Fractions
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.
The percent sign (%) itself evolved from the Italian abbreviation “per cento” (“for a hundred”), used by Italian merchants and bankers from the 15th century onward to express interest rates and commercial discounts without repeatedly writing “out of 100.” Percentages remain the dominant way fractions are communicated in daily life precisely because a shared “out of 100” scale makes comparison effortless — a 75% exam score, a 20% discount, and a 60% battery level are all instantly comparable in a way that 3/4, 1/5, and 3/5 are not at a glance.
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.