Fraction Calculator

A fraction calculator works out sums, differences, products and quotients of fractions exactly. Enter proper fractions, improper fractions, mixed numbers or whole numbers. It finds the lowest common denominator when adding or subtracting, simplifies the result, and gives it as a fraction, a mixed number and a decimal.

Try:

How to use the fraction calculator

  1. Type the first fraction, for example 1/2 or 1 3/4.
  2. Choose add, subtract, multiply or divide.
  3. Type the second fraction and press Calculate.

Formula

ab+cd=ad+bcbd\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}
ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Worked example: 1/2 + 1/3

  • First fraction: 1/2
  • Operation: Add (+)
  • Second fraction: 1/3

✓ Answer checked

56\frac{5}{6}
Decimal
≈0.8333333333\approx 0.8333333333
Step-by-step working (4 steps)

  1. Find a common denominator Lowest common denominator

    The lowest common denominator of 2 and 3 is 6.

    lcm⁡(2,3)=6\operatorname{lcm}(2, 3) = 6

  2. Rewrite both fractions

    Scale each fraction so both have the same denominator.

    12+13=36+13\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{1}{3}

  3. Add the numerators

    Keep the denominator and combine the tops.

    =56= \frac{5}{6}

  4. Simplify Simplest form

    Divide the top and bottom by their greatest common factor.

    =56= \frac{5}{6}
Formulas used
ab±cd=ad±bcbd\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}
ab×cd=acbd\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}
ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
How this was checked
  • ✓ Reversing the operation on the answer gives back the first fraction.
  • ✓ Decimal arithmetic gives the same value.

Frequently asked questions

How do you add fractions with different denominators?

Rewrite both fractions with a common denominator, then add the numerators. For 1/2 + 1/3, use 6: 3/6 + 2/6 = 5/6.

How do you divide fractions?

Flip the second fraction and multiply. For example, 3/2 ÷ 3/4 = 3/2 × 4/3 = 2.

Can I enter mixed numbers?

Yes. Type the whole number, a space, then the fraction, such as 1 1/2.

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