Fraction Calculator

Add, subtract, multiply, divide and simplify fractions and mixed numbers, with each step explained.

Try an example:

How fractions work

A fraction $\frac{a}{b}$ means $a$ parts out of $b$ equal parts. The denominator (bottom) says how big each part is; the numerator (top) says how many parts you have. Two fractions are equal when they name the same amount, so $\frac{2}{4} = \frac{1}{2}$ .

How to use the fraction calculator

Type or paste your problem into the box above — for example 3/4 + 5/6. Use ^ for powers, / for fractions and sqrt() for square roots, or describe it in words.
Press Enter. The solver works through the problem with every step shown; switch Steps off if you only want the final answer.
Ask a follow-up in the same chat — "why did you do that?" or "now check it" — and it answers with the earlier working in context.

The four operations

Add or subtract: rewrite both over a common denominator, then combine the numerators — $\frac{a}{b} + \frac{c}{d} = \frac{a d + b c}{b d}$ .
Multiply: multiply the tops and multiply the bottoms — $\frac{a}{b} \times \frac{c}{d} = \frac{a c}{b d}$ .
Divide: multiply by the reciprocal — $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$ .
Simplify: divide the top and bottom by their greatest common factor.

Working with mixed numbers

Convert mixed numbers to improper fractions before calculating: $2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$ . Convert back at the end if the question asks for a mixed number.

Worked example: $\frac{3}{4} + \frac{5}{6}$

Find the lowest common denominatorThe LCD of 4 and 6 is 12.
Rewrite each fraction $\frac{3}{4} = \frac{9}{12}$ and $\frac{5}{6} = \frac{10}{12}$
Add the numerators $\frac{9}{12} + \frac{10}{12} = \frac{19}{12}$
Write as a mixed number $\frac{19}{12} = 1 \frac{7}{12}$ , which is already in lowest terms.

Common mistakes to avoid

Adding the denominators

$\frac{1}{2} + \frac{1}{3}$ is not $\frac{2}{5}$ . Rewrite both over a common denominator first: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$ .

Flipping the wrong fraction

When dividing, take the reciprocal of the second fraction (the divisor), not the first.

Leaving answers unsimplified

$\frac{12}{18}$ should become $\frac{2}{3}$ . Check whether the top and bottom share a factor.

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Questions students ask

Can it handle mixed numbers?

Yes. Put a space between the whole number and the fraction, like 2 1/3, and the steps convert it to an improper fraction first.

Does it simplify the answer?

Always. The final answer is in lowest terms, with the mixed-number or decimal form when it's useful.

Can it simplify algebraic fractions?

Yes. For example, $\frac{x ^{2} - 9}{x + 3}$ simplifies to $x - 3$ for $x \neq = - 3$ : it factors the top and bottom and cancels the common factor.

How do I type a fraction?

Use a slash: 3/4. Put brackets around a compound top or bottom, such as (x + 1)/(x - 2).