GCSE Percentages Revision
This guide covers every percentage topic that appears on GCSE Maths papers from AQA, Edexcel and OCR. Work through each section in order, or jump to the topic you need. All worked examples are written in exam style so you can see exactly how to set out your answers for maximum marks.
Topics on this page
- Percentage of an amount
- Percentage increase and decrease
- Expressing one quantity as a percentage of another
- Percentage change
- Reverse percentages
- Compound interest and repeated percentage change
- Percentage problems in context
- Exam-style worked examples
- Common mistakes
- Exam tips
1. Percentage of an amount
This is the most fundamental percentage skill. Convert the percentage to a decimal (divide by 100) and multiply by the amount.
Amount × (Percentage ÷ 100)
Example: Find 18% of 350.
0.18 × 350 = 63
This topic appears on both Foundation and Higher tier papers. Try the Percentage of a Number Calculator.
2. Percentage increase and decrease
Use a single multiplier to apply a percentage change in one step. This is the method expected at GCSE.
Increase: Original × (1 + r)
Decrease: Original × (1 - r)
where r is the percentage as a decimal (e.g. 15% = 0.15)
Increase example: Increase £340 by 12%.
£340 × 1.12 = £380.80
Decrease example: Decrease £450 by 20%.
£450 × 0.80 = £360
3. Expressing one quantity as a percentage of another
Divide the part by the whole, then multiply by 100. Always make sure both values are in the same units before you divide.
(Part ÷ Whole) × 100
Example: Express 36p as a percentage of £1.50.
Convert £1.50 to pence: 150p
36 ÷ 150 × 100 = 24%
4. Percentage change
Percentage change compares the size of the change to the original value. A positive result is an increase; a negative result is a decrease.
(New value - Old value) ÷ Old value × 100
Example: A house is bought for £175,000 and sold for £210,000. Calculate the percentage profit.
(210,000 - 175,000) ÷ 175,000 × 100
35,000 ÷ 175,000 × 100 = 20%
Use the Percentage Change Calculator to verify your answers.
5. Reverse percentages
A reverse percentage question gives you the result after a percentage change and asks for the original value. Identify the multiplier that was applied, then divide by it. Do not subtract the percentage from the result.
Original = Result ÷ Multiplier
Example: A television costs £680 after a 15% reduction. Calculate the original price.
A 15% reduction means the multiplier was 0.85
£680 ÷ 0.85 = £800
Reverse percentages appear frequently on Higher tier papers, often worth 3 marks. The Reverse Percentage Calculator shows the method clearly.
6. Compound interest and repeated percentage change
Higher tier topic
Compound interest appears on both Foundation and Higher papers, but multi-step depreciation and growth questions are typically Higher tier.
Compound interest means interest is calculated on the accumulated total, not just the original amount. The same idea applies to repeated percentage decreases, such as depreciation of a car's value.
Amount = Principal × (1 + r)n
r = interest rate as a decimal, n = number of time periods
Compound interest example: A bank account pays 3.5% compound interest per year. How much is £2,000 worth after 3 years?
£2,000 × 1.0353
= £2,000 × 1.108718...
= £2,217.44
Depreciation example: A car depreciates by 18% per year. It is currently worth £9,500. What will it be worth after 2 years?
£9,500 × 0.822
= £9,500 × 0.6724
= £6,388 (to the nearest pound)
7. Percentage problems in context
GCSE papers regularly set percentage questions within real-world scenarios such as wage increases, price reductions, tax, population growth, and profit or loss. The maths is the same; the challenge is identifying which type of calculation is needed and extracting the correct values from the question.
Read the question carefully to determine whether you are being asked for a new value, an original value, a percentage, or a comparison. Watch out for questions that involve two separate percentage changes applied one after the other: you cannot simply add the percentages together.
Key point
A 10% increase followed by a 10% decrease does not return you to the original value. It leaves you 1% below the starting point. 100 × 1.10 × 0.90 = 99.
Exam-style worked examples
Example 1: Percentage of an amount
Calculate 18% of 350.
0.18 × 350 = 63
Example 2: Percentage decrease
A coat costs £120. It is reduced by 35% in a sale. Calculate the sale price.
Multiplier = 1 - 0.35 = 0.65
£120 × 0.65 = £78
Example 3: Percentage change
A house is bought for £175,000 and sold for £210,000. Calculate the percentage profit.
(210,000 - 175,000) ÷ 175,000 × 100
35,000 ÷ 175,000 × 100 = 20%
Example 4: Reverse percentage (Higher)
A television costs £680 after a 15% reduction. Calculate the original price.
Multiplier for a 15% decrease = 0.85
Original = £680 ÷ 0.85
= £800
Example 5: Expressing as a percentage
In a class of 32 students, 24 passed an exam. What percentage passed?
24 ÷ 32 × 100 = 75%
Example 6: Compound interest
A bank account pays 3.5% compound interest per year. How much is £2,000 worth after 3 years? Give your answer to the nearest penny.
£2,000 × 1.035³ = £2,000 × 1.10872...
= £2,217.44
Example 7: Depreciation (Higher)
A car depreciates by 18% per year. It is currently worth £9,500. What will it be worth after 2 years? Round to the nearest pound.
£9,500 × 0.82² = £9,500 × 0.6724
= £6,388
Example 8: Two-step context problem
A flat is bought for £180,000. Its value increases by 6% in the first year, then falls by 4% in the second year. What is the flat worth at the end of the second year?
After year 1: £180,000 × 1.06 = £190,800
After year 2: £190,800 × 0.96 = £183,168
Example 9: Reverse percentage (profit)
A shop sells a phone for £276, which includes 15% profit on the cost price. What was the cost price?
£276 represents 115% of the cost price (100% + 15%)
£276 ÷ 1.15 = £240
Common mistakes
Finding the percentage then forgetting to apply it
To increase £80 by 15%, students sometimes calculate 15% of £80 (= £12) and stop there, forgetting to add it to the original. Using the multiplier (£80 × 1.15 = £92) avoids this entirely.
Using the wrong original in a reverse percentage
If a price after a 20% reduction is £80, subtracting 20% from £80 gives £64, which is wrong. You must divide by the multiplier: £80 ÷ 0.80 = £100.
Adding percentages from different bases
A 10% increase followed by a 10% decrease does not cancel out. The second percentage acts on a different base. 100 × 1.10 × 0.90 = 99, not 100.
Using simple interest for a compound interest question
If a question says "compound interest", use the formula A = P × (1 + r)n. Using simple interest (P + P × r × n) will give a lower figure and lose marks.
Wrong units when expressing as a percentage
When expressing one quantity as a percentage of another, both values must be in the same unit. For example, expressing 36p as a percentage of £1.50 requires converting £1.50 to 150p first.
Exam tips
Always state the multiplier
Writing down your multiplier (e.g. "multiplier = 0.85") earns a method mark even if you make an arithmetic error. It also helps you spot when you have used the wrong multiplier.
Read the question twice
Before calculating, identify whether the question asks for the new value, the original value, the percentage change, or an amount of interest earned. Answering the wrong thing is a common cause of lost marks.
Show clear working
On any question worth 2 or more marks, working is essential. Even if your final answer is wrong, you can score method marks for a correct approach.
Know your grade boundaries
GCSE Maths is graded 1 to 9. Foundation tier covers grades 1 to 5. Higher tier covers grades 4 to 9. Compound interest, depreciation and multi-step reverse percentage questions are typically Higher tier and worth 3 marks. Securing these correctly can make a significant difference to your grade boundary position. Grade boundaries vary each year but a grade 5 (strong pass) on Higher tier typically requires around 40 to 50% of available marks.
Use a non-calculator strategy for Paper 1
All three GCSE maths boards include a non-calculator paper. Build up compound percentages using the 10%, 5% and 1% method, or use doubling and halving tricks. See the percentage tricks guide for shortcuts.
Calculators for GCSE revision
Percentage of a Number
Find any percentage of any amount instantly.
Percentage Increase Calculator
Work out new values after a percentage increase.
Percentage Decrease Calculator
Calculate sale prices and reductions.
Percentage Change Calculator
Find the percentage change between two values.
Reverse Percentage Calculator
Find the original value before a change.
X is P% of What Calculator
Find the whole when you know a part and its percentage.
Ready to practise?
Try 15 GCSE-style practice questions with full worked answers and mark allocations.
GCSE Practice Questions