A price increases from £50 to £60. What is the percentage increase?
Increase ÷ original × 100.
Increase = 10 → 10 ÷ 50 × 100 = 20%.
Percentage Change
Percentage change measures how a value increases or decreases compared to its original amount. It builds on percentages and leads into growth and decay for repeated change in financial maths and real-world problems.
Overview
Percentage change measures how much a value has increased or decreased compared with the original value.
\( \text{Percentage change} = \dfrac{\text{change}}{\text{original}} \times 100 \)
Always divide by the original value, not the new value, when calculating percentage change.
What you should understand after this topic
- Calculate the amount of change
- Identify whether the change is an increase or decrease
- Calculate percentage change correctly
- Understand why the original value is used in the calculation
- Avoid common mistakes in exam questions
Key Definitions
Original Value
The starting value before the change happened.
New Value
The value after the change happened.
Change
The difference between the new value and the original value.
Percentage Increase
When the new value is bigger than the original value.
Percentage Decrease
When the new value is smaller than the original value.
Percentage Change
The size of the change written as a percentage of the original value.
Key Rules
Find the change first
\( \text{Change} = \text{new} - \text{original} \)
Use the original value
Always divide by the original, not the new value.
Multiply by 100
Convert the decimal to a percentage.
State increase or decrease
Decide whether the value went up or down.
Quick Pattern Check
Value goes up
Percentage increase
Value goes down
Percentage decrease
Same value
0% change
Original matters most
The percentage is always based on the original value.
How to Solve
Step 1: Understand the formula
Percentage change compares how much a value has changed relative to the original value. It builds on ideas from percentages.
\( \text{Percentage change} = \dfrac{\text{change}}{\text{original}} \times 100 \)
Exam tip: Always divide by the original value.
Step 2: Identify original and new values
Exam thinking: The original value is always the base.
Original value
The starting value.
New value
The final value after change.
Step 3: Find the change
Work out the difference between the values.
\( \text{Change} = |\text{new} - \text{original}| \)
Example: \( 50 - 40 = 10 \).
Step 4: Divide by the original value
\( \frac{10}{40} = 0.25 \)
Step 5: Multiply by 100
\( 0.25 \times 100 = 25\% \)
Step 6: Decide increase or decrease
Exam tip: State increase or decrease in your final answer.
Increase
New value is greater than original.
Decrease
New value is smaller than original.
Step 7: Quick method summary
See growth and decay for repeated percentage change.
- Find the difference.
- Divide by the original value.
- Multiply by 100.
- State increase or decrease.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on calculating percentage increase and decrease.
Edexcel
A jacket increases in price from £40 to £50. Calculate the percentage increase.
Edexcel
The price of a phone decreases from £600 to £540. Calculate the percentage decrease.
Edexcel
A town's population rises from 18,000 to 19,260. Find the percentage increase.
Edexcel
The number of students in a college falls from 1,200 to 1,050. Calculate the percentage decrease.
Edexcel
A car's value increases from £8,000 to £8,640. Find the percentage increase.
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, emphasising reverse percentage change and real-life contexts.
AQA
After a 20% increase, the price of a bicycle is £360. Find the original price.
AQA
A television is reduced by 15% to £425. Find the original price.
AQA
A worker's salary increases by 4% from £25,000. Calculate the new salary.
AQA
The number of visitors to a museum rises by 12% from 45,000. Find the new number of visitors.
AQA
A shop reduces its prices by 30%. If an item originally costs £80, find the sale price.
OCR
Exam-style questions aligned with OCR GCSE Mathematics, focusing on reasoning, multi-step problems, and interpreting percentage change.
OCR
The population of a city increases from 250,000 to 287,500. Calculate the percentage increase.
OCR
The price of petrol rises from £1.40 per litre to £1.54 per litre. Calculate the percentage increase.
OCR
A laptop is reduced from £900 to £765 in a sale. Calculate the percentage decrease.
OCR
A company's profit falls from £120,000 to £102,000. Calculate the percentage decrease.
OCR
Explain how to calculate percentage change and state the formula used.
Exam Checklist
Step 1
Identify the original value clearly.
Step 2
Work out the amount of change.
Step 3
Divide by the original value, not the new value.
Step 4
Multiply by 100 and state increase or decrease.
Most common exam mistakes
Wrong base value
Using the new value instead of the original value.
No ×100
Leaving the answer as a decimal instead of a percentage.
No label
Forgetting to say whether it is increase or decrease.
Wrong change
Subtracting in the wrong order or using the wrong numbers.
Common Mistakes
These are common mistakes students make when calculating percentage change in GCSE Maths.
Dividing by the wrong value
Incorrect
A student divides by the new value instead of the original value.
Correct
Percentage change is always based on the original value. Use \(\frac{\text{change}}{\text{original}} \times 100\).
Forgetting to multiply by 100
Incorrect
A student leaves the answer as a decimal.
Correct
After finding the fraction or decimal, multiply by 100 to convert it into a percentage.
Not stating increase or decrease
Incorrect
A student gives a number without saying whether it increased or decreased.
Correct
Always state whether the change is an increase or a decrease, as this is part of the final answer.
Using the wrong value for the change
Incorrect
A student subtracts in the wrong order or uses incorrect values.
Correct
Change is found by subtracting the original value from the new value. Be careful with the order.
Confusing percentage change with finding a percentage
Incorrect
A student calculates a percentage of a number instead of the change.
Correct
Percentage change compares two values. It is different from finding a percentage of a single amount.
Try It Yourself
Practise calculating percentage increases and decreases.
Foundation
Foundation Practice
Calculate percentage increases and decreases.
A value increases from 80 to 100. Find the percentage increase.
Find increase first.
Increase = 20 → 20 ÷ 80 × 100 = 25%.
A price decreases from £40 to £30. What is the percentage decrease?
Decrease ÷ original × 100.
Decrease = 10 → 10 ÷ 40 × 100 = 25%.
A value decreases from 90 to 72. Find the percentage decrease.
Find the decrease first.
Decrease = 18 → 18 ÷ 90 × 100 = 20%.
A student divides by the new value instead of the original. What is wrong?
Always use original value.
Percentage change is always based on the original value.
A price increases from £20 to £25. Find the percentage increase.
Increase = 5.
5 ÷ 20 × 100 = 25%.
A value changes from 100 to 90. What is the percentage change?
Decrease = 10.
10 ÷ 100 × 100 = 10% decrease.
A value increases from 200 to 260. Find the percentage increase.
Increase = 60.
60 ÷ 200 × 100 = 30%.
Which formula finds percentage change?
Use original value.
Correct formula: (change ÷ original) × 100.
A value decreases from 120 to 96. Find the percentage decrease.
Decrease = 24.
24 ÷ 120 × 100 = 20%.
Higher
Higher Practice
Solve percentage change and reverse percentage problems.
A price increases by 20% to £120. What was the original price?
Use multiplier 1.2.
Original = 120 ÷ 1.2 = £100.
A value increases by 25% to 150. Find the original value.
Use multiplier 1.25.
150 ÷ 1.25 = 120.
A price decreases by 10% to £90. What was the original price?
Use multiplier 0.9.
Original = 90 ÷ 0.9 = £100.
A value decreases by 20% to 64. Find the original value.
Use multiplier 0.8.
64 ÷ 0.8 = 80.
A value increases from 50 to 75. What is the percentage increase?
Increase = 25.
25 ÷ 50 × 100 = 50%.
A value decreases from 200 to 150. Find the percentage decrease.
Decrease = 50.
50 ÷ 200 × 100 = 25%.
A student calculates percentage change using the new value. Why is this incorrect?
Original is always base.
Percentage change is always based on original value.
A price increases by 15% to £230. Find the original price.
Use multiplier 1.15.
230 ÷ 1.15 = £200.
A value halves. What is the percentage decrease?
Half means 50% reduction.
Halving is a 50% decrease.
A value increases by 10% to 330. Find the original value.
Use multiplier 1.1.
330 ÷ 1.1 = 300.
Games
Practise this topic with interactive games.
Games coming soon.