Fraction Calculator

Calculate with fractions and mixed numbers while keeping every common-denominator and simplification step visible.

Drag & drop or upload an image or PDF

Enter a fraction problem, such as 7/12 + 5/18

Use / for a fraction and include the operation, such as 7/12 + 5/18. Write a mixed number as 2 1/3.

Try an example

Fractions keep a value exact

A fraction records a numerator divided by a nonzero denominator. Unlike a rounded decimal, it can preserve an exact value through several operations.

Addition and subtraction need equivalent fractions with a common denominator. Multiplication works across numerators and denominators, while division uses the reciprocal of the second fraction. The final result should be reduced so its numerator and denominator share no factor greater than one.

How to use the fraction calculator

Enter the problem as written

Type or paste the full expression. You can also upload a clear photo or PDF and check the extracted text before solving.

Read the working, not only the answer

Each transformation is separated and explained so you can compare it with your own method.

Ask about any step

Continue in the same solution to request another method, check a restriction, or ask why a rule applies.

Adding fractions with different denominators

Cross-multiplication creates a common denominator. The resulting fraction may still need to be reduced.

\frac{a}{b} + \frac{c}{d} = \frac{a d + b c}{b d}, b \neq = 0, d \neq = 0

A reliable way to work through it

Use the least common denominator

For addition or subtraction, rewrite both fractions with the least common multiple of their denominators.

Multiply or divide directly

Multiply numerator by numerator and denominator by denominator. For division, first replace the second fraction with its reciprocal.

Reduce at the end

Divide the numerator and denominator by their greatest common divisor, and keep the sign in the numerator.

Worked example

Add 7/12 and 5/18

lcm (12, 18) = 36

Use 36 as the least common denominator.

\frac{7}{12} = \frac{21}{36}, \frac{5}{18} = \frac{10}{36}

Multiply each numerator and denominator by its missing factor.

\frac{21}{36} + \frac{10}{36} = \frac{31}{36}

Add the numerators once the denominators match.

g cd (31, 36) = 1

The numerator and denominator have no common factor, so the result is reduced.

The exact sum is 31/36.

Common mistakes to check

Adding denominators

The denominator names the size of each part. It must be made common, not added to the other denominator.

Flipping the wrong fraction

When dividing, take the reciprocal of the divisor, which is the second fraction.

Leaving a reducible result

A correct calculation can still be incomplete if numerator and denominator share a common factor.

GCF and LCM CalculatorFind common factors and multiples through prime factorization or the Euclidean algorithm, with sign and zero cases handled.Percentage CalculatorSolve percent-of, percent-change, increase, decrease, and reverse-percentage questions with the base value clearly identified.Rational Expression CalculatorSimplify algebraic fractions and keep the original domain restrictions with the answer.Simplify CalculatorCombine like terms, reduce fractions, and rewrite expressions in a cleaner equivalent form.

Questions students ask

Can the calculator use mixed numbers?

Yes. Enter a mixed number with a space, such as 2 1/3. It will be converted to an improper fraction before the operation.

Why can a denominator not be zero?

Division by zero is undefined, so a fraction with denominator zero does not represent a number.

Does the answer include a decimal?

The exact reduced fraction is the main answer. A decimal approximation can also be given when it is useful.

Can this simplify fractions with variables?

Use the rational expression calculator for algebraic fractions. This page is focused on numerical fractions and mixed numbers.