To convert a percentage to a fraction, write the percentage value over 100 and simplify. For example, 75% becomes 75/100. Dividing the numerator and denominator by 25 produces the simplified fraction 3/4.
Enter a numerator and denominator to calculate the percentage, decimal, simplified fraction, ratio, and conversion steps.
Simplifying the resulting fraction gives its most compact equivalent form.
Percentage to Fraction Formula
Percent means out of 100, so any percentage can initially be written with a denominator of 100.
The resulting fraction should then be simplified when possible.
You can reverse-check the result with the Fraction to Percentage Calculator.
Example: Convert 75% to a Fraction
Write 75% as 75/100.
The greatest common factor of 75 and 100 is 25.
Divide both values by 25 to obtain 3/4.
Example: Convert 40% to a Fraction
Write 40% as 40/100.
Divide the numerator and denominator by 20.
The simplified fraction is 2/5.
Example: Convert 12.5% to a Fraction
Write 12.5% as 12.5/100.
Remove the decimal by multiplying both values by 10, producing 125/1000.
Divide both values by 125 to obtain 1/8.
How to Handle Decimal Percentages
First write the percentage value over 100.
Multiply the numerator and denominator by 10 for one decimal place, 100 for two decimal places, or another appropriate power of ten.
Simplify the resulting whole-number fraction.
Multiply the numerator and denominator by the same power of ten before simplifying.
Example: Convert 33.3% to a Fraction
Write 33.3% as 33.3/100.
Multiply both values by 10 to get 333/1000.
This fraction does not simplify further using whole-number factors.
Repeating Percentages
A rounded percentage may not reproduce the exact original fraction.
For example, 33.33% written over 100 becomes 3333/10000, not exactly 1/3.
The exact repeating percentage 33.333...% corresponds to 1/3.
Percentages Greater Than 100%
Write percentages above 100 over 100 in the same way.
For example, 150% becomes 150/100.
Simplifying by 50 produces 3/2, an improper fraction.
Convert the Result to a Mixed Number
An improper fraction may be rewritten as a mixed number.
The fraction 3/2 equals the mixed number 1 1/2.
Both forms are equivalent to 150%.
Negative Percentages
Keep the negative sign when writing the percentage over 100.
For example, minus 25% becomes minus 25/100.
Simplifying produces minus 1/4.
How to Simplify the Fraction
Find the greatest common factor shared by the numerator and denominator.
Divide both values by that factor.
Continue until no whole-number factor greater than one divides both values.
Common Percentage and Fraction Equivalents
The table below lists several useful reverse conversions.
| Percentage | Fraction over 100 | Simplified fraction |
|---|---|---|
| 10% | 10/100 | 1/10 |
| 12.5% | 12.5/100 | 1/8 |
| 20% | 20/100 | 1/5 |
| 25% | 25/100 | 1/4 |
| 40% | 40/100 | 2/5 |
| 50% | 50/100 | 1/2 |
| 60% | 60/100 | 3/5 |
| 75% | 75/100 | 3/4 |
| 80% | 80/100 | 4/5 |
| 100% | 100/100 | 1/1 |
| 125% | 125/100 | 5/4 |
| 150% | 150/100 | 3/2 |
Common Mistakes
Do not place the percent sign inside the fraction.
Do not divide only the numerator when simplifying.
When removing decimals, multiply both the numerator and denominator by the same value.
Remember that a rounded repeating percentage may not convert back to the exact original fraction.
Conclusion
Write the percentage value over 100, remove any decimals, and simplify.
The method works for whole, decimal, negative, and above-100 percentages.
Verify the fraction by entering it into the Fraction to Percentage Calculator.
FAQs
How do I convert a percentage to a fraction?
Write the percentage value over 100 and simplify.
What is 75% as a fraction?
Seventy-five over 100 simplifies to 3/4.
What is 12.5% as a fraction?
It equals 1/8.
Can percentages above 100% become fractions?
Yes. They produce improper fractions, such as 150% equalling 3/2.
How do I handle a decimal percentage?
Write it over 100, remove the decimal by multiplying both parts by a power of ten, and simplify.