PercentagesEdexcel GCSE Maths: Revision notes
Section 1
What does a percentage mean and how do we interpret it multiplicatively?
A percentage is a fraction out of 100. Percentages and percentage changes can be interpreted as a fraction (e.g. 25% = 1/4) or a decimal (e.g. 25% = 0.25), and used multiplicatively — multiplying a quantity directly by the decimal equivalent.
- 25% of 80 = 0.25 × 80 = 20
This multiplicative view is essential for percentage change, reverse percentage and compound problems.
Section 2
How do we express one quantity as a percentage of another and compare quantities?
To express quantity A as a percentage of quantity B: divide A by B, then multiply by 100.
- Express 18 as a percentage of 40: (18 ÷ 40) × 100 = 45%
This method also allows two quantities to be compared using percentages, even from different totals, and it works for percentages greater than 100% (when A is bigger than B).
- Express 60 as a percentage of 40: (60 ÷ 40) × 100 = 150%
Write the formula "(part ÷ whole) × 100" at the top of your working — examiners give a method mark for showing the correct structure even if arithmetic slips.
Section 3
How do we calculate percentage increase and decrease?
Method 1 (find and add/subtract): find the percentage of the amount, then add (increase) or subtract (decrease).
- Increase £60 by 20%: 20% of £60 = £12, so £60 + £12 = £72
Method 2 (multiplier, faster): multiply directly by (1 + percentage) for an increase, or (1 − percentage) for a decrease.
- Increase by 20%: multiply by 1.20
- Decrease by 15%: multiply by 0.85
The multiplier method is quicker and essential for multi-step and compound problems.
A £45 jacket increases by 8%: £45 × 1.08 = £48.60
Section 4
How do we solve reverse percentage problems?
A reverse percentage (original value) problem gives you the value after a percentage change and asks for the original value before the change.
- Write the final amount as a percentage of the original (e.g. after a 20% increase, the final amount is 120% of the original)
- Divide the final amount by this percentage (as a decimal) to find 100% (the original)
Example: A price after a 15% increase is £69. 115% = £69, so 1% = £69 ÷ 115 = £0.60, and 100% = £60.
A common error is subtracting the percentage from the final value directly (e.g. £69 − 15% of £69) instead of dividing by the correct multiplier — this gives the wrong original value.
Section 5
How do we calculate simple interest?
Simple interest is calculated only on the original amount (the principal) each year, not on any interest already earned.
Formula: Simple Interest = (P × R × T) ÷ 100, where P is the principal, R is the rate (%), and T is the time in years.
- £500 invested at 3% simple interest for 4 years: (500 × 3 × 4) ÷ 100 = £60 interest, giving a total of £560
Must Know
- Percentage of an amount: multiply the amount by the percentage as a decimal
- Express A as a % of B: (A ÷ B) × 100
- Percentage increase/decrease multiplier: (1 + r) or (1 − r) where r is the decimal rate
- Reverse percentage: divide the final value by the multiplier to find the original (100%)
- Simple interest formula: I = (P × R × T) ÷ 100
- Percentages above 100% are valid and represent more than the whole
That's the notes covered.
Carry on to the next subtopic.