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Fraction calculator

Addition, subtraction, multiplication and division of proper and mixed fractions with step-by-step solutions.
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A simple and convenient calculator will help you quickly solve any mathematical problems with two or more fractions.

The tool supports working with common, mixed fractions and decimal numbers, performs addition, subtraction, multiplication and division, including for fractions with different denominators.

The calculator not only provides the final answer but also shows a detailed step-by-step solution.

How to:

Adding fractions

Steps to add two fractions:

  1. Convert mixed numbers to improper fractions.
  2. Find the LCM of the denominators — that is the common denominator. Bring each fraction to it by multiplying numerator and denominator by the appropriate factor.
  3. Add the numerators; the denominator stays the same.
  4. Find the GCD of the numerator and denominator and reduce the fraction.
  5. If the numerator is greater than the denominator, extract the whole part.
Example. 1/2 + 1/3
  1. Common denominator: LCM(2, 3) = 6
  2. 1/2 = 3/6, 1/3 = 2/6
  3. 3/6 + 2/6 = 5/6
12 + 13  =  36 + 26  =  56

Subtracting fractions

Steps to subtract two fractions:

  1. Convert mixed numbers to improper fractions.
  2. Find the LCM of the denominators — that is the common denominator. Bring each fraction to it by multiplying numerator and denominator by the appropriate factor.
  3. Subtract the second numerator from the first; the denominator stays the same.
  4. Find the GCD of the numerator and denominator and reduce the fraction.
  5. If the numerator is greater than the denominator, extract the whole part.
Example. 3/4 − 1/6
  1. Common denominator: LCM(4, 6) = 12
  2. 3/4 = 9/12, 1/6 = 2/12
  3. 9/12 − 2/12 = 7/12
34 − 16  =  912 − 212  =  712

Multiplying fractions

Steps to multiply two fractions:

  1. Convert mixed numbers to improper fractions.
  2. Multiply the numerators together and the denominators together.
  3. Find the GCD of the numerator and denominator and reduce the fraction.
  4. If the numerator is greater than the denominator, extract the whole part.
Example. 2/3 × 3/4
  1. Multiply numerators: 2 × 3 = 6
  2. Multiply denominators: 3 × 4 = 12
  3. Reduce: GCD(6, 12) = 6, result 1/2
23 × 34  =  612  =  12

Dividing fractions

Steps to divide two fractions:

  1. Convert mixed numbers to improper fractions.
  2. Flip the second fraction (swap its numerator and denominator), then multiply.
  3. Multiply the numerators together and the denominators together.
  4. Find the GCD of the numerator and denominator and reduce the fraction.
  5. If the numerator is greater than the denominator, extract the whole part.
Example. 5/6 ÷ 2/3
  1. Flip the second fraction: 2/3 → 3/2
  2. Multiply: 5/6 × 3/2 = 15/12
  3. Reduce: GCD(15, 12) = 3, result 5/4 = 1 1/4
56 ÷ 23  =  56 × 32  =  1512  =  114
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