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Fraction Calculator

This fraction calculator adds, subtracts, multiplies and divides fractions and mixed numbers. It shows the answer in lowest terms, as a mixed number and as a decimal, along with the steps used to get there.

First fraction

Operation
Second fraction

Leave the whole number empty for a simple fraction.

Result

1/2 + 1/3 = 5/6

Simplified fraction5/6
Mixed number5/6
Decimal0.833333
Common denominator6
Rewritten3/6 + 2/6 = 5/6

Results update as you type.

How to Use the Fraction Calculator

  1. Enter the first fraction. Put the numerator on top and the denominator below. For a mixed number, add the whole number in the box on the left.
  2. Pick the operation: + add, − subtract, × multiply or ÷ divide.
  3. Enter the second fraction the same way.
  4. Read the answer. You get the simplified fraction, the mixed number, the decimal and the working.

The Four Fraction Rules

Adding and subtracting

Fractions can only be added or subtracted when they have the same denominator.

a/b + c/d = (a·(L/b) + c·(L/d)) / L, where L is the least common multiple of b and d.

Multiplying

a/b × c/d = (a × c) / (b × d)

Dividing

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

Simplifying

Divide the top and bottom by their greatest common divisor (GCD) until no number other than 1 divides both.

Worked Examples

Adding mixed numbers: 1 1/2 + 2 3/4

  1. Convert to improper fractions: 1 1/2 = 3/2 and 2 3/4 = 11/4.
  2. Common denominator of 2 and 4: 4.
  3. Rewrite: 3/2 = 6/4, so 6/4 + 11/4 = 17/4.
  4. As a mixed number: 17 ÷ 4 = 4 remainder 1, so 4 1/4.
  5. As a decimal: 4.25.

Subtracting: 5/6 − 3/8

  1. Common denominator of 6 and 8: 24.
  2. Rewrite: 5/6 = 20/24 and 3/8 = 9/24.
  3. Subtract: 20/24 − 9/24 = 11/24. It’s already in lowest terms.

Dividing: 2/3 ÷ 4/9

  1. Flip the second fraction: 4/9 becomes 9/4.
  2. Multiply: 2/3 × 9/4 = 18/12.
  3. Simplify by the GCD of 6: 3/2, or 1 1/2.

Tips and Common Mistakes

Don’t add the denominators

1/2 + 1/3 is not 2/5. The denominator tells you the size of the pieces, and you can only add pieces of the same size. Rewrite both as sixths first.

Simplify early when multiplying

In 4/9 × 3/8 you can cancel the 4 with the 8 and the 3 with the 9 before multiplying, which gives 1/3 × 1/2 = 1/6. The calculator gets the same answer, but cancelling first keeps hand calculations small.

Watch the sign on mixed numbers

−2 1/2 means −(2 + 1/2) = −5/2, not −2 + 1/2. That’s why the minus sign goes on the whole number in the calculator.

Fractions in measurements

Fractions show up constantly in DIY work: 5/8-inch drywall, 3 1/2-inch boards, 1/4-inch gaps. When you add up cuts from a tape measure, add the fractions here first, then use our deck calculator or other project calculators for the material totals.

For equations with unknowns, like x/3 + 1/2 = 2, use the algebra calculator.

Frequently Asked Questions

How do you add fractions with different denominators?

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

How do you multiply fractions?

Multiply the numerators together and the denominators together, then simplify. For 2/3 × 3/4 that gives 6/12, which simplifies to 1/2. You don't need a common denominator to multiply.

How do you divide fractions?

Flip the second fraction upside down (take its reciprocal) and multiply. 3/4 ÷ 1/8 becomes 3/4 × 8/1 = 24/4, which is 6. Dividing by a fraction is the same as multiplying by its reciprocal.

How do you simplify a fraction?

Divide the numerator and denominator by their greatest common divisor. For 18/24 the greatest common divisor is 6, so it simplifies to 3/4. The calculator always shows answers in lowest terms.

How do I enter a mixed number like 2 3/4?

Type the whole number in the left box and the fraction in the stacked boxes: 2, then 3 over 4. Leave the whole-number box empty for a simple fraction. For a negative mixed number, put the minus sign on the whole number, like −2 and 3/4.

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

Divide the numerator by the denominator. The quotient is the whole number and the remainder goes over the original denominator. 17/4 is 4 remainder 1, so it equals 4 1/4.

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