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Fraction calculator

Add, subtract, multiply and divide fractions, with the result simplified and shown as a decimal and a mixed number.

First fraction
Operation
Second fraction

Result

1/2 + 1/3

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Enter two fractions to see the result.

As a decimal
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As a mixed number
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Simplify a fraction

12/18 simplifies to
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As a mixed number
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How it works

A fraction represents part of a whole as a numerator over a denominator. Fractions can be added, subtracted, multiplied or divided, then simplified by dividing both numerator and denominator by their greatest common divisor.

  1. Enter two fractions

    Whole numbers for each numerator and denominator.

  2. Pick an operation

    Add, subtract, multiply or divide.

  3. Read the result

    Already simplified, with the decimal and mixed number shown too.

Fraction rules

Addition and subtraction

Find a common denominator, then add or subtract the numerators: a/b + c/d = (ad + bc) / bd.

Multiplication

Multiply numerators together and denominators together: a/b × c/d = ac / bd.

Division

Multiply by the reciprocal of the second fraction: a/b ÷ c/d = a/b × d/c = ad / bc.

Dividing by zero

A denominator of 0 is not a valid fraction, and dividing by a fraction equal to 0 is not defined, so both are flagged as errors rather than silently treated as 1. A mixed number, such as 1 1/2, is shown whenever the result is greater than 1 or less than -1.

Frequently asked questions

How do you add fractions with different denominators?

Find a common denominator and convert each fraction, then add the numerators. For 1/2 + 1/3: the formula is (ad + bc) / bd = (1 times 3 + 1 times 2) / (2 times 3) = 5/6. The calculator applies this cross-multiplication method automatically and simplifies the result using the greatest common divisor.

How do you multiply two fractions?

Multiply numerators together and denominators together: (a/b) times (c/d) equals ac/bd. For 2/3 times 3/4: (2 times 3) / (3 times 4) equals 6/12, which simplifies to 1/2. No common denominator is needed for multiplication, which makes it simpler than adding fractions.

How do you divide one fraction by another?

Multiply by the reciprocal: (a/b) divided by (c/d) equals (a/b) times (d/c) equals ad/bc. For 3/4 divided by 1/2: 3/4 times 2/1 equals 6/4, which simplifies to 3/2, or the mixed number 1 1/2. The phrase "keep, change, flip" is a common way to remember this: keep the first fraction, change division to multiplication, flip the second fraction.

What is simplifying a fraction and how is it done?

Simplifying, or reducing, means dividing the numerator and denominator by their greatest common divisor. For 12/18: the greatest common divisor of 12 and 18 is 6, so 12/18 equals 2/3. A fraction is fully simplified when the greatest common divisor of its numerator and denominator is 1. Every result on this page is already simplified.

What happens when the denominator of a fraction is zero?

Division by zero is undefined in mathematics, so a fraction with a denominator of 0 is not valid. This calculator flags it as an error instead of silently substituting another value. Dividing by a fraction whose numerator is 0, which is the same as dividing by zero, is flagged the same way.