Reverse percentages
Objective. Find an original amount after a percentage change.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Reverse percentages find the original amount before a percentage change was applied, working backwards from the new value. Because the new amount equals the original multiplied by a percentage multiplier, dividing the new amount by that multiplier recovers the original value. For example, if a price after a 10% increase is £66, the multiplier was 1.1, so the original price was £66 ÷ 1.1 = £60. It is essential to identify whether the change was an increase or decrease first, since this determines whether the multiplier is above or below 1.
Worked example
After a 15% decrease, a jacket costs £51. Use reverse percentages to find the original price.
- 1Write the decrease as a multiplier: 100% − 15% = 85%, so 0.85
- 2Set up the equation: original × 0.85 = £51
- 3Divide both sides by 0.85: original = £51 ÷ 0.85
- 4Calculate the result: £60
Answer: £60
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Practice
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Start practisingCommon mistake. Pupils often subtract the percentage directly from the new amount, turning £66 after a 10% increase into £66 − £6.60 = £59.40, instead of correctly dividing by the multiplier 1.1 to get £60.
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