Fraction Calculator
Enter two fractions — mixed numbers work too — pick an operation, and get the answer simplified, as a mixed number, as a decimal, and as a percentage, with the working shown.
Adding needs a common denominator; multiplying does not
This asymmetry is where most fraction mistakes come from.
Adding and subtracting requires both fractions to describe pieces of the same size. Thirds and quarters cannot be combined until both are rewritten as twelfths. The calculator uses the least common multiple of the two denominators and shows it.
Multiplying needs no such step. Multiply the numerators, multiply the denominators, done. 3/4 × 5/6 = 15/24. Nothing has to match.
Dividing is multiplying by the reciprocal — flip the second fraction and multiply. 3/4 ÷ 5/6 becomes 3/4 × 6/5. The reason is that dividing by 5/6 asks "how many five-sixths fit in here", which is the same as scaling by 6/5.
Simplifying
A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. Divide both by their greatest common divisor and you are done in a single step — 15/24 has a GCD of 3, giving 5/8.
The "before simplifying" output shows the raw result and what it was divided by, which is useful for checking homework where the working matters as much as the answer.
Mixed numbers
2 3/4 means 2 + 3/4, which is 11/4 as an improper fraction: multiply the whole number by the denominator and add the numerator.
Enter mixed numbers using the whole number field. For negative mixed numbers, put the minus sign on the whole number — −2 3/4 means −(2 + 3/4), which is −11/4, not −2 + 3/4. This trips people up constantly, and it is why the calculator applies the sign to the whole quantity.
Improper fractions are not wrong. Most algebra is easier to do with 11/4 than with 2 3/4, and teachers who require mixed numbers are usually asking for a specific format rather than a more correct answer.
Decimals that do not terminate
1/3 as a decimal is 0.3333… forever. The decimal output rounds; the fraction does not.
This is a real reason to keep fractions as fractions in measurement and construction work. A tape measure reads in sixteenths, and 0.4375 is less useful on site than 7/16 — which is why the tile and stair calculators on this site display fractions rather than decimals.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both over a common denominator, then add the numerators only. For 3/4 + 5/6, the least common denominator is 12, giving 9/12 + 10/12 = 19/12. Never add the denominators together — that is the single most common fraction error.
Do you need a common denominator to multiply fractions?
No. Multiply the numerators together and the denominators together, then simplify. Only addition and subtraction require a common denominator, because only those operations combine pieces that must be the same size.
How do you divide fractions?
Flip the second fraction and multiply. 3/4 ÷ 5/6 becomes 3/4 × 6/5 = 18/20 = 9/10. Dividing by 5/6 asks how many five-sixths fit into the first fraction, which is the same as scaling it by 6/5.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator and add the numerator, keeping the same denominator. 2 3/4 becomes (2 × 4 + 3)/4 = 11/4. For negative mixed numbers the sign applies to the whole quantity, so −2 3/4 is −11/4.
Is an improper fraction wrong?
No. 11/4 and 2 3/4 are the same number, and improper fractions are usually easier to work with in algebra. Teachers who ask for mixed numbers are specifying a format, not correcting an error. This calculator shows both.