Fraction Calculator

Type two fractions, mixed numbers or whole numbers and pick an operation. You get the answer in lowest terms, as a mixed number and as a decimal, with each step shown the way a teacher would write it.

Mixed numbers: whole number, a space, then the fraction (1 1/2).

1 1/2 + 2/3 =
13/6
= 2 1/6
As a mixed number
2 1/6
As a decimal
≈ 2.1666666667
  • Step 1: Convert the mixed number to an improper fraction: 1 1/2 → (1 × 2 + 1)/2 = 3/2.
  • Step 2: Find a common denominator. The least common denominator is the least common multiple of 2 and 3, which is 6.
  • Step 3: Rewrite each fraction over 6: 3/2 = (3 × 3)/(2 × 3) = 9/6; 2/3 = (2 × 2)/(3 × 2) = 4/6.
  • Step 4: Add the numerators and keep the denominator: (9 + 4)/6 = 13/6.
  • Step 5: Simplify: the GCD of 13 and 6 is 1, so 13/6 is already in lowest terms.
  • Step 6: Convert to a mixed number: 13 ÷ 6 = 2 remainder 1, so 13/6 = 2 1/6.
  • Step 7: As a decimal: 13 ÷ 6 = 2.1666…, where the digit 6 repeats forever (written 2.1(6)). Rounded to 10 places: 2.1666666667.

How each operation works

Adding and subtracting need a common denominator, because you can only add parts of the same size. Find the least common multiple of the two denominators, rewrite each fraction with that denominator by multiplying its top and bottom by the same number, then add or subtract the numerators. The denominator stays the same.

Multiplying is easier: multiply the numerators together and the denominators together. No common denominator is needed. Dividing turns into multiplying: flip the second fraction upside down (its reciprocal) and multiply.

Whatever the operation, finish by simplifying. Divide the numerator and denominator by their greatest common divisor (GCD). If the GCD is 1, the fraction is already in lowest terms.

Mixed numbers and negative fractions

Convert mixed numbers to improper fractions before you do anything else: multiply the whole number by the denominator and add the numerator, so 2 1/2 becomes (2 × 2 + 1)/2 = 5/2. Working with the whole numbers and fractions separately is a common source of wrong answers, especially for multiplication.

A minus sign in front of a mixed number applies to the whole thing: -1 1/2 means -(1 + 1/2) = -3/2, not -1 + 1/2. Type it as "-1 1/2". Decimals work too: 0.75 is read as 75/100, which simplifies to 3/4.

Why the decimal sometimes repeats

A fraction in lowest terms has a decimal that ends only when its denominator has no prime factors other than 2 and 5. So 3/8 = 0.375 ends, but 1/3 = 0.333… and 1/6 = 0.1666… go on forever. The calculator shows the repeating digits, and the fraction itself is the exact answer — the decimal is rounded when it repeats.

Fraction rules

a/b + c/d = (a × d + c × b) / (b × d), or use the least common denominatora/b − c/d = (a × d − c × b) / (b × d)a/b × c/d = (a × c) / (b × d)a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)Simplify: divide a and b by GCD(a, b)
  • a and c are the numerators (top numbers); b and d are the denominators (bottom numbers), which can't be 0
  • GCD = greatest common divisor, the largest whole number that divides both
  • the least common denominator is the least common multiple of b and d

Worked example: 1 1/2 + 2/3

  1. Convert the mixed number: 1 1/2 = (1 × 2 + 1)/2 = 3/2.
  2. The least common multiple of 2 and 3 is 6, so 6 is the common denominator.
  3. Rewrite: 3/2 = (3 × 3)/(2 × 3) = 9/6, and 2/3 = (2 × 2)/(3 × 2) = 4/6.
  4. Add the numerators: 9/6 + 4/6 = 13/6.
  5. The GCD of 13 and 6 is 1, so 13/6 is already in lowest terms.
  6. As a mixed number: 13 ÷ 6 = 2 remainder 1, so the answer is 2 1/6.
  7. As a decimal: 2.1666…, where the 6 repeats forever.

Frequently asked questions

How do you divide fractions?

Keep the first fraction, flip the second, and multiply. For example, 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4, which simplifies to 3/2, or 1 1/2.

How do you simplify a fraction?

Find the greatest common divisor of the numerator and denominator and divide both by it. For 18/24 the GCD is 6, so 18/24 = 3/4.

Can I multiply mixed numbers without converting them?

Not by multiplying the parts separately. 2 1/2 × 1 1/2 is not 2 × 1 plus 1/2 × 1/2. Convert first: 5/2 × 3/2 = 15/4 = 3 3/4.

Do I have to use the least common denominator?

No, any common denominator gives the right answer; the least one just keeps the numbers small. For 1/4 + 1/6, using 24 gives 6/24 + 4/24 = 10/24, which simplifies to 5/12. Using the least common denominator, 12, gives 3/12 + 2/12 = 5/12 directly.

How do I turn a fraction into a decimal?

Divide the numerator by the denominator. 3/8 = 3 ÷ 8 = 0.375. Some fractions never end: 1/3 = 0.333…, with the 3 repeating forever.

Sources

Last reviewed for 2026. How we calculate.