How to Convert Fractions to Percentages — Step-by-Step Guide
Converting fractions to percentages is a fundamental math skill used in cooking, finance, academics, and everyday life. This guide walks you through the process with clear examples and a handy reference table.
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The Two-Step Method
Percentage = (Numerator ÷ Denominator) × 100
- Divide the numerator (top number) by the denominator (bottom number)
- Multiply the result by 100 to get the percentage
Step-by-Step Examples
Example 1: Convert 3/4 to a percentage
- Step 1: Divide 3 by 4 → 3 ÷ 4 = 0.75
- Step 2: Multiply by 100 → 0.75 × 100 = 75%
Example 2: Convert 2/3 to a percentage
- Step 1: Divide 2 by 3 → 2 ÷ 3 = 0.6666...
- Step 2: Multiply by 100 → 0.6666... × 100 = 66.67%
Note: This is a repeating decimal, so we round to 2 decimal places.
Example 3: Convert mixed number 1 3/8 to a percentage
- Step 1: Convert to improper fraction → (1 × 8 + 3) / 8 = 11/8
- Step 2: Divide 11 by 8 → 11 ÷ 8 = 1.375
- Step 3: Multiply by 100 → 1.375 × 100 = 137.5%
Example 4: Convert 5/16 to a percentage
- Step 1: Divide 5 by 16 → 5 ÷ 16 = 0.3125
- Step 2: Multiply by 100 → 0.3125 × 100 = 31.25%
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Common Fractions to Percentages 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 | 0.166... | 16.67% |
| 5/6 | 0.833... | 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% |
| 3/10 | 0.3 | 30% |
| 7/10 | 0.7 | 70% |
| 9/10 | 0.9 | 90% |
| 1/12 | 0.0833... | 8.33% |
Special Cases & Tips
- Repeating decimals: Fractions like 1/3, 1/6, 1/7, 1/9 produce repeating decimals. Round to the desired number of decimal places.
- Percentages over 100%:Improper fractions (numerator > denominator) give percentages over 100%. For example, 5/4 = 125%.
- Shortcut for denominators of 100: If the denominator is 100, the numerator IS the percentage. 47/100 = 47%.
- Shortcut for denominators that divide 100: For denominators like 2, 4, 5, 10, 20, 25, 50 — multiply the numerator by (100 ÷ denominator). For 3/5: 3 × 20 = 60%.
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Frequently Asked Questions
How do you convert a fraction to a percentage?
Divide the numerator by the denominator, then multiply by 100. For example, 3/4 = 3 ÷ 4 = 0.75, then 0.75 × 100 = 75%.
What is 1/3 as a percentage?
1/3 as a percentage is approximately 33.33% (repeating). Divide 1 by 3 to get 0.3333..., then multiply by 100.
How do you convert a mixed number to a percentage?
First convert the mixed number to an improper fraction, then divide and multiply by 100. For example, 2 1/4 = 9/4 = 2.25 × 100 = 225%.
What is 7/8 as a percentage?
7/8 = 7 ÷ 8 = 0.875 × 100 = 87.5%.
How do you convert a percentage back to a fraction?
Write the percentage over 100 and simplify. For example, 75% = 75/100. The GCD of 75 and 100 is 25, so 75/100 = 3/4.
Why do some fractions give repeating decimals?
Fractions with denominators that have prime factors other than 2 and 5 produce repeating decimals. For example, 1/3 = 0.333... because 3 is not a factor of any power of 10.