How Percentage Calculations Work
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin 'per centum', meaning 'by the hundred'. Percentages are used everywhere — from calculating discounts and tax rates to expressing test scores and investment returns. There are three core percentage problems: finding X% of Y, finding what percentage X is of Y, and finding the percentage change between two values.
Three Core Calculations Explained
1. What is 15% of $85? → 85 × 0.15 = $12.75. 2. 45 is what percent of 180? → (45 ÷ 180) × 100 = 25%. 3. A price went from $40 to $52 — what is the percentage increase? → ((52 − 40) ÷ 40) × 100 = 30%.
Common Percentage Quick Reference
| Percentage | Fraction | Decimal | Quick Trick |
|---|
| 10% | 1/10 | 0.10 | Divide by 10 |
| 20% | 1/5 | 0.20 | Divide by 5 |
| 25% | 1/4 | 0.25 | Divide by 4 |
| 33.3% | 1/3 | 0.333 | Divide by 3 |
| 50% | 1/2 | 0.50 | Divide by 2 |
| 75% | 3/4 | 0.75 | Multiply by 0.75 |
