Knowledge Organiser: Reverse Percentages
Part of Percentages · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Reverse Percentages within Percentages for GCSE Mathematics. Revise Percentages in Number for GCSE Mathematics with 14 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 16 of 16 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 16 of 16
Practice
14 questions
Recall
22 flashcards
Knowledge Organiser: Reverse Percentages
Key Terms
- Reverse percentage: Finding the original value before a percentage change was applied
- Multiplier: The decimal that was applied to get the final amount
- Original amount: The value before the percentage change — what we are finding
- VAT: Value Added Tax, added at 20% — final price is 120% of pre-VAT price
Must-Know Facts
- After a 20% decrease: the final amount is 80% of the original (multiplier = 0.80)
- After a 15% increase: the final amount is 115% of the original (multiplier = 1.15)
- Original = final amount ÷ multiplier
- Never find a percentage of the final amount — that gives the wrong answer
- Always check by multiplying your original by the multiplier to get the final amount back
Key Formulas
- Original = final ÷ multiplier
- For a decrease of n%: multiplier = 1 - (n ÷ 100)
- For an increase of n%: multiplier = 1 + (n ÷ 100)
- Check: original × multiplier = final amount
Common Mistakes
- Subtracting/adding the % from the given value: If £120 is after a 20% increase, do NOT do £120 − 20% of £120 — divide by 1.2
- Wrong multiplier: For a 20% increase, divide by 1.2 (not 0.8); for a 20% decrease, divide by 0.8 (not 1.2)
- Identifying the direction: Read carefully — is the given value after an increase or decrease?
- Not checking: Multiply your answer by the multiplier to verify it gives the stated final amount
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Read this section alongside the surrounding pages in Percentages. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Percentages
Which calculation correctly finds 35% of £240 using the decimal method?
Which formula correctly expresses one quantity as a percentage of another?
Quick Recall Flashcards
14 questions on Percentages — practise free
Instant marking, adaptive difficulty, and 22 spaced repetition flashcards. Free until your GCSEs.
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