Sheet № 236 · Foundation + Higher · AQA · Edexcel · OCR
Percentage Increase and Decrease Multipliers –
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, depreci
§Key definitions
Question:
Increase £240 by 20%.
Answer:
£240 increased by 20% is £288.
Check:
24 x 1.25 = 30 ✓
Q1 (Foundation):
Decrease £350 by 30%.
Q2 (Foundation):
After a 15% decrease, a coat costs £68. Find the original price.
§Formulas to memorise
Multiplier = 1 + (percentage / 100)
Multiplier = 1 - (percentage / 100)
New amount = Original amount x Multiplier
Final amount = Original amount x Multiplier^n
Original amount = Final amount / Multiplier
Percentage increase:: [FORMULA: Multiplier = 1 + (percentage / 100)]
Percentage decrease:: [FORMULA: Multiplier = 1 - (percentage / 100)]
Applying the multiplier:: [FORMULA: New amount = Original amount x Multiplier]
Repeated percentage changes:: [FORMULA: Final amount = Original amount x Multiplier^n]
Read the question — and identify the percentage and whether it is an increase or decrease.
Worked example
Increase £240 by 20%.
Working:
⚠ 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.