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Fraction Calculator

Work with fractions and mixed numbers the way you would on paper: find the common denominator, cancel by the greatest common divisor, and see the answer as a fraction, a mixed number and a decimal.

First fraction
Operation
Second fraction

Leave the whole number empty for a simple fraction such as 5/6, or enter only a whole number. For a negative mixed number, put the minus sign on the whole number (−2 1/3).

Result

1 2/3 + 5/6 =

5/2

= 2 1/2 as a mixed number

Simplest form
5/2
Mixed number
2 1/2
Decimal
2.5
Percent
250%
Show the working
  1. Write 1 2/3 as an improper fraction: whole × denominator + numerator(1 × 3 + 2)/3 = 5/3
  2. Find the least common denominator (LCD)LCD(3, 6) = 6
  3. Rewrite both fractions with the denominator 65/3 + 5/6 = 10/6 + 5/6
  4. Add the numerators and keep the denominator(10 + 5)/6 = 15/6
  5. Simplify: divide the numerator and denominator by their greatest common divisor, 3GCD(15, 6) = 3; (15 ÷ 3)/(6 ÷ 3) = 5/2
  6. Write it as a mixed number: divide the numerator by the denominator5 ÷ 2 = 2 remainder 1 = 2 1/2
  7. Divide the numerator by the denominator5 ÷ 2 = 2.5

The fraction is exact — nothing is rounded. A bar over digits marks a repeating decimal: 0.41 with a bar over the 6 means 0.41666…

How to use the fraction calculator

Each fraction has three boxes: a whole number, a numerator (the top number) and a denominator (the bottom number). Fill in only what you need:

  • A simple fraction such as ⅚: leave the whole number empty, enter 5 and 6.
  • A mixed number such as 1⅔: enter 1, 2 and 3.
  • A whole number such as 4: enter 4 and leave the other two boxes empty.
  • A negative number: put the minus sign on the whole number for a mixed number (−2 1/3), or on the numerator for a simple fraction (−3/4).

Choose the operation and the answer appears straight away: in simplest form, as a mixed number when it is bigger than 1, and as a decimal. Open Show the working to follow each step — converting mixed numbers, finding the common denominator, and cancelling by the greatest common divisor.

Fraction rules

For two fractions a/b and c/d (b and d not zero):

a/b + c/d = (a × (L ÷ b) + c × (L ÷ d)) ÷ L

a/b − c/d = (a × (L ÷ b) − c × (L ÷ d)) ÷ L

a/b × c/d = (a × c) ÷ (b × d)

a/b ÷ c/d = a/b × d/c = (a × d) ÷ (b × c)

L
the least common denominator: the smallest number both b and d divide into (LCD of 3 and 6 is 6)
GCD
the greatest common divisor, the largest number that divides both the numerator and the denominator

A mixed number w n/d becomes the improper fraction (w × d + n)/d before any arithmetic. To simplify the answer, divide the numerator and denominator by their GCD. For example, 2/3 × 3/4 = 6/12, and GCD(6, 12) = 6, so the answer is 1/2. Dividing works the same way after flipping the second fraction: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

The calculator uses exact whole-number arithmetic for every step, however large the numbers get, so the fraction is never rounded. Only the decimal is shortened when its repeating block is very long.

Worked example: 1⅔ + ⅚

  1. Convert the mixed number: 1⅔ = (1 × 3 + 2)/3 = 5/3.
  2. The least common denominator of 3 and 6 is 6, so 5/3 becomes 10/6 (multiply top and bottom by 2). 5/6 already has denominator 6.
  3. Add the numerators: 10/6 + 5/6 = 15/6.
  4. Simplify: the greatest common divisor of 15 and 6 is 3, and 15 ÷ 3 = 5, 6 ÷ 3 = 2, giving 5/2.
  5. As a mixed number: 5 ÷ 2 = 2 remainder 1, so the answer is 2½, or 2.5 as a decimal.

Tips and common mistakes

  • Don’t add the denominators. 1/2 + 1/3 is not 2/5. Rewrite both over 6 first: 3/6 + 2/6 = 5/6.
  • Any common denominator works, the least is tidiest. Multiplying the two denominators (3 × 6 = 18) also gives a correct answer, but you then have more to simplify at the end.
  • Cancel before multiplying when doing it by hand: in 4/9 × 3/8, the 4 and 8 share a factor of 4 and the 3 and 9 a factor of 3, leaving 1/3 × 1/2 = 1/6.
  • Repeating decimals are exact as fractions. 1/3 = 0.333… never ends, so the fraction is the more precise answer.

To turn a fraction into a percentage of something, use the percentage calculator. To compare quantities such as 3 : 5, or to scale a recipe, use the ratio calculator.

Frequently asked questions

How do you add fractions with different denominators?

Find a common denominator — ideally the least common multiple of the two denominators — and rewrite both fractions over it. Then add the numerators and keep the denominator. For 1/2 + 1/3, the common denominator is 6: 3/6 + 2/6 = 5/6.

How do you divide fractions?

Flip the second fraction (take its reciprocal) and multiply. 2/3 ÷ 4/5 becomes 2/3 × 5/4 = 10/12, which simplifies to 5/6. Dividing by a fraction smaller than 1 makes the answer bigger.

How do you simplify a fraction?

Divide the numerator and the denominator by their greatest common divisor. For 18/24, the largest number that divides both is 6, so 18/24 = 3/4. If the greatest common divisor is 1, the fraction is already in simplest form.

How do I turn an improper fraction into a mixed number?

Divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator over the same denominator. For 17/5: 17 ÷ 5 = 3 remainder 2, so 17/5 = 3 2/5.

How do I convert a decimal to a fraction?

Write the decimal over a power of ten and simplify. 0.375 has three decimal places, so it is 375/1000; the greatest common divisor of 375 and 1000 is 125, giving 3/8.

Last reviewed September 15, 2026