Percentages is one of the rare topics in the GCSE Maths curriculum that we can immediately see the benefits of understanding in our daily lives - from calculating discounts in sales to a bank's interest rates. A percentage is a fraction of 100, meaning "per cent" or "per hundred" e.g. 50% means half of something (50 out of 100).
There may be various GCSE Maths number problems in the exam to test your understanding of percentages. Common examples are finding a percentage of an amount, or calculating percentage changes in values. This article will begin with the basics of percentages and build to more complex topics, including step by step examples and exam questions to test your understanding.
If you need further help, TeachTutti has a list of qualified GCSE Maths tutors to support your GCSE Maths revision of percentages and related topics, whether you are sitting the exam with AQA, Edexcel or OCR.
Calculate the percentage of an amount
The ability to calculate the percentage of an amount is a skill required both in GCSE exams and in real life, such as finding out the VAT added to a payment.
Step-by-step approach
- Turn the percentage into a decimal - Divide the percentage by 100 e.g. 25% becomes 0.25 (25 ÷ 100 = 0.25).
- Multiply the decimal by the total amount - Multiply the percentage-converted decimal by the number you’re trying to find a percentage of. For instance, if you want to find 25% of £80, the calculation is 80 x 0.25 = 20. This means that 25% of £80 is £20.
Find the percentage amount without a calculator
A calculator is the easiest way to calculate percentages. However, you may have to work out the amount without a calculator, such as because calculators are not permitted in your exam or because you don't have one to hand in a real-life situation. Here are a few alternative approaches:
- Breaking down percentages: If you need to find 25%, you can divide the total by 4. This is because 25% is the same as one-quarter e.g. you can also find 25% of £80 by dividing it by 4.
- Using fraction equivalents: You can turn the percentage into its equivalent fraction and divide by this number. For example, 10% of a value can be found by dividing by 10.
Example 1
We need to find 15% of £60:
- Turn 15% to a decimal by dividing 15 by 100 = 0.15.
- Multiply this by 60 (60 × 0.15 = 9).
- 15% of £60 is £9.
1
What is 30% of £120?
Percentage increase and percentage decrease
You will often be asked in your GCSE examination to calculate percentage increases and decreases. We have listed a step-by-step breakdown for both calculations below.
Find the percentage increase
- Get the increased amount - Subtract the original value from the new value.
- Divide the increase by the original value.
- Multiply by 100 - This will turn the result into a percentage.
For example, if the price of a jumper rises from £40 to £50:
- Find the increase: £50 - £40 = £10.
- Divide the increase by the original price: £10 ÷ £40 = 0.25.
- Multiply by 100: 0.25 × 100 = 25%.
This means the price increased by 25%.
Find the percentage decrease
- Find the decreased amount - Subtract the new value from the original value.
- Divide the decrease by the original value.
- Multiply by 100 - This will return the percentage decrease.
For example, if the price of a phone goes from £300 to £240:
- Find the decrease: £300 - £240 = £60.
- Divide the decrease by the original price: £60 ÷ £300 = 0.2.
- Multiply by 100: 0.2 × 100 = 20%.
The price has decreased by 20%.
Percentage multipliers
A percentage multiplier can speed up the calculation for a percentage change. If the amount has increased, you add the percentage to 100% and turn it into a decimal multiplier. You subtract the percentage from 100% if the amount has dropped and turn this value into a decimal.
For example, to increase £40 by 20%:
- Multiply by 1.2. 40 × 1.2 = 48
To decrease £60 by 30%, multiply by 0.7:
- 60 × 0.7 = 42
2
What is the percentage increase when a bike increases in cost from £150 to £180?
Percentage change examples
Changes in percentage are common questions in GCSE Maths. You will be expected to find a percentage increase or decrease. We have provided a step-by-step approach to percentage change and real-life examples.
Step-by-step approach to percentage change
- Find the difference between the two numbers.
- Divide the difference by the original value.
- Multiply the result by 100 to find the percentage change.
For example, the cost of a product has increased from £100 to £120:
- The increase difference is £20 (£120 - £100).
- The value is 0.2 when you divide by the original value (£20 ÷ £100).
- The answer is a 20% increase when you multiply by 100 (0.2 × 100 = 20%).
Example 1: Decrease
A video game has been reduced to £80. It originally cost £80. Find the percentage decrease:
- Subtract the new price from the original: £80 - £60 = £20.
- Divide by the original price: £20 ÷ £80 = 0.25.
- Multiply by 100 to get 25%.
This means the price has dropped by 25%.
3
What is the percentage decrease when a dress is discounted from £120 to £90?
Convert percentages, decimals and fractions
You can solve percentage problems far more effectively by understanding how to convert between percentages, decimals and fractions. This has increased importance in your GCSE exams where you need to answer questions quickly.
Percentages to decimals
Divide by 100 to turn a percentage into a decimal:
- 50% becomes 0.5 (50 ÷ 100 = 0.5).
- 25% becomes 0.25 (25 ÷ 100 = 0.25).
Decimals to percentages
Multiply a decimal by 100 to turn it into a percentage:
- 0.75 becomes 75% (0.75 × 100 = 75).
- 0.2 becomes 20% (0.2 × 100 = 20).
Percentages to fractions
All you need to do to write a percentage as a fraction is express the percentage over 100. Then you should simplify the fraction if this is possible:
- 50% becomes 50/100 = 1/2?.
- 25% becomes 25/100 = 1/4?.
For example, let's try to convert 75% into both a decimal and a fraction:
- Turn 75% into a decimal: 0.75.
- Turn 75% into a fraction: 75/100 = 3/4?.
4
What is 40% as a decimal and a fraction?
Final thoughts - Finding a percentage
We have covered percentages from basic to advanced in this GCSE Maths revision guide, including how to calculate a percentage, decimals and percentages, and using percentage multipliers. It is a vital life skill, whether you are calculating discounts, working out percentage increases, or converting between percentages and fractions.
Follow the link to test your knowledge with GCSE percentage worksheets by MathsGenie. for GCSE to test your knowledge. You can also find past papers by RevisionMaths on all exam boards, including AQA and OCR.
If you need extra help, TeachTutti has qualified GCSE Maths tutors with enhanced DBS checks who can support your learning with in-person or online tuition.
This post was updated on 30 Nov, -0001.
