Fraction Calculator — add, subtract, multiply, divide fractions

How it works

The four operations on fractions follow fixed rules, given by Wolfram MathWorld:

• Add / subtract: a/b ± c/d = (ad ± cb) / bd. Put both fractions over the common denominator bd, then add or subtract the numerators.
• Multiply: a/b × c/d = ac / bd. Multiply the numerators together and the denominators together.
• Divide: a/b ÷ c/d = ad / bc. Invert the second fraction (swap its numerator and denominator) and multiply.

These rules "will not necessarily [give] reduced fractions", so the final step is always to reduce the answer to lowest terms by dividing out the greatest common divisor. The calculator does this automatically and also shows the result as a mixed number and a decimal.

Worked example

Take 1/2 + 1/3. The common denominator is 2 × 3 = 6, so 1/2 = 3/6 and 1/3 = 2/6. Adding the numerators gives 3 + 2 = 5 over 6 — the answer is 5/6, which is already in lowest terms and equals about 0.8333 as a decimal.

Frequently asked questions

How do you add fractions with different denominators?

Rewrite both fractions over a common denominator, add the numerators, then reduce. The shortcut is a/b + c/d = (ad + cb)/bd. For 1/2 + 1/3, that is (3 + 2)/6 = 5/6.

How do you multiply fractions?

Multiply the numerators together and the denominators together: a/b × c/d = ac/bd. Then reduce. For example, 2/3 × 3/4 = 6/12, which simplifies to 1/2.

How do you divide fractions?

Invert the second fraction and multiply: a/b ÷ c/d = ad/bc. Dividing 3/4 by 1/2 gives 3/4 × 2/1 = 6/4, or 3/2 (1 1/2).

Why does the answer get reduced automatically?

The arithmetic rules often produce a fraction that is not in lowest terms — for instance 6/12. Reducing by the greatest common divisor gives the simplest equivalent form, 1/2, which is the standard way to present the answer.

Can the result be a whole or mixed number?

Yes. If the numerator is a multiple of the denominator you get a whole number (1/2 + 1/2 = 1), and an improper result is also shown as a mixed number, such as 3/2 = 1 1/2.

What happens if I divide by zero?

Dividing by the fraction 0 (a zero numerator on the second fraction) is undefined, so the calculator returns no result. Every other combination of nonzero fractions has a valid answer.