GCSE Maths • Foundation & Higher
GCSE Percentages Revision Guide
Learn to calculate, compare and reverse percentage changes accurately.
Foundation
Percentage Multipliers
Financial Maths
What You'll Learn
Interpret and Convert Percentages
Move accurately between common fractions, decimals and percentages and understand a percentage as an operator.
Find a Percentage of an Amount
Use a decimal multiplier, common fraction or unit percentage method to calculate part of a quantity.
Calculate Percentage Increase and Decrease
Find the change or use a multiplier to calculate a new value after one percentage change.
Find Percentage Change
Divide the actual change by the original amount, multiply by 100 and interpret the direction correctly.
Work Backwards to an Original Value
Identify the percentage remaining or final multiplier, then divide the final amount by that multiplier.
Model Repeated Growth and Decay
Apply the same multiplier repeatedly or raise it to a power for compound interest and depreciation.
KEY RULES AND FORMULAE Rules
Percentage Lessons
Percentage Of An Amount
Calculate percentages using decimal multipliers, unit percentages and familiar fraction equivalents in numerical and money contexts.
Percentage Increase
Find an increase, calculate percentage change and use multipliers to obtain a larger final value efficiently.
Percentage Decrease
Calculate discounts and reductions, use decrease multipliers and distinguish the decrease amount from the final value.
Reverse Percentages
Work backwards from a final amount by identifying the correct multiplier and applying the inverse operation.
Compound Interest And Depreciation
Model repeated growth and decay with powers of multipliers, then round financial answers at the appropriate stage.
CORE SUBTOPICS
Fractions, Decimals and Percentages
Recognise equivalent forms such as 3/4 = 0.75 = 75% and choose the most efficient form.
Percentages Greater Than 100%
Interpret values such as 125% as 1.25 times the original quantity rather than as an impossible percentage.
One Quantity as a Percentage of Another
Divide the part by the whole, multiply by 100 and identify the correct comparison quantity.
Simple Interest
Calculate the same percentage of the original principal for each period and distinguish this from compound growth.
Discounts, VAT, Profit and Loss
Translate financial language into percentage operations and identify whether the question requires a change or a final amount.
Rounding and Estimation
Keep full calculator values through multi-step methods, round at the end and estimate to check that the answer is sensible.
Worked Example
Successive Percentage Changes
QUESTION
A laptop costs £800. Its price is reduced by 15%, then the reduced price is increased by 10%. Find the final price and the overall percentage change from the original price.
- Given information: The two percentages are applied successively, so the second change is based on the reduced price, not on £800.
- Method: Use a decrease multiplier followed by an increase multiplier, then compare the final price with the original price.
- Write the multipliers: a 15% decrease uses 0.85, and a 10% increase uses 1.10.
- Apply the decrease: £800 × 0.85 = £680.
- Apply the increase to the new price: £680 × 1.10 = £748.
- Find the overall change: £800 - £748 = £52, so the price has decreased overall.
- Convert the change to a percentage of the original: (£52 ÷ £800) × 100 = 6.5%.
- Final answer: The final price is £748, representing an overall decrease of 6.5%.
- Independent answer check: A single calculation gives £800 × 0.85 × 1.10 = £748. Reversing gives £748 ÷ (0.85 × 1.10) = £800, confirming the calculation.
- One common mistake: Do not combine the changes as -15% + 10% = -5%. The 10% increase is calculated from £680, so the overall decrease is 6.5%.
- Common GCSE Mistakes
- Using the Percentage Instead of the Multiplier
- Dividing by the Final Amount
- Stopping at the Discount Amount
- Multiplying in a Reverse Question
- Assuming Equal Increases and Decreases Cancel
- Rounding Too Early
- Exam Tips
- Underline whether the question asks for the percentage amount, the final amount, the original amount or the percentage change.
- Write the multiplier before calculating; it makes the direction of the percentage change clear and earns useful method evidence.
- For percentage change, label the original value and place it in the denominator before multiplying by 100.
- Keep full calculator values during repeated change, then round money to the nearest penny or follow the stated accuracy instruction.
- Check with estimation or an inverse operation: an increase should produce a larger value, and dividing a final value by its multiplier should recover the original.
Ready to Practice?
Printable Worksheet
Practise percentage amounts, multipliers, change, original values and repeated growth through a carefully sequenced question set
Interactive Quiz
Generate a topic-specific percentages knowledge check with fresh questions, automatic marking and feedback linked to relevant lessons.
Exam-Style Questions
Apply percentage methods in multi-step money, population, growth and depreciation contexts while showing clear working.
Watch the Percentage Tutorial
Clear, step-by-step explanation of expanding brackets, simplifying complex expressions, and solving for x. Perfect for visual learners who need a breakdown of the rules in action.
- 12 minute comprehensive guide
- High-definition whiteboard walk-through
Frequently Asked Questions
A percentage is a number of parts per hundred. For example, 35% means 35/100, which is 0.35. Percentages can describe a proportion, compare quantities or act as an operator. To find 35% of an amount, multiply the amount by 0.35.
Convert the percentage to a decimal by dividing by 100, then multiply by the amount. For example, 18% of 250 is 0.18 × 250 = 45. For familiar percentages, a mental method using 10%, 5%, 1% or fraction equivalents may be quicker.
For an increase of p%, use 1 + p/100. For a decrease, use 1 - p/100. An increase of 12% therefore uses 1.12, while a decrease of 12% uses 0.88. The multiplier gives the new amount directly, not just the amount of change.
A reverse-percentage question gives the final amount and asks for the original. Identify the multiplier that produced the final amount, then divide by it. If £72 is the price after a 20% discount, 80% remains, so the original price is £72 ÷ 0.80 = £90.
Tier placement depends on the exam board. AQA lists original-value percentage problems in basic Foundation content and growth or decay problems, including compound interest, in additional Foundation content. They are therefore relevant to Foundation and Higher students on AQA, although Higher questions may use more demanding multi-step contexts.
Estimate the direction and size first. A decrease must produce a smaller non-negative value in an ordinary price context, while an increase must produce a larger one. You can also reverse a multiplier calculation: divide the final amount by the multiplier and check that you recover the original value.
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