Basic Percentages
What Is a Percentage?
The word "percentage" comes from "per cent," which literally means "out of 100." So 50% means 50 out of 100, which is the same as the fraction ½ or the decimal 0.5. Percentages are a universal way to express parts of a whole, making it easy to compare amounts across different contexts.
Percentage: A fraction expressed with a denominator of 100. Any fraction, decimal, or ratio can be converted to a percentage, and vice versa.
Key Conversions
- Fraction to Percentage: Find an equivalent fraction with denominator 100, then the numerator is the percentage.
Example: 3/4 = 75/100 = 75%
- Decimal to Percentage: Multiply by 100
Example: 0.25 × 100 = 25%
- Percentage to Decimal: Divide by 100
Example: 45% ÷ 100 = 0.45
- Percentage to Fraction: Write as a fraction out of 100, then simplify
Example: 40% = 40/100 = 2/5
Quick Reference: Common Percentages
50% = 0.5 = 1/2
25% = 0.25 = 1/4
75% = 0.75 = 3/4
10% = 0.1 = 1/10
20% = 0.2 = 1/5
33⅓% = 0.333... = 1/3
Finding a Percentage of an Amount (Without Calculator)
Some percentages are easy to work with because they have simple fraction equivalents. By using these "building blocks," you can find any percentage without a calculator.
Easy Building Block Percentages
50% = ÷ 2 (halve)
25% = ÷ 4 (quarter)
10% = ÷ 10
1% = ÷ 100
Strategy: Build Other Percentages
- 20%: Find 10%, then double it
- 5%: Find 10%, then halve it
- 30%: Find 10%, then multiply by 3
- 15%: Find 10% and 5%, then add them
- 12%: Find 10%, 1%, then add 10% + 1% + 1%
- Percentages over 100%: 150% = 100% (the original) + 50%
Example: Find 35% of 80
Step 1: Find 10%: 80 ÷ 10 = 8
Step 2: Find 30% (three lots of 10%): 8 × 3 = 24
Step 3: Find 5% (half of 10%): 8 ÷ 2 = 4
Step 4: Add together: 24 + 4 = 28
Answer: 35% of 80 = 28
Finding a Percentage of an Amount (With Calculator)
When you have a calculator, the most efficient method uses multipliers. A multiplier is simply the decimal equivalent of the percentage.
Multiplier: The decimal form of a percentage. To find a percentage of an amount, multiply the amount by the multiplier. For example, the multiplier for 35% is 0.35.
Percentage of an Amount (Multiplier Method)
Amount × (Percentage ÷ 100) = Result
OR
Amount × Multiplier = Result
Example: Find 23% of 650
Step 1: Convert 23% to a decimal multiplier: 23 ÷ 100 = 0.23
Step 2: Multiply: 0.23 × 650 = 149.5
Answer: 23% of 650 = 149.5