Fraction Calculator

Add, subtract, multiply or divide fractions and see the simplified result, decimal and mixed number.

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Your fraction result will appear here.

About the Fraction Calculator

Different fraction operations need different arithmetic rules, especially when denominators do not match. This calculator adds, subtracts, multiplies or divides fractions and reduces the answer to a simpler form.

Fraction operations follow different rules. Addition and subtraction need a common denominator, while multiplication works across numerators and denominators directly. Division uses the reciprocal of the second fraction.

How to Use the Fraction Calculator

  1. Enter the numerator and denominator for the first fraction.
  2. Choose the operation: add, subtract, multiply or divide.
  3. Enter the numerator and denominator for the second fraction, making sure neither denominator is zero.
  4. Calculate the result and review the simplified fraction, improper fraction or mixed-number form as needed.

How the Calculation Works

For addition or subtraction, a common denominator is found and the numerators are adjusted before combining. For a/b + c/d, the result before simplification is (ad + bc) ÷ bd.

For multiplication, (a/b)(c/d) = ac/bd. For division, a/b ÷ c/d = ad/bc, provided the second fraction is not zero. The final numerator and denominator are reduced by their greatest common factor.

Worked example

Fraction Calculator Worked Example

2/3 + 5/8

Use a common denominator of 24. Convert 2/3 to 16/24 and 5/8 to 15/24. Add the numerators: 16 + 15 = 31, so the result is 31/24, which is 1 7/24 as a mixed number.

Result guide

Understanding Your Fraction Calculator Result

A simplified fraction has the same value as the unsimplified result. Keep an improper fraction when algebra or later arithmetic is easier in that form, and use a mixed number when it communicates a measurement more naturally.

Before you rely on the answer

Assumptions and Limitations

  • Denominators are non-zero.
  • Division by a zero-valued second fraction is invalid.
  • Inputs represent exact rational values rather than rounded decimal approximations.

Practical tip

Using This Result in Practice

Before multiplying large fractions, look for factors that can cancel across a numerator and denominator. This keeps the intermediate numbers smaller and makes the arithmetic easier to check.

Related calculations

Useful Calculations to Continue With

If your starting value is a decimal, convert it first with the Decimal to Fraction Calculator.

If the problem begins with whole numbers plus fractions, use the Mixed Number Calculator for a more direct entry format.

Common questions

Fraction Calculator FAQ

Why do fractions need a common denominator for addition?

The denominator defines the size of the parts. Fractions can only be added directly when the parts are the same size.

How do you divide fractions?

Multiply the first fraction by the reciprocal of the second. For example, 2/3 ÷ 4/5 becomes 2/3 × 5/4.

What makes a fraction simplified?

The numerator and denominator share no common factor greater than 1.