Percentage multipliers provide the fastest and most reliable way to increase or decrease an amount by a given percentage. Instead of calculating the percentage separately and adding or subtracting it, you simply multiply by a single decimal number. This one-step method is essential for GCSE Maths, especially for compound interest, depreciation, repeated changes and reverse percentage problems. It is tested at both Foundation and Higher tier across AQA, Edexcel and OCR. This guide explains how multipliers work and shows you how to apply them confidently.
What Are Percentage Multipliers?
A percentage multiplier is a single decimal number that you multiply by to apply a percentage increase or decrease in one step.
Key Formulas
Percentage increase:
For example, a 15% increase uses the multiplier 1 + 0.15 = 1.15.
Percentage decrease:
For example, a 15% decrease uses the multiplier 1 - 0.15 = 0.85.
Applying the multiplier:
Repeated percentage changes:
Where n is the number of times the change is applied.
Finding the original after a percentage change
If you know the final amount after a percentage change, divide by the multiplier to find the original.
Step-by-Step Method
- Read the question and identify the percentage and whether it is an increase or decrease.
- Calculate the multiplier: add the decimal to 1 for an increase, subtract it from 1 for a decrease.
- Multiply the original amount by the multiplier.
- For repeated changes, raise the multiplier to the power of the number of repetitions.
- For reverse problems, divide the final amount by the multiplier.
Worked Example 1 — Foundation Level
Question: Increase £240 by 20%.
Working:
Multiplier = 1 + 0.20 = 1.20
New amount = 240 x 1.20 = £288
Answer: £240 increased by 20% is £288.
Worked Example 2 — Higher Level
Question: A laptop costs £600. It is reduced by 12% in a sale. An extra 5% is then taken off the sale price. What is the final price?
Working:
Step 1: First reduction multiplier = 1 - 0.12 = 0.88
Step 2: Second reduction multiplier = 1 - 0.05 = 0.95
Step 3: Combined multiplier = 0.88 x 0.95 = 0.836
Step 4: Final price = 600 x 0.836 = £501.60
Note: A 12% decrease followed by a 5% decrease is NOT the same as a 17% decrease. The second percentage is applied to the already-reduced price.
Answer: The final price is £501.60.
Worked Example 3 — Exam Style
Question: After a 25% increase, the price of a ticket is £30. What was the original price?
Working:
Multiplier for 25% increase = 1.25
Original price = 30 / 1.25 = £24
Check: 24 x 1.25 = 30 ✓
Answer: The original price was £24.
Common Mistakes
- Adding percentages for successive changes. A 10% increase then a 10% decrease does NOT return to the original. The multipliers are 1.10 then 0.90, giving a combined multiplier of 0.99, which is a 1% overall decrease.
- Using the wrong multiplier direction. A 30% decrease is 0.70 (not 1.30). A 30% increase is 1.30 (not 0.30).
- Multiplying by the percentage instead of the multiplier. To increase by 8%, multiply by 1.08, not by 0.08 or by 8.
- Subtracting instead of dividing for reverse problems. To find the original price before a 20% increase, divide by 1.20. Do NOT subtract 20% from the final price.
Exam Tips
- Always write down your multiplier — it earns a method mark and reduces the chance of error.
- For compound interest and depreciation, use the multiplier raised to a power. This is much faster than calculating year by year.
- If two successive percentage changes are applied, multiply their individual multipliers together to get the combined multiplier.
- For reverse percentage questions, clearly state "divide by the multiplier" to show the examiner your method.
- Know common multipliers by heart: 10% increase = 1.10, 25% decrease = 0.75, VAT at 20% = 1.20.
Practice Questions
Q1 (Foundation): Decrease £350 by 30%.
Q2 (Foundation): After a 15% decrease, a coat costs £68. Find the original price.
Q3 (Higher): A house increases in value by 6% each year. It is currently worth £200,000. What will it be worth in 4 years?
Practise percentage multiplier questions with instant feedback free on GCSEMathsAI.
Related Topics
- Percentages: Increase and Decrease
- Reverse Percentages
- Compound Interest and Depreciation
- Percentage Change
Summary
- A percentage increase multiplier = 1 + percentage/100 (e.g., 15% increase = 1.15).
- A percentage decrease multiplier = 1 - percentage/100 (e.g., 15% decrease = 0.85).
- New amount = Original x Multiplier. This is a single-step calculation.
- For repeated changes, raise the multiplier to the power of the number of repetitions.
- Successive percentage changes are NOT additive. Multiply the individual multipliers together.
- To find the original after a percentage change, divide the final amount by the multiplier.
- The multiplier method is the foundation for compound interest, depreciation and reverse percentage problems.
Test your understanding
5 quick MCQs to identify any misconceptions on this topic.
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