GCSE Maths → Number → Percentages
GCSE Percentages Revision
Percentages are one of the most useful GCSE maths topics. They appear in discounts, interest, tax, profit, loss, ratio, probability, statistics, and many real-life worded questions.
Students often struggle with percentages because there are several different question types: finding a percentage of an amount, percentage increase, percentage decrease, percentage change, and reverse percentages.
Video explanation
A short Worthing Maths Tutor video explanation for GCSE percentages revision can be embedded here later to improve student engagement and time on page.
What does percent mean?
Percent means out of 100. So 25% means 25 out of 100.
Finding a percentage of an amount
To find a percentage of an amount, convert the percentage to a decimal and multiply.
Example 1: Find 20% of £80
So 20% of £80 is £16.
Example 2: Find 15% of 60
Percentage increase
Percentage increase means increasing an amount by a given percentage. You can do this by finding the increase and adding it on, or by using a multiplier.
Example 3: Increase £50 by 20%
20% of £50 is:
Add the increase:
The new amount is £60.
Example 4: Increase 80 by 15% using a multiplier
A 15% increase means 100% + 15% = 115%.
Percentage decrease
Percentage decrease means reducing an amount by a given percentage.
Example 5: Decrease £120 by 25%
25% of £120 is:
Subtract the decrease:
The new amount is £90.
Example 6: Decrease 200 by 30% using a multiplier
A 30% decrease means 100% - 30% = 70%.
Percentage change
Percentage change compares the change to the original amount.
Example 7: Percentage increase from 40 to 50
The change is:
Compare with the original amount:
The percentage increase is 25%.
Reverse percentages
Reverse percentage questions give the final amount after a percentage increase or decrease and ask for the original amount.
Example 8: Reverse percentage increase
A price after a 20% increase is £72. Find the original price.
A 20% increase means the final amount is 120% of the original.
Example 9: Reverse percentage decrease
A price after a 25% decrease is £90. Find the original price.
A 25% decrease means the final amount is 75% of the original.
Common mistakes in GCSE percentages
- Confusing 20% with 0.02 instead of 0.20.
- Finding the percentage change using the final amount instead of the original amount.
- Using the wrong multiplier for increase or decrease.
- Multiplying instead of dividing in reverse percentage questions.
- Forgetting that percent means out of 100.
Practice questions
- Find 10% of 90.
- Find 25% of 64.
- Increase £80 by 20%.
- Decrease £150 by 30%.
- Find the percentage increase from 50 to 65.
- A price after a 10% increase is £44. Find the original price.
- A price after a 20% decrease is £96. Find the original price.
Answers
- 9
- 16
- £96
- £105
- 30%
- £40
- £120
GCSE percentages FAQ
What does percent mean?
Percent means out of 100. For example, 25% means 25 out of 100, which is the same as 1/4 or 0.25.
How do you find a percentage of an amount?
Convert the percentage to a decimal or fraction, then multiply by the amount.
What is percentage increase?
Percentage increase means increasing an amount by a given percentage, often by using a multiplier greater than 1.
What is a reverse percentage?
A reverse percentage question gives the final amount after a percentage change and asks you to find the original amount.
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