Find 50% of 80.
50% means half.
Half of 80 is 40.
Percentages
Percentages represent values out of 100 and are widely used in financial maths, including discounts, profit and interest. GCSE questions often test percentage calculations in real-life contexts.
Overview
A percentage means “out of 100”.
It is a way of expressing part of a whole using 100 as the standard.
\( 35\% = \frac{35}{100} = 0.35 \)
Percentages are used in discounts, interest, profit, loss, exam results, data and real-life comparisons.
You need to be confident converting and calculating with them.
What you should understand after this topic
- Understand what a percentage means
- Convert between percentages, decimals and fractions
- Find a percentage of an amount
- Work out percentage increase and decrease
- Solve exam-style percentage problems
Key Definitions
Percentage
A number written out of 100.
Percent Sign
The symbol % meaning “per hundred”.
Percentage of an Amount
A part of a quantity found using a percentage.
Percentage Increase
How much a value goes up as a percentage.
Percentage Decrease
How much a value goes down as a percentage.
Multiplier
A number used to increase or decrease by a percentage in one step.
Key Rules
Percentage to decimal
Divide by 100.
Decimal to percentage
Multiply by 100.
Find a percentage of an amount
Convert the percentage to a decimal and multiply.
Use multipliers
Increase: \(1 + \text{decimal}\), Decrease: \(1 - \text{decimal}\)
Quick Equivalences
| Percentage | Decimal | Fraction |
|---|---|---|
| 50% | 0.5 | \(\frac{1}{2}\) |
| 25% | 0.25 | \(\frac{1}{4}\) |
| 75% | 0.75 | \(\frac{3}{4}\) |
| 10% | 0.1 | \(\frac{1}{10}\) |
| 20% | 0.2 | \(\frac{1}{5}\) |
How to Solve
Step 1: Understand percentages
A percentage means 'out of 100'.
\( 60\% = \frac{60}{100} = 0.6 \)
Exam tip: Percent always means divide by 100.
Step 2: Convert between forms
\( 37\% = 0.37 \)
\( 0.48 = 48\% \)
\( 20\% = \frac{1}{5} \)
Percentage → decimal
Divide by 100 (move decimal left).
Decimal → percentage
Multiply by 100 (move decimal right).
Percentage → fraction
Write over 100 and simplify.
Step 3: Find a percentage of an amount
Convert the percentage to a decimal, then multiply.
\( 35\% \text{ of } 80 = 0.35 \times 80 = 28 \)
Step 4: Non-calculator methods
Break percentages into easier parts.
Exam tip: This is often faster without a calculator.
10%
Divide by 10.
5%
Half of 10%.
1%
Divide by 100.
Example
15% = 10% + 5%.
Step 5: Using multipliers (introduction)
Multipliers are used for percentage change.
See growth and decay for full methods.
Increase by 10%
Multiply by 1.10
Decrease by 20%
Multiply by 0.80
Step 6: Exam method summary
See percentage change for increases and decreases.
- Convert the percentage if needed.
- Choose a method (decimal or breakdown).
- Multiply or calculate step-by-step.
- Check your answer makes sense.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics.
Edexcel
Write 35% as a decimal.
Edexcel
Write 0.62 as a percentage.
Edexcel
Find \( 25\% \) of \( 240 \).
Edexcel
Increase \( 80 \) by \( 15\% \).
Edexcel
Decrease \( 450 \) by \( 20\% \).
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on percentage reasoning and real-life applications.
AQA
Express \( \frac{3}{5} \) as a percentage.
AQA
A jacket costs £60. In a sale, the price is reduced by 25%. Work out the sale price.
AQA
A student's score increased from 50 to 65. Find the percentage increase.
AQA
A value decreases from 200 to 150. Find the percentage decrease.
AQA
A student says that increasing a number by 10% and then decreasing it by 10% returns it to its original value.
Tick one box. Yes ☐ No ☐
Give a reason for your answer.
OCR
Exam-style questions aligned with OCR GCSE Mathematics, emphasising problem-solving, reverse percentages, and financial mathematics.
OCR
After a 20% increase, a price becomes £72. Work out the original price.
OCR
A shop reduces the price of a television from £500 to £425. Find the percentage reduction.
OCR
£800 is invested at an annual simple interest rate of 5%. Calculate the total amount after 3 years.
OCR
A population of 12,000 increases by 3% per year. Calculate the population after one year.
OCR
Explain the difference between a 50% increase and a 50% decrease of the same value.
Exam Checklist
Step 1
Check whether you need a conversion, amount, increase or decrease.
Step 2
Use the original amount for percentage change questions.
Step 3
Convert percentages carefully to decimals before multiplying.
Step 4
Use multipliers when the question involves repeated or direct percentage change.
Most common exam mistakes
Conversion errors
Moving the decimal point the wrong way.
Percentage change
Dividing by the new amount instead of the original amount.
Multiplier errors
Using 1.15 for a 15% decrease instead of 0.85.
Fraction form
Not simplifying after writing the percentage over 100.
Common Mistakes
These are common mistakes students make when working with percentages in GCSE Maths.
Forgetting percentage means “out of 100”
Incorrect
A student treats a percentage as a whole number without considering its meaning.
Correct
A percentage represents a fraction out of 100. For example, \(25\% = \frac{25}{100} = 0.25\).
Incorrect decimal conversion
Incorrect
A student divides by 10 instead of 100 when converting a percentage to a decimal.
Correct
To convert a percentage to a decimal, divide by 100. For example, \(35\% = 0.35\).
Using the wrong base value
Incorrect
A student uses the new amount instead of the original amount when calculating percentage change.
Correct
Percentage calculations are usually based on the original amount. Always identify the correct starting value.
Mixing up multipliers for increase and decrease
Incorrect
A student uses the wrong multiplier, such as \(0.8\) for an increase.
Correct
For increases, use multipliers greater than 1 (e.g. 20% increase → \(1.20\)). For decreases, use multipliers less than 1 (e.g. 20% decrease → \(0.80\)).
Not simplifying after converting
Incorrect
A student converts a percentage to a fraction but leaves it unsimplified.
Correct
Always simplify fractions where possible. For example, \(50\% = \frac{50}{100} = \frac{1}{2}\).
Try It Yourself
Practise calculating percentages of quantities and solving related problems.
Foundation
Foundation Practice
Find percentages of amounts and simple increases/decreases.
Find 10% of 70.
Divide by 10.
10% of 70 = 7.
Find 25% of 200.
25% means a quarter.
200 ÷ 4 = 50.
Find 20% of 90.
10% is 9, so double it.
20% = 18.
Increase 60 by 10%.
Find 10% and add.
10% of 60 is 6 → 60 + 6 = 66.
Decrease 50 by 20%.
Find 20% then subtract.
20% of 50 = 10 → 50 - 10 = 40.
What is 5% of 200?
10% is 20, so halve it.
5% = 10.
Find 1% of 300.
Divide by 100.
1% of 300 = 3.
A student says 10% of 50 is 500. What is wrong?
10% means divide by 10.
10% of 50 is 5, not 500.
Find 15% of 40.
10% + 5%.
10% = 4, 5% = 2 → total = 6.
Higher
Higher Practice
Work with multipliers and reverse percentages.
Increase 80 by 15%.
Use multiplier 1.15.
80 × 1.15 = 92.
Decrease 120 by 25%.
Use multiplier 0.75.
120 × 0.75 = 90.
A price increases by 20%. What multiplier is used?
Add 1 to the percentage.
Multiplier = 1.2.
A price decreases by 30%. What multiplier is used?
1 - 0.3.
Multiplier = 0.7.
After a 10% increase, a price is £110. What was the original price?
Divide by 1.1.
110 ÷ 1.1 = 100.
After a 20% increase, a price is £60. Find the original price.
Divide by 1.2.
60 ÷ 1.2 = 50.
After a 25% decrease, a value is 75. What was the original?
Divide by 0.75.
75 ÷ 0.75 = 100.
After a 10% decrease, a value is 45. Find the original.
Divide by 0.9.
45 ÷ 0.9 = 50.
A student uses ×1.2 to decrease by 20%. What is wrong?
Decrease uses less than 1.
Decrease multiplier should be 0.8, not 1.2.
Find 12% of 250.
10% + 2%.
10% = 25, 2% = 5 → total = 30.
Games
Practise this topic with interactive games.
Games coming soon.
Percentages Video Tutorial
Frequently Asked Questions
What does percentage mean?
Percentage means ‘out of 100’.
How do I find a percentage of an amount?
Convert the percentage to a decimal or fraction and multiply.
What is percentage increase?
It is the amount added expressed as a percentage of the original value.