Percentage change is how much a value has changed (increased or decreased) from its original amount. It is common in GCSE Maths exam questions, such as exercises on price, population, and data sets. To calculate a percentage change, you need to divide the change by the original value, and multiply by 100. A "successive change" is multiple percentage changes back-to-back. A "reverse percentage" means finding the original value from the change after a given percentage has been applied.
This guide explains the formula for percentage change. You will learn how to calculate a change in percentage, both for calculator and non-calculator questions. We will also explore successive and reverse percentage changes. Quiz questions are included to test your understanding.
This article is suitable for GCSE Maths revision across all major exam boards, including AQA. If you need further help, TeachTutti has qualified GCSE Maths tutors who can teach you in person or online.
Calculate the percentage change
A percentage change calculates the amount a value changes after the percentage is applied. The rule is:
Percentage change = (Change / Original) x 100
Put simply, the change is the new value minus the original value. A positive result means the value has increased. A negative result means a percentage decrease. Remember to always calculate using the original value.
Example 1:
- A price has increased from £8 to £10. The change is 2 (10 - 8).
- Divide by the original: 2 / 8 = 0.25.
- Multiply by 100 to get 25%. This means there has been a 25% increase.
Example 2:
- A class size drops from 30 to 27. The change is -3 (27 - 30).
- Divide by the original: -3 / 30 = -0.1.
- Multiply by 100 to get -10%. This means there has been a 10% decrease (the minus sign shows the direction of the percentage change).
Always leave rounding until the end. This is important in non-calculator questions, where seeing a simple fraction can save time. For example, 3/30 could be more easily calculated as 1/10. If you need to use units, such as kilometres or pounds, be sure to include them so your answer matches the context.
1
The price of a jacket changes from £40 to £46. What is the percentage change?
Worked examples
Using a calculator
Shop discount
A jumper costs £56 and is reduced to £47.60:
- The change is -8.40 (47.60 - 56). This means it is a decrease.
- Divide by the original price: -8.40 / 56 = -0.15.
- If you multiply by 100, the percentage decrease is 15%.
- In a calculator paper, enter the value directly and only round at the end if required.
Successive change example (price rise, then discount)
A bike costs £200. It increases by 10% and if reduced by 10% the following month:
- The price is £220 after the price increase (200 x 1.10).
- The price is £198 after the price reduction (220 x 0.90).
- This means the overall change is -1% (198 - 200 = -2. Now -2 / 200 = -0.01).
- This shows that two equal percentage changes in opposite directions don't cancel to zero. This is because each percentage is applied to a different base.
Reverse percentage example (find the original from a final amount)
A laptop is £540 after a discount is applied of 10%:
- The sale price is 90% of the original. This means the calculation is 540 = 0.90 x original.
- Divide by 0.90 to find the starting price: original = 540 / 0.90 = £600.
- To write the discount as a percentage change from the original, do the following: 540 - 600 = -60 -> -60 / 600 = -0.10. This means it is a 10% decrease.
- If you need to work backwards, multiplying is the fastest method (e.g. 0.90 for a 10% decrease, or 1.10 for a 10% increase).
Without a calculator
Exam test scores
A student's mark on a test paper changed from 35 to 42. The total mark is 50:
- The change is 7 (42 - 35).
- Divide by the original: 7/35 simplifies to 1/5, which equals 0.2.
- Multiply by 100 to get 20%. This means it's a 20% increase.
- Always show the fraction simplification step. It keeps the arithmetic neat and avoids rounding errors.
Successive and reverse percentage change
Successive changes
An exam question may expect you to apply more than one percentage change in a row. For example, a rise in value followed by a drop. Use a multiplier for each step and work step-by-step.
Let's call the object x:
- If you need to increase the percentage of x, multiply by 1 + x / 100.
- If you need to decrease the percentage of x, multiply by 1 - x / 100.
- Remember that the second change is applied to a new value. This means identical percentages in the opposite direction will not cancel each other out.
Example 1
A phone costs £300. The price increases 12% in April and decreases 12% in May:
- The price is £336 in April (£300 x 1.12).
- The price drops £295.68 in May (£336 x 0.88).
- The overall change from the original price is -4.32 (295.68 - 300).
- The overall percentage change is -1.44% (-4.32 / 300 = -0.0144 x 100 = -1.44).
- The increase of 12% and the decrease of 12% don't cancel each other out because the second percentage change is taken from a larger value.
Example 2
A bike is £200. The cost rises 5%, and then rises another 5%:
- Using multipliers, the new value is £220.50 (200 x 1.05 x 1.05 can be simplified to 200 x 1.1025).
- The overall price increase is 10.25% (220.50 - 200 = 20.50, and 20.50 / 200 = 0.10252. Multiplied by 100 is 10.25).
Reverse changes
A reverse percentage means working backwards from the given value to find the original value before the percentage change was applied.
For example:
- The price is £72 after a 20% increase. This means £72 represents 120% (1.20) of the original price.
- You can undo the change by dividing by the multiplier: 72 / 1.20 = £60.
- If the final amount is after a percentage decrease, divide by the decrease multiplier. For example, if the cost is £45 after a 25% discount, this means £45 is 75% (multiplier 0.75) of the original. The original price is £60 (45 / 0.75).
When deciding if you need to multiply or divide, check if you need to take a step forward or back. Taking a step forward means using the multiplier, such as 1.2 to add 20%. Going back means dividing by the same amount. Round the final value at the end, unless the question requires a certain level of accuracy.
2
A bike costs £308 after a 12% decrease. What was the original price?
Calculate percentage - Quiz questions
Percentage increase
3
A population changes from 12,000 to 13,080. What is the percentage change?
4
A hoodie costs £48. The price increases 15% and then falls to 10%. What is the percentage change from the original price?
Percentage decrease
5
The class size changes from 32 to 28. What is the percentage change?
6
A mobile phone costs £200. The price increases to 8% and then drops to 12%. What is the percentage change from the original price?
Reverse percentage
7
A laptop costs £780 after an increase of 30%. What was the original price?
8
A phone costs £504 after a 12% price increase. What was the original price?
Final thoughts - Calculate percentage change
A question on percentage change expects you to compare the change with the original, convert this to a percentage, and then show the increase/decrease in value. Always choose the quickest path, such as using a simpler fraction if possible (e.g. 1/5 instead of 7/35), or using a multiplier when the question asked you to "increase by 12%" (1.12) or "decrease by 20%" (0.80). If you are confronted with a reverse question, divide by the multiplier to return to the original value.
For further reading, you can test yourself with past paper questions on percentage change by MathsGenie. If you're a visual learning, you may enjoy playing the Divided Islands Maths game by BBC Bitesize to cement your understanding of percentage change and other maths topics.
If you need support with this or related topics, TeachTutti has top GCSE Maths tutors who can provide personalised help, such as preparing revision cards. Every tutor has an enhanced DBS check.
