.

Worked example: A price after a 25% increase is £100. Find the original.

The final amount is 1.25 times the original.

Divide £100 by 1.25.

Check £80 × 1.25.

Answer: £80.

Check your understanding: A discounted price is £72 after 10% off. What was the original?

Answer: £80.

Why: £72 is 90% of the original; 72/0.9 = 80.