Increase an amount by a given percentage using a multiplier (e.g. +30% → ×1.30)
Decrease an amount by a given percentage using a multiplier (e.g. −20% → ×0.80)
Apply percentage changes to real-life contexts: VAT, discounts, pay rises
Calculate successive percentage changes by multiplying multipliers in sequence
Real-World Applications
Retail: Applying discounts and price rises — a 25% off sale means multiplying by 0.75, while a 20% VAT increase means multiplying by 1.20.
Finance: Investment growth and inflation are calculated as percentage increases — money growing at 5% per year is multiplied by 1.05 each year.
Employment: Salary increases and deductions such as pension contributions are expressed as percentages — essential for understanding your take-home pay.
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To increase an amount by a percentage, use a multiplier. Add the percentage (as a decimal) to 1. This is one step and is ideal with a calculator.
Increase by r% → multiply by \(\left(1 + \dfrac{r}{100}\right)\) e.g. increase by 30% → multiply by 1.30
Example 1 — Increase £240 by 30%
Method A: Find and add
Step 1
30% of £240 = 0.30 × 240 = £72
Step 2
New amount = £240 + £72 = £312
Method B: Multiplier (faster)
Step 1
Multiplier = 1 + 0.30 = 1.30
Step 2
£240 × 1.30 = £312
Example 2 — A salary of £24,500 increases by 4%. What is the new salary?
Step 1
Multiplier = 1 + 0.04 = 1.04
Step 2
£24,500 × 1.04 = £25,480
Example 3 — A price of £85 has 20% VAT added. What is the new price?
Step 1
VAT is an increase: multiplier = 1 + 0.20 = 1.20
Step 2
£85 × 1.20 = £102
Tip: The multiplier method needs just one calculation. Add 1 to the percentage as a decimal: 35% increase → 1.35. Always faster with a calculator.
✓ Quick Check 1 — Percentage Increase
Question 1 of 10
Percentage Decrease
Percentage decrease works the same way but the multiplier is less than 1. Subtract the decimal from 1 instead of adding it.
Decrease by r% → multiply by \(\left(1 - \dfrac{r}{100}\right)\) e.g. decrease by 20% → multiply by 0.80
Example 4 — A coat is £160. It has 15% off. What is the sale price?
Step 1
Decrease multiplier = 1 − 0.15 = 0.85
Step 2
£160 × 0.85 = £136
Example 5 — A car was £12,000. It decreases in value by 18%. New value?
Step 1
Multiplier = 1 − 0.18 = 0.82
Step 2
£12,000 × 0.82 = £9,840
Example 6 — A TV was £600. It is reduced by 35%. What is the sale price?
Step 1
Multiplier = 1 − 0.35 = 0.65
Step 2
£600 × 0.65 = £390
Warning: Increase → multiplier > 1. | Decrease → multiplier < 1. Never confuse the two — check your answer makes sense.
✓ Quick Check 2 — Percentage Decrease
Question 1 of 10
Successive Percentage Changes
When two or more percentage changes happen one after another, apply the multipliers in sequence. You cannot simply add the percentages — you must multiply the multipliers together.
Common mistake: A 10% increase then a 10% decrease does NOT equal 0% overall. You must multiply: 1.10 × 0.90 = 0.99 (a 1% net decrease).
Example 7 — £200 increases by 10%, then decreases by 10%. Final price?
Example 9 — A house worth £180,000 rises 5% per year for 2 years. Final value?
Step 1
Year 1: £180,000 × 1.05 = £189,000
Step 2
Year 2: £189,000 × 1.05 = £198,450
Note
Combined multiplier: 1.05 × 1.05 = 1.1025 (a 10.25% increase, not 10%)
Key rule: For successive changes, multiply the multipliers. Never add or subtract percentages directly. Two 10% increases = 1.10 × 1.10 = 1.21 = 21% increase overall.
✓ Quick Check 3 — Successive Percentage Changes
Question 1 of 10
Practice: Percentage Increase and Decrease
Enter your answers and click Check to see how you did.
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Question
Answer
Result
1
Increase £300 by 20%
2
Decrease £200 by 15%
3
Add 20% VAT to £45
4
25% off £160
5
Salary £30,000 up 3%
6
10% then 10% increase on £100
7
20% off then 10% off £500
8
Decrease £750 by 8%
9
Increase £80 by 15%
10
Decrease £450 by 12%
⚠ Things to Watch Out For
Calculating the percentage of the INCREASE, not the original: A 20% increase on £80: find 20% of £80 (=£16), then add to £80 (=£96). Don't find 20% of the final amount.
Forgetting to add/subtract after finding the percentage: Find the percentage change, then APPLY it. Many students find 20% = £16 and stop, forgetting to add it to get £96.
Multiplier shortcuts: +20% → ×1.20. −15% → ×0.85. These are quicker and less error-prone than the two-step method.
Successive percentage changes don't add: +10% then −10% does NOT return to the original. 100 × 1.1 × 0.9 = 99, not 100. Apply changes one at a time.
Percentage decrease below zero: A 100% decrease gives zero. A percentage decrease cannot exceed 100% (you can't decrease by more than the whole amount).