Turn Percentages into Simplified Fractions Instantly

Converting a percentage into a fraction is a fundamental math skill, but when dealing with decimals or irregular numbers, doing it by hand gets tedious. This tool was built to handle the heavy lifting, giving you not just the final answer, but the exact step-by-step mathematical process used to get there.

Whether you are working on a math assignment, scaling a recipe, or calculating financial data, this calculator provides the exact simplified fraction, including mixed numbers for percentages over 100%.

How the Conversion Process Works

1. Rewrite the percentage as a decimal

The word “percent” literally means “per one hundred.” To remove the percentage sign, we divide the value by 100.

For example, 45% becomes 0.45.

2. Set up the initial fraction

Next, we take that decimal and place it over a denominator of 1.

0.45/1

3. Convert the numerator to a whole number

Fractions shouldn’t contain decimals. To fix this, we count the number of decimal places in the numerator. We then multiply both the top and the bottom by 10 for every decimal place (i.e., 10^n). Since 0.45 has two decimal places, we multiply the top and bottom by 100:

0.45 x 100 / 1 x 100 = 45/100

4. Find the Greatest Common Factor (GCF) and reduce

To simplify the fraction, we find the highest number that evenly divides both the numerator and the denominator. For 45 and 100, the GCF is 5. Dividing both sides by 5 gives us the simplified fraction:

45 ÷ 5 / 100 ÷ 5 = 9/20

5. Convert improper fractions to mixed numbers

If your original percentage was greater than 100% (e.g., 125%), your resulting fraction will be “improper” (the top number is larger than the bottom). The final step divides the numerator by the denominator to extract the whole number, leaving the remainder as the final simplified fraction. For 125%, the result 5/4 becomes 1 1/4.

Standard Percent to Fraction Formula

If you prefer to visualize the formula used for these conversions, it can be written as:

Fraction = P/100

Where P is the percentage. Once placed in this format, you simply simplify the equation by finding the greatest common divisor.

Common Conversions

Percentage	Decimal	Simplified Fraction
10%	0.1	1/10
12.5%	0.125	1/8
20%	0.2	1/5
25%	0.25	1/4
33.33%	0.333…	1/3
50%	0.5	1/2
66.66%	0.666…	2/3
75%	0.75	3/4
100%	1.0	1/1
150%	1.5	1 1/2

FAQs

Q1. Can I convert a percentage with a decimal?

A: Yes. If you enter a value like 12.5%, the calculator will automatically multiply the numerator and denominator to clear the decimal (creating 125/1000) before simplifying it down to 1/8.

Q2. What happens if I enter a percentage larger than 100?

A: Percentages over 100 represent a whole plus a part. The calculator will process this and return a mixed number. For instance, 250% will be calculated as 250/100, which reduces to 5/2, and is finally presented as the mixed number 2 1/2.

Q3. Why did my answer come out exactly the same as the step 3 fraction?

A: If your result doesn’t look any smaller than the initial fraction (for example, 17% becomes 17/100), it means the numerator and denominator share no common factors other than 1. The fraction is already in its simplest form.

Sources: CalculatorSoup, RapidTables, Inch Calculator, Mad for Math, Calculator Online, JAIN University, GigaCalculator, Math Master, Size.ly, Alcula.

Related Calculator:

• Fraction to Percent Calculator.