Fraction Calculator: Add, Subtract, Multiply and Divide Fractions, Simplify and Mixed Numbers

Do fraction arithmetic and see each step.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the top and bottom of the first fraction, choose the operation and enter the second fraction.

The calculator shows the common denominator for adding and subtracting, the reciprocal for dividing, and simplifies the result.

Formulas used

  • \frac{a}{b}+\frac{c}{d} = \frac{ad + bc}{bd}
  • \frac{a}{b}\times\frac{c}{d} = \frac{ac}{bd}
  • \frac{a}{b}\div\frac{c}{d} = \frac{ad}{bc}

Worked example

With the default numbers in the calculator above:

  1. The two fractions in lowest terms: 3/4 and 5/6
  2. Common denominator (the lowest common multiple of the denominators): 12
  3. Add or subtract the numerators over that denominator: 19/12
  4. Simplify by dividing top and bottom by the highest common factor: 19/12
  5. As a mixed number: 1 7/12
  6. As a decimal and a percent: 1.58 = 158.33 %

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Operation Divide (/).

  1. The two fractions in lowest terms: 3/4 and 5/6
  2. Divide: multiply by the reciprocal of the second fraction: 18/20
  3. Simplify by dividing top and bottom by the highest common factor: 9/10
  4. As a mixed number: 9/10
  5. As a decimal and a percent: 0.90 = 90.00 %

Common questions

How do I add fractions with different denominators?

Change them to a common denominator, add the tops and keep the bottom.

How do I divide by a fraction?

Multiply by its reciprocal, which is the fraction turned upside down.

How do I simplify a fraction?

Divide the top and the bottom by their highest common factor.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school mathematics text (fractions).

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