What a percentage represents
Percent means “per hundred.” The statement 35% can be written as the fraction 35/100 or the decimal 0.35. These are three ways to express the same proportion.
Method 1: Find a percentage of a number
Use this method when you know the percentage and the number. Multiply the number by the percentage, then divide by 100.
Number × Percentage ÷ 100
Example: What is 18% of 250?
- Multiply 250 by 18: 250 × 18 = 4,500.
- Divide by 100: 4,500 ÷ 100 = 45.
18% of 250 is 45.
Method 2: Find what percent one number is of another
Use this method when you know the part and the whole. Divide the part by the whole, then multiply by 100.
Part ÷ Whole × 100
Example: 24 is what percent of 80?
- Divide the part by the whole: 24 ÷ 80 = 0.3.
- Multiply by 100: 0.3 × 100 = 30%.
24 is 30% of 80.
Method 3: Find the whole from a part and a percentage
If 30 is 15% of an unknown number, divide the part by the decimal percentage.
Whole = Part ÷ (Percentage ÷ 100)
30 ÷ 0.15 = 200
The whole is 200.
Convert decimals and fractions to percentages
Decimal to percentage
Multiply by 100. The decimal 0.425 becomes 42.5%.
Fraction to percentage
Divide the numerator by the denominator, then multiply by 100. The fraction 3/8 becomes 0.375, or 37.5%.
Common mistakes
- Swapping the part and the whole.
- Forgetting to divide or multiply by 100.
- Rounding an intermediate step too early.
- Treating percentage points as percentage change.