Fraction Calculator
Add, subtract, multiply and divide fractions and mixed numbers. Answers come back in lowest terms, as a mixed number, as a decimal and as a percentage, with the working shown at each step. The arithmetic is exact — whole numbers are used throughout, so nothing is lost to rounding.
Calculate with fractions
How to use this calculator
- Enter the first fraction. Leave the whole number blank for a simple fraction, or fill it in for a mixed number such as 2 1/3.
- Choose add, subtract, multiply or divide.
- Enter the second fraction the same way.
- Press Calculate. You get the answer in lowest terms, as a mixed number, as a decimal and as a percentage, along with the working.
How fraction arithmetic works
Adding and subtracting requires a common denominator. This calculator uses the lowest common multiple of the two denominators rather than simply multiplying them, so the working stays closer to what you would do by hand. Once the denominators match, the numerators are added or subtracted and the result is reduced.
Multiplying needs no common denominator: multiply the numerators together and the denominators together, then reduce.
Dividing means multiplying by the reciprocal — flip the second fraction, then multiply. Dividing by zero is undefined, so a second fraction with a numerator of zero is rejected.
Every result is reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor, found with the Euclidean algorithm. Results are exact: the arithmetic is done on whole numbers throughout, and the decimal is produced only at the end for display, so nothing is lost to floating point rounding.
Frequently Asked Questions
How do I add fractions with different denominators?
Convert both fractions so they share a denominator, then add the numerators. This calculator uses the lowest common multiple of the two denominators and shows each step, so 1/4 + 1/6 becomes 3/12 + 2/12 = 5/12.
How do I enter a mixed number?
Put the whole part in the whole number box and the fractional part in the numerator and denominator boxes. For 2 1/3, enter 2, 1 and 3. Negative mixed numbers work too: enter the minus sign on the whole number and the whole quantity is treated as negative.
How do I simplify a fraction to its lowest terms?
Divide the numerator and the denominator by their greatest common divisor. 18/24 has a greatest common divisor of 6, so it reduces to 3/4. This calculator reduces every result automatically and shows the unreduced form alongside it.
Can I convert a fraction to a decimal or a percentage?
Yes. Every result is shown as a fraction in lowest terms, as a mixed number where the fraction is improper, as a decimal, and as a percentage. A recurring decimal is shown to ten significant figures rather than rounded to two.
What happens if I divide by zero?
Dividing by zero is undefined, so the calculator refuses it and tells you which input is the problem. A denominator of zero is rejected for the same reason.