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CalcSolver

Fraction Calculator

Add, subtract, multiply or divide two fractions. The result is shown in lowest terms, as a mixed number and as a decimal, with the full working so you can see how it’s done.

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Formula

a/b + c/d = (ad + bc)/bd · a/b − c/d = (ad − bc)/bd · a/b × c/d = ac/bd · a/b ÷ c/d = ad/bc

How it works

  1. 1

    To add or subtract, rewrite both fractions over a common denominator, then combine the numerators.

  2. 2

    To multiply, multiply the numerators together and the denominators together.

  3. 3

    To divide, flip the second fraction (its reciprocal) and multiply.

  4. 4

    Finally, simplify by dividing the top and bottom by their greatest common divisor (GCD).

Worked examples

Adding fractions

Calculate 1/2 + 3/4.

  1. Common denominator = 4
  2. 1/2 = 2/4
  3. 2/4 + 3/4 = 5/4
  4. As a mixed number: 1 1/4

Answer: 5/4 (1 1/4, or 1.25)

Dividing fractions

Calculate 2/3 ÷ 4/5.

  1. Multiply by the reciprocal: 2/3 × 5/4
  2. = 10/12
  3. Simplify: 5/6

Answer: 5/6

Frequently asked questions

How do you add fractions with different denominators?
Find a common denominator (the product of the two denominators always works), rewrite each fraction over it, add the numerators, then simplify.
How do you divide fractions?
Keep the first fraction, flip the second one (its reciprocal), and multiply. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
What does “lowest terms” mean?
A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. Divide both by their greatest common divisor to get there.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. For example, 2/3 × 3/4 = 6/12 = 1/2.
What is a mixed number?
A mixed number combines a whole number and a fraction, like 1 1/4. Any improper fraction (top bigger than bottom) such as 5/4 can be written as a mixed number.
Can I enter negative fractions?
Yes. Put the minus sign on the numerator (for example −3 over 4). The calculator handles negative results and keeps the sign on the numerator in the answer.