Formulas
A percent is one hundredth: 15% is 15/100 = 0.15. Each card above uses one of these formulas.
- Percent of a number: X% of Y = Y × X / 100. Example: 15% of 200 is 30.
- What percent X is of Y: X / Y × 100. Example: 30 is 25% of 120.
- Percentage change: (new − old) / old × 100. From 80 to 100 is a 25% increase; from 100 back to 80 is a 20% decrease.
- Add a percentage: Y × (1 + X / 100). Subtract: Y × (1 − X / 100).
- Whole from a part: if 45 is 15% of a number, the number is 45 / 15 × 100 = 300.
- Percentage included in a total: part = total × X / (100 + X). A price of 1200 that includes 20% tax contains 200 of tax and 1000 without it.
Common mistakes
Adding 20% and then subtracting 20% does not bring you back: 100 + 20% = 120, but 120 − 20% = 96. To remove a percentage that was added, use the last card or divide by 1.2.
A change from 4% to 5% is one percentage point but a 25% relative increase. Both are correct; they answer different questions.