Fraction Calculator

Add, subtract, multiply and divide fractions, with the answer simplified to lowest terms, as a mixed number and as a decimal, plus the working shown.

How to use the fraction Calculator

  1. Enter the numerator (top) and denominator (bottom) of the first fraction. For a whole number, use a denominator of 1.
  2. Choose add, subtract, multiply or divide.
  3. Enter the second fraction. For a mixed number such as 2 1/3, convert it first: 2 × 3 + 1 = 7, so enter 7/3.
  4. The result updates instantly as you type. There is no button to press.
  5. Use Copy result to copy the figures, or Copy link to share a link that reopens the fraction Calculator with the same inputs.

How it works

Fractions represent parts of a whole: the denominator (bottom) says how many equal parts the whole is cut into, and the numerator (top) says how many of those parts you have. This calculator does the four basic operations and always reduces the answer to lowest terms.

Adding and subtracting need a common denominator, because you can only add parts of the same size. The calculator uses the least common multiple (LCM) of the two denominators, rewrites both fractions over it, then adds or subtracts the numerators. Multiplying is simpler: multiply the tops together and the bottoms together. Dividing by a fraction is the same as multiplying by its reciprocal, so the second fraction is flipped and then multiplied.

The answer is then simplified by dividing the top and bottom by their greatest common divisor (GCD), found with Euclid's algorithm. Improper fractions, where the top is bigger than the bottom, are also shown as mixed numbers, and every answer is given as a decimal and a percentage. The working line shows each step, so you can follow along or check homework.

Formula

a/b + c/d = (a·d + c·b) / (b·d) a/b − c/d = (a·d − c·b) / (b·d) a/b × c/d = (a·c) / (b·d) a/b ÷ c/d = (a·d) / (b·c)

The calculator uses the least common multiple instead of b·d for addition and subtraction, which keeps the numbers smaller, then divides the result by the GCD of its numerator and denominator.

Example

1/2 + 1/3: the least common multiple of 2 and 3 is 6, so 1/2 = 3/6 and 1/3 = 2/6, and 3/6 + 2/6 = 5/6 ≈ 0.8333. For 3/4 ÷ 2/5, flip the second fraction and multiply: 3/4 × 5/2 = 15/8, which is the mixed number 1 7/8 or 1.875.

Frequently asked questions

How do I simplify a fraction?

Divide the numerator and denominator by their greatest common divisor. For 18/24, the GCD is 6, so 18/24 = 3/4.

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator and add the numerator. 2 3/5 becomes (2 × 5 + 3)/5 = 13/5.

How do I turn a fraction into a decimal?

Divide the numerator by the denominator. 3/8 = 3 ÷ 8 = 0.375. Some fractions, such as 1/3, give repeating decimals.