Percentage Cheat Sheet
Bookmark this page. Every percentage shortcut you'll ever need.
Quick Mental Math
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PercentageAmountTrick
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Mental Math Shortcuts for Percentages
The master key: 10% is just moving the decimal point one place left. Everything else builds from there.
10% of anything = move the decimal left one place
5% = half of 10% | 15% = 10% + 5% | 20% = 10% × 2
5% = half of 10% | 15% = 10% + 5% | 20% = 10% × 2
The "Flip Trick"
8% of 25 = 25% of 8 = 2. You can always swap the percentage and the number — whichever is easier to calculate. This works because multiplication is commutative: a × b = b × a.
| Hard Way | Easy Way | Answer |
|---|---|---|
| 8% of 50 | 50% of 8 | 4 |
| 4% of 75 | 75% of 4 | 3 |
| 12% of 25 | 25% of 12 | 3 |
| 6% of 50 | 50% of 6 | 3 |
| 3% of 200 | 200% of 3 | 6 |
Common Percentages to Memorize
| Fraction | Percentage | Decimal |
|---|---|---|
| 1/2 | 50% | 0.50 |
| 1/3 | 33.3% | 0.333 |
| 1/4 | 25% | 0.25 |
| 1/5 | 20% | 0.20 |
| 1/8 | 12.5% | 0.125 |
| 1/10 | 10% | 0.10 |
| 2/3 | 66.7% | 0.667 |
| 3/4 | 75% | 0.75 |
Percentage Formulas Quick Reference
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X/100 | 10% of 80 = 8 |
| X is what % of Y? | (X/Y) × 100 | 8 is 10% of 80 |
| % change | (New−Old)/Old × 100 | 80→88 = +10% |
| % off final price | Price × (1 − %/100) | $80 at 10% off = $72 |
| Original before X% off | Sale price ÷ (1 − %/100) | $72 was $80 before 10% off |
| Reverse: after X% gain | Result ÷ (1 + %/100) | $88 before 10% gain = $80 |
Frequently Asked Questions
Start with 10% (move the decimal left). Then combine: 15% = 10% + half of 10%. 20% = 10% doubled. 5% = half of 10%. 1% = move decimal two places left. You can build any percentage from these building blocks.
Percentage change = ((New Value − Old Value) / Old Value) × 100. Positive result = increase, negative = decrease. Example: $80 to $72 = (72−80)/80 × 100 = −10%.
Because the second 10% is calculated on the already-reduced amount. $100 → 10% off = $90 → 10% increase = $99 (not $100). The base changes between operations. You're always 1% short.
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