Changing an amount by a percent
Prices go up, populations grow, and sales take money off. To change an original amount by a percent:
| Change | Two-step way | One-step way |
|---|---|---|
| Percent increase | Find the percent, add it on | Multiply by (1 + rate) |
| Percent decrease | Find the percent, take it off | Multiply by (1 − rate) |
Increase: two steps
Example: Increase $60 by 15%.
- 15% of 60 = 0.15 × 60 = $9
- 60 + 9 = $69
Increase: one step with a multiplier
100% + 15% = 115% = 1.15
60 × 1.15 = $69
Decrease: two steps
Example: Decrease 80 kg by 25%.
- 25% of 80 = 20
- 80 − 20 = 60 kg
Decrease: one step
100% − 25% = 75% = 0.75
80 × 0.75 = 60 kg
Multipliers table
| Change | Multiplier |
|---|---|
| +5% | 1.05 |
| +13% (Ontario HST) | 1.13 |
| +50% | 1.5 |
| +100% (double) | 2 |
| −10% | 0.9 |
| −30% | 0.7 |
| −50% (half) | 0.5 |
Markup
Stores buy products and add a markup to set the selling price. A store buys a jacket for $40 and marks it up 60%: 40 × 1.6 = $64.
Successive changes
A 10% increase followed by a 10% decrease does not bring you back to the start:
- $100 × 1.10 = $110
- $110 × 0.90 = $99
The second change is a percent of a different (bigger) amount.
Worked examples
Example 1: A town of 12,000 grows by 8%. New population?
12,000 × 1.08 = 12,960.
Example 2: A $250 bike is reduced by 20%. Sale price?
250 × 0.8 = $200.
Example 3: A salary of $45,000 rises 3%. New salary?
45,000 × 1.03 = $46,350.
Common mistakes
- Stopping after step 1 and giving only the increase or decrease ($9 instead of $69).
- Using 0.15 instead of 1.15 for an increase.
- Expecting equal up-and-down percents to cancel.
Try it yourself
- Increase 50 by 20%.
- Decrease 90 by 10%.
- What multiplier gives a 35% decrease?
- A $30 item has 13% tax added. Total?
- A price of $200 rises 25%, then falls 20%. Final price?
Answers: 1) 60 2) 81 3) 0.65 4) $33.90 5) $200
Quick recap
- Percent increase: × (1 + rate). Percent decrease: × (1 − rate).
- The result is the new amount.
- Successive percent changes don’t simply add.