How to use the fraction calculator
Type the numerator (top number) and denominator (bottom number) of each fraction, choose an operation and read the answer. The result is reduced to lowest terms automatically and also shown as a mixed number and a decimal. Negative fractions are fine – just put a minus sign on the numerator. Denominators cannot be zero.
Rules for fraction arithmetic
Adding and subtracting: fractions need a common denominator. Multiply each numerator by the other fraction's denominator, then add or subtract:
Example: 3/4 + 5/6 = (18 + 20) / 24 = 38/24 = 19/12 = 1 7/12.
Multiplying: multiply the numerators together and the denominators together.
Dividing: multiply by the reciprocal of the second fraction – "keep, change, flip".
Simplifying fractions
A fraction is in simplest form when the numerator and denominator share no common factor other than 1. The calculator finds the greatest common divisor (GCD) with Euclid's algorithm – repeatedly replacing the larger number with the remainder of dividing it by the smaller – and divides both parts by it. For instance, the GCD of 38 and 24 is 2, giving 19/12.
Mixed numbers and decimals
When the numerator is larger than the denominator (an improper fraction), it can be written as a whole number plus a proper fraction: 19/12 = 1 7/12. Converting to a decimal is simply division: 19 ÷ 12 = 1.5833… Some fractions, such as 1/3, give repeating decimals, which is why exact fractions are preferred in many calculations, from recipes to engineering drawings.
Everyday uses
Fractions appear constantly outside the classroom. Doubling a recipe that calls for 3/4 cup of flour gives 1 1/2 cups. Woodworkers add measurements such as 5/8 inch and 3/16 inch (the answer is 13/16 inch). Musicians count beats in fractions of a measure, and investors once quoted share prices in eighths and sixteenths of a dollar. Converting to a decimal is handy for calculators and spreadsheets, but keeping the exact fraction avoids rounding errors that accumulate over several steps.
Frequently asked questions
How do you add fractions with different denominators?
Find a common denominator (multiplying the two denominators always works), convert both fractions, add the numerators and simplify.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second. For example, 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.
How do I enter a mixed number?
Convert it to an improper fraction first: multiply the whole number by the denominator and add the numerator. 2 1/3 becomes 7/3.
What does simplified mean?
It means the numerator and denominator have been divided by their greatest common divisor so no further reduction is possible.
Last reviewed 2026-10-27. This fraction calculator is provided for general information; verify important decisions with a qualified professional.