Fraction Calculator

How to use Fraction Calculator

1. Type the whole part, numerator and denominator of the first fraction. Leave Whole as 0 for a plain fraction such as 3/4.
2. Do the same for the second fraction and pick the operation: add, subtract, multiply or divide.
3. Read the simplified fraction, the mixed number and the decimal value.
4. Follow the step list to see the common denominator, the arithmetic and the simplification.

How fraction arithmetic works

A fraction is a numerator divided by a denominator. To add or subtract fractions the denominators must match, so the calculator finds the least common multiple of the two denominators, rewrites both fractions over it and then combines the numerators. For example 1 1/2 + 3/4 becomes 3/2 + 3/4, then 6/4 + 3/4 = 9/4, which is 2 1/4 or 2.25.

To multiply you multiply the numerators together and the denominators together. To divide you multiply by the reciprocal of the second fraction, which means flipping its numerator and denominator. Dividing by a fraction whose numerator is zero is impossible, so the tool tells you instead of returning a meaningless value.

Finally the result is reduced by dividing the numerator and denominator by their greatest common divisor, found with the Euclidean algorithm.

When this calculator is useful

• Checking school homework and seeing the working behind an answer.
• Scaling recipes, where amounts such as 2 1/3 cups need to be doubled or halved.
• Woodworking and sewing measurements in inches, where mixed numbers are the norm.
• Combining shares, parts of a project or portions of a budget.
• Comparing results from other calculators by converting to exact fractions.

Tips and limits

Always check that the denominator is not zero; a fraction with a zero denominator is undefined. If you only need a quick decimal, the decimal line shows up to twelve digits, but the fraction is the exact answer.

Whole numbers, numerators and denominators are limited to 60 digits each and must be whole numbers; decimals such as 0.75 should first be written as 75/100. Everything happens on your device, so your numbers stay private.

Why use this fraction calculator tool

• Exact arithmetic. Calculations use big integers, so there is no rounding error and very large numerators and denominators still give exact results.
• Always simplified. Results are reduced with the greatest common divisor and shown as a fraction, a mixed number and a decimal.
• Written steps. Each answer lists the improper fractions, common denominator or reciprocal, and the final simplification so you can check homework.
• Private. Everything is computed in your browser. Nothing you type is uploaded or stored.

Frequently asked questions

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