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Reverse Percentages Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Reverse percentages
A method used to find the original value before a percentage increase or decrease.
Key idea of reverse percentages
Work backwards using the percentage given to find the original value.
Finding the original value after a percentage increase
Divide the final value by (1 + percentage increase as a decimal).
Finding the original value after a percentage decrease
Divide the final value by (1 - percentage decrease as a decimal).
Percentage increase formula for reverse percentages
Original value = Final value ÷ (1 + percentage increase as a decimal).
Percentage decrease formula for reverse percentages
Original value = Final value ÷ (1 - percentage decrease as a decimal).
Example: 20% increase, final value £120
Original value = £120 ÷ 1.2 = £100.
Example: 15% decrease, final value £85
Original value = £85 ÷ 0.85 = £100.
Common mistake in reverse percentages
Do not subtract or add the percentage directly to the final value; always divide by the correct factor.
Steps to solve reverse percentage problems
1. Identify if it’s an increase or decrease. 2. Convert the percentage to a decimal. 3. Divide the final value by the appropriate factor (1 + or 1 - the decimal).
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