A percentage multiplier is a single decimal you multiply by to apply a percentage change in one step: increasing by 20% means multiplying by 1.20; decreasing by 15% means multiplying by 0.85. Multipliers make compound percentage problems and reverse percentage calculations far more efficient than the step-by-step method.
What is a percentage multiplier?
When something increases by p%, you multiply by 1 + p/100. When it decreases by p%, you multiply by 1 − p/100. The result is always a single decimal greater than 0.
Multipliers for common percentage changes:
| Change | Multiplier | Calculation |
|---|---|---|
| 10% increase | 1.10 | 1 + 0.10 |
| 25% increase | 1.25 | 1 + 0.25 |
| 5% increase | 1.05 | 1 + 0.05 |
| 100% increase | 2.00 | 1 + 1.00 |
| 10% decrease | 0.90 | 1 − 0.10 |
| 20% decrease | 0.80 | 1 − 0.20 |
| 3.5% decrease | 0.965 | 1 − 0.035 |
| VAT at 20% | 1.20 | 1 + 0.20 |
A multiplier between 0 and 1 represents a decrease; a multiplier greater than 1 represents an increase.
How do you apply a single percentage multiplier?
New value = Original value × multiplier
Example 1 — Increase: A jacket costs £85. It is reduced in a sale by 30%. Find the sale price.
- Multiplier:
1 − 0.30 = 0.70 - Sale price:
£85 × 0.70 = **£59.50** ✓
Example 2 — Decrease: A car is worth £12 500. After one year it depreciates by 18%. Find its value after one year.
- Multiplier:
1 − 0.18 = 0.82 - Value:
£12 500 × 0.82 = **£10 250** ✓
Example 3 — Compound interest (two years): £3 000 is invested at 4% per annum compound interest. Find the value after 2 years.
- Year 1:
£3 000 × 1.04 = £3 120 - Year 2:
£3 120 × 1.04 = £3 244.80 - Or in one step:
£3 000 × 1.04² = £3 000 × 1.0816 = **£3 244.80** ✓
How do you use multipliers for successive percentage changes?
The great power of multipliers is that successive changes multiply together:
$$\text{Final value} = \text{Original} \times m_1 \times m_2 \times m_3 \times \cdots$$
Example: A price increases by 10%, then decreases by 10%. What is the overall percentage change?
Combined multiplier: 1.10 × 0.90 = 0.99
This is a multiplier of 0.99, which represents a 1% decrease overall — not zero change, as many students expect. The increase and decrease do not cancel exactly.
Example: An investment grows by 5% in year 1 and 8% in year 2. Overall multiplier: 1.05 × 1.08 = 1.134. This is a 13.4% increase over two years (not simply 5 + 8 = 13%).
How do you find the percentage change from a multiplier?
If you have been told or can calculate the multiplier:
$$\text{Percentage change} = (\text{multiplier} - 1) \times 100%$$
- Multiplier 1.134 →
(1.134 − 1) × 100 = 13.4%increase. - Multiplier 0.85 →
(0.85 − 1) × 100 = −15%→ 15% decrease.
How do you reverse a percentage change?
To find the original value before a percentage change was applied, divide by the multiplier:
$$\text{Original value} = \frac{\text{New value}}{\text{multiplier}}$$
Example: After a 20% increase, an item costs £96. What was the original price?
- Multiplier for 20% increase:
1.20 - Original price:
£96 ÷ 1.20 = **£80** ✓
Why not find 20% of £96 and subtract? That would give £96 − £19.20 = £76.80 — wrong! The 20% was applied to the original, not to £96. Always divide by the multiplier to reverse.
What mistakes do students make?
- Reversing by finding the percentage of the new value. To reverse a 20% increase, divide by 1.20 — do not subtract 20% of the new (already increased) value.
- Adding successive percentages. A 5% increase and an 8% increase is not a 13% increase. Multiply the multipliers:
1.05 × 1.08 = 1.134, so it is a 13.4% increase. - Using the wrong multiplier for a decrease. A 30% decrease uses multiplier 0.70, not 1.30 (that would be a 30% increase). Always check: decrease → multiplier < 1.
- Misreading "decrease by 100%". A 100% decrease means the multiplier is 0 — the value becomes nothing. A 100% increase means the multiplier is 2 — the value doubles.
Frequently asked questions
What is the multiplier for a 2.5% increase?
A 2.5% increase adds 2.5/100 = 0.025 to 1. The multiplier is 1.025. So a price of £200 increased by 2.5% becomes £200 × 1.025 = £205.
How do you work out n years of compound interest using a multiplier?
For compound interest at rate r% per year over n years: Final value = Principal × (1 + r/100)^n. The multiplier (1 + r/100) is applied n times — equivalent to raising it to the power n. This is the same as the compound interest formula A = P(1 + r/100)^n.
If an item goes up by 15% then down by 15%, what is the overall change?
Combined multiplier: 1.15 × 0.85 = 0.9775. This is less than 1, so there is an overall decrease. Percentage change: (0.9775 − 1) × 100 = −2.25% — a decrease of 2.25%. The increases and decreases do not cancel because they apply to different base values.
Can a multiplier be greater than 2?
Yes. A 150% increase gives multiplier 1 + 1.50 = 2.50. A 200% increase gives multiplier 3.00 (the value trebles). There is no upper limit on the multiplier, but in practice GCSE questions rarely use multipliers above 2.
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