How to Find Percentages: A Complete Guide
Percent means "per hundred." 25% = 25⁄100 = 0.25. Here are the three main types of percentage problems and how to solve them.
Type 1: What is X% of Y?
Convert the percent to a decimal (divide by 100), then multiply.
Example: What is 20% of 80?
0.20 × 80 = 16
Answer: 16
Example: What is 15% of 200?
Answer: 30
Type 2: What percent is X of Y?
Divide X by Y, then multiply by 100.
Example: What percent is 12 of 48?
0.25 × 100 = 25%
Answer: 25%
Example: What percent is 7 of 28?
0.25 × 100 = 25%
Type 3: X is Y% of what number?
Divide X by the decimal form of the percent.
Example: 24 is 30% of what number?
24 ÷ 0.30 = 80
Answer: 80
Check: 30% of 80 = 0.30 × 80 = 24 ✓
Percent increase and decrease
Percent change = (new − old) ÷ old × 100
Example: A price goes from $50 to $60. What's the percent increase?
0.20 × 100 = 20%
Answer: 20% increase
Quick reference
- X% of Y → 0.0X × Y
- X is what % of Y → (X ÷ Y) × 100
- X is Y% of what → X ÷ 0.0Y
Common mistakes
Moving the decimal wrong: To convert a percent to a decimal, move the decimal point two places to the LEFT: 25% = 0.25, not 2.5.
Confusing "of" with addition: "25% of 80" means 0.25 × 80 = 20. It does not mean 25 + 80.
Percent increase vs. percent of: A 20% increase on 50 is 50 + (0.20 × 50) = 60, not 0.20 × 50 = 10.
More examples
Example: What is 15% of 200?
0.15 × 200 = 30
Answer: 30
Example: A shirt costs $40 and is 30% off. What's the sale price?
Sale price = $40 − $12 = $28
Example: Convert 3/8 to a percent.
0.375 × 100 = 37.5%
Practice problems
1. What is 40% of 250?
Show answer
2. A test has 60 questions and you got 45 right. What percent?
Show answer
3. Convert 7/20 to a percent.
Show answer
Strengthen your number sense with Arithmia — a cozy math game that builds fluency through puzzle play.