This topic summary covers Knowledge Organiser: 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.
Knowledge Organiser: Percentages
Key Terms
- Percentage: Parts per hundred — "per cent" means "out of 100"
- Multiplier: The decimal you multiply by to apply a percentage change
- Percentage increase: Multiply by (100 + %) ÷ 100
- Percentage decrease: Multiply by (100 − %) ÷ 100
- Reverse percentage: Finding the original value before a percentage change
Must-Know Facts
- 50% = 0.5 = 1/2; 25% = 0.25 = 1/4; 10% = 0.1 = 1/10
- 20% increase → multiply by 1.2 (NOT 0.2)
- 15% decrease → multiply by 0.85 (NOT 1.85)
- To express as a %: (part ÷ whole) × 100
- Reverse %: divide by the multiplier (e.g. after 20% off → ÷ 0.8)
- 10% then 10% decrease ≠ 0% — it gives −1% overall (1.1 × 0.9 = 0.99)
Key Formulas
- % of amount: amount × (% ÷ 100)
- % change: (new − old) ÷ old × 100%
- Increase by r%: × (1 + r/100)
- Decrease by r%: × (1 − r/100)
- Reverse %: known value ÷ multiplier
Common Mistakes
- Finding 10% then doubling for 20%: Valid but students often add incorrectly — double-check arithmetic
- % increase/decrease: Must multiply by the multiplier, not just add/subtract the percentage value
- % change direction: (new − old) ÷ old, NOT ÷ new — always divide by the original
- Reverse percentage: Don't subtract the % from the given value — divide by the multiplier
- Writing % as decimal: 5% = 0.05, NOT 0.5 — divide by 100, not 10
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
Percentage to decimal
Divide by 100
75% = 0.75
8% = 0.08
150% = 1.5
Move decimal point 2 places left
What is a percentage?
Parts per hundred
Percent = per cent = per 100
% symbol means 'out of 100'
50% = 50/100 = half