How to Convert a Fraction to a Percentage
Converting a fraction to a percentage is a two-step process: divide the numerator by the denominator, then multiply by 100.
Percentage = (Numerator ÷ Denominator) × 100
Example: Convert 3/4 to a percentage: 3 ÷ 4 = 0.75 × 100 = 75%
Common Fraction to Percentage Table
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 2/3 | 0.666... | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
| 1/6 | 0.1666... | 16.67% |
| 5/6 | 0.8333... | 83.33% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/10 | 0.1 | 10% |
| 1/12 | 0.0833... | 8.33% |
| 1/16 | 0.0625 | 6.25% |
| 1/20 | 0.05 | 5% |
| 1/100 | 0.01 | 1% |
Converting Mixed Numbers
A mixed number like 2 3/4 has a whole number part and a fraction part. To convert:
- Convert to an improper fraction: 2 3/4 = (2×4 + 3)/4 = 11/4
- Divide: 11 ÷ 4 = 2.75
- Multiply by 100: 2.75 × 100 = 275%
Or more simply: convert the fraction part only (3/4 = 75%) and add it to the whole number as hundreds (2 × 100% = 200%). Total: 200% + 75% = 275%.
Step-by-Step Examples
Example 1: Test Score
You got 17 out of 20 on a quiz. What percentage?
17/20 = 17 ÷ 20 = 0.85 × 100 = 85%
Example 2: Recipe Scaling
A recipe calls for 2/3 cup of sugar. What percentage of a full cup?
2/3 = 2 ÷ 3 = 0.6667 × 100 = 66.67%
Example 3: Sports Stats
A basketball player made 7 out of 12 free throws. What's their percentage?
7/12 = 7 ÷ 12 = 0.5833 × 100 = 58.33%
Converting the Other Way: Percentage to Fraction
Put the percentage over 100, then simplify:
| Percentage | As Fraction | Simplified |
|---|---|---|
| 25% | 25/100 | 1/4 |
| 40% | 40/100 | 2/5 |
| 75% | 75/100 | 3/4 |
| 12.5% | 12.5/100 = 125/1000 | 1/8 |
| 33.33% | 33.33/100 | ≈ 1/3 |
Frequently Asked Questions
Why does 1/3 not convert to an exact percentage?
Because 1 divided by 3 produces a repeating decimal (0.33333...). The exact percentage is 33.333...% with the 3 repeating forever. We typically round to 33.33% or use the fraction notation 33 1/3%.
How do I convert a fraction to a percentage on a calculator?
Divide the top number by the bottom number, then multiply by 100. On most calculators: type the numerator, press ÷, type the denominator, press =, then press × 100 =.
What's the difference between 1/4 and 25%?
They represent the same value, just expressed differently. 1/4 is a fraction, 25% is a percentage, and 0.25 is a decimal. All three mean "one quarter" or "25 out of 100."