Converting Fractions to Percentages
A percentage is a fraction out of 100. Converting a fraction to a percentage tells you how many parts out of 100 something represents — an essential everyday skill.
What is a Percentage?
The word percent means per hundred. So 45% means 45 out of every 100. The link to fractions: 45% = 45/100.
Method 1 – Multiply the Fraction by 100
Percentage = (Numerator divided by Denominator) times 100. Or equivalently: multiply the fraction by 100/1 and attach the % sign.
3/4 times 100 = 300/4 = 75%.
2/5 times 100 = 200/5 = 40%.
7/8 times 100 = 700/8 = 87.5%. Answer: 87.5%.
Method 2 – Decimal Route
Convert to decimal first, then multiply by 100.
5 divided by 6 = 0.8333... times 100 = 83.33% (rounded).
Method 3 – Equivalent Fraction Over 100
If you can scale the denominator to 100, the numerator becomes the percentage directly.
25 times 4 = 100. 17 times 4 = 68. So 17/25 = 68/100 = 68%.
Quick Reference Table
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/3 | 0.333... | 33.33% |
| 2/3 | 0.666... | 66.67% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
Real-Life Examples
A test score of 18 out of 24: 18/24 = 3/4 = 75%. A sale sign says 3/10 off: that is 30% off. A survey shows 7 out of 20 people prefer tea: 7/20 = 35%.
Mixed Numbers to Percentages
Convert to improper: 7/4. 7/4 times 100 = 700/4 = 175%. (Over 100% because the value is more than 1.)
Key Takeaways
- Multiply any fraction by 100 to get the percentage.
- Percentages over 100% are possible when the fraction is greater than 1.
- Memorise the common fraction-decimal-percentage equivalents for speed.
- The decimal route works for any fraction, including those that do not simplify neatly.
Practice Questions
- Convert 9/20 to a percentage.
- Convert 5/12 to a percentage (round to 2 decimal places).
- A student got 34 out of 40. What percentage is that?
- Write 2 and 1/2 as a percentage.
- A shop has sold 3/8 of its stock. What percentage remains?