Mental Math for Percentages
Almost any percentage can be broken into combinations of 10%, 5%, 1%, and 50%. Once you know these anchor values, the rest is arithmetic.
The anchor values
| Percentage | How to find it | Example: 240 |
|---|---|---|
| 50% | Divide by 2 | 120 |
| 25% | Divide by 4 | 60 |
| 10% | Move decimal left one place | 24 |
| 5% | Half of 10% | 12 |
| 1% | Move decimal left two places | 2.4 |
| 0.5% | Half of 1% | 1.2 |
The 1% building block
Every percentage is a multiple of 1%. To find 1% of a number, simply divide by 100 (move the decimal point two places left). Then scale up:
- 7% of 350: 1% = 3.50, so 7% = 3.50 × 7 = 24.50
- 13% of 200: 1% = 2, so 13% = 2 × 13 = 26
- 3% of 90: 1% = 0.90, so 3% = 0.90 × 3 = 2.70
The symmetry trick
Percentages commute: X% of Y = Y% of X. This is useful when one of the two numbers is a “round” percentage.
- 4% of 25? Swap: 25% of 4 = 1 (much easier)
- 8% of 50? Swap: 50% of 8 = 4
- 35% of 20? Swap: 20% of 35 = 7 (move decimal: 10% of 35 = 3.5, doubled = 7)
Splitting awkward percentages
Break any percentage into sums of round values:
- 15% = 10% + 5%
- 17.5% = 10% + 5% + 2.5% (or: 10% + 7.5%, where 7.5% = half of 15%)
- 22% = 20% + 2% (where 20% = 2 × 10%)
- 37.5% = 25% + 12.5% (where 12.5% = half of 25%)
Worked example: 17.5% tip on a $48 bill
- 10% of 48 = 4.80
- 5% of 48 = 2.40 (half of 10%)
- 2.5% of 48 = 1.20 (half of 5%)
- 17.5% = 4.80 + 2.40 + 1.20 = $8.40
Quick discount checks
When shopping, quickly estimate what you’ll actually pay after a discount:
- 10% off: subtract the first digit (or first two digits for hundreds). $79 − 10% ≈ $71
- 20% off: find 10%, double it, subtract. $79: 10% = 7.90, ×2 = 15.80, $79 − $15.80 = $63.20
- 25% off: divide by 4 and subtract. $80 ÷ 4 = 20, $80 − $20 = $60
- 33% off: divide by 3 and subtract. $90 ÷ 3 = 30, $90 − $30 = $60
- 50% off: divide by 2. $84 ÷ 2 = $42
Working backwards from a sale price
If you know the sale price and the discount, you can recover the original: divide the sale price by (1 − discount as a decimal).
- Sale price $68, 20% off: original = 68 ÷ 0.80 = $85
- Sale price $75, 25% off: original = 75 ÷ 0.75 = $100
Mentally: “What number, when I take a fifth away, leaves me with 68?” — the same as finding 68 × 5/4 = 85.
Practice problems
Try these without a calculator, then verify with the Percentage Of Calculator:
- 15% of 60
- 8% of 250
- 22% of 50
- 35% of 80
- 17.5% of $120 (a restaurant bill)
Answers
- 9 (10% = 6, 5% = 3)
- 20 (1% = 2.50, ×8)
- 11 (10% = 5, 20% = 10, 2% = 1)
- 28 (25% = 20, 10% = 8, 35% = 28)
- $21 (10% = $12, 5% = $6, 2.5% = $3)
Related tools
- Percentage Of Calculator — verify your mental calculations
- Tip Calculator — restaurant tipping made instant
- Discount Calculator — find sale prices instantly