Percent to Fraction Calculator
Convert any percentage to a simplified fraction with step-by-step simplification.
Simplification Steps
How to Convert Percentages to Fractions
Converting a percentage to a fraction is a fundamental math skill that comes up in school, work, and everyday life. Whether you are reducing a test score to its simplest form, working on a recipe, or solving a math problem, converting percentages to fractions gives you a precise, exact representation. Our free online percent to fraction calculator handles this conversion instantly, complete with step-by-step simplification so you can see exactly how the result is derived.
The Percent to Fraction Formula
The formula is simple: divide the percentage value by 100. Since "percent" means "per hundred," this directly converts the percentage into a fraction with a denominator of 100. Then, simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
Common Percent to Fraction Conversions
Here are some frequently used conversions that are worth memorizing:
| Percent | Unsimplified | Simplified |
|---|---|---|
| 10% | 10/100 | 1/10 |
| 20% | 20/100 | 1/5 |
| 25% | 25/100 | 1/4 |
| 33.33% | 33.33/100 | 1/3 |
| 50% | 50/100 | 1/2 |
| 75% | 75/100 | 3/4 |
| 80% | 80/100 | 4/5 |
| 90% | 90/100 | 9/10 |
Step-by-Step Example
Let us convert 45% to a fraction. First, write it as 45/100. Next, find the GCD of 45 and 100. The factors of 45 are 1, 3, 5, 9, 15, 45. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. The largest common factor is 5. Divide both the numerator and denominator by 5: 45/5 = 9 and 100/5 = 20. So 45% as a simplified fraction is 9/20.
Handling Decimal Percentages
When your percentage includes a decimal, such as 12.5%, you first multiply both the numerator and denominator by 10 (or as many times as needed) to eliminate the decimal. So 12.5% becomes 12.5/100, which equals 125/1000. Then simplify: the GCD of 125 and 1000 is 125, so the final answer is 1/8. Our calculator handles this automatically.
Why Convert Percentages to Fractions?
Fractions are exact, while percentages can sometimes be rounded. For example, 33.33% is an approximation of one-third, but the fraction 1/3 is precise. In mathematical proofs, engineering calculations, and cooking measurements, fractions give you the exact value without any rounding error. Our percent to fraction calculator shows you every simplification step, so you can follow along and learn the process.
Frequently Asked Questions
To convert a percent to a fraction, divide the percentage number by 100, then simplify the resulting fraction to its lowest terms.
Formula: Percent / 100 = Fraction, then simplify
Example: 75% = 75/100 = 3/4
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. For example, 60/100 has a GCD of 20, so 60/100 simplifies to 3/5.
50% as a fraction is 1/2. To find this, divide 50 by 100 to get 50/100, then simplify by dividing both the numerator and denominator by 50.
Yes, every percentage can be expressed as a fraction. Whole number percents divide evenly by 100. Decimal percents like 12.5% become 12.5/100, which simplifies to 1/8.
Both represent parts of a whole. A fraction shows a part as a ratio of two numbers (numerator/denominator), while a percentage shows a part as a number out of 100. They are mathematically equivalent: 1/4 = 25% = 0.25.