Skip to content
CalcWorld

Browse all tools

Fraction Calculator

The fraction calculator adds, subtracts, multiplies and divides fractions and mixed numbers, and gives the answer in lowest terms. 2 3/4 − 1 1/2 = 1 1/4, with every step shown.

Sources: OpenStax Prealgebra 2e Updated

First fraction
Operation
Second fraction

1/2 + 1/3

5/6

Decimal
≈ 0.833333
Show steps Here’s how we got it

  1. Find the least common denominator

    LCM(2, 3) = 6

    This is the smallest number that both denominators divide into.

  2. Rewrite both fractions over 6

    1/2 = 1 × 3/2 × 3 = 3/6

    1/3 = 1 × 2/3 × 2 = 2/6

    Multiplying the top and the bottom by the same number does not change the value.

  3. Add the numerators

    3/6 + 2/6 = 3 + 2/6 = 5/6

    The denominator stays the same.

  4. Simplify

    5/6 is already in lowest terms

    5 and 6 share no common factor other than 1.

Fraction rules for adding, subtracting, multiplying and dividing

Adding and subtracting need a common denominator, as in OpenStax Prealgebra. Multiplying and dividing do not.

ab+cd=ad+bcbdab−cd=ad−bcbd\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \qquad \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}
ab×cd=acbdab÷cd=ab×dc=adbc\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \qquad \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}

The formulas above use bd as the common denominator, which always works. The calculator uses the least common denominator instead, the smallest number both denominators divide into, because it keeps the numbers small. The result is the same once the fraction is simplified, using the greatest common divisor from the GCF calculator.

How to subtract mixed numbers: 2 3/4 − 1 1/2

A recipe needs 1 1/2 cups of flour and you have 2 3/4 cups. How much is left after baking?

  1. Turn mixed numbers into improper fractions

    2 3/4 = 2 × 4 + 3/4 = 11/4

    1 1/2 = 1 × 2 + 1/2 = 3/2

    Multiply the whole number by the denominator, then add the numerator.

  2. Find the least common denominator

    LCM(4, 2) = 4

    This is the smallest number that both denominators divide into.

  3. Rewrite both fractions over 4

    11/4 already has the denominator 4

    3/2 = 3 × 2/2 × 2 = 6/4

    Multiplying the top and the bottom by the same number does not change the value.

  4. Subtract the numerators

    11/4 − 6/4 = 11 − 6/4 = 5/4

    The denominator stays the same.

  5. Simplify

    5/4 is already in lowest terms

    5 and 4 share no common factor other than 1.

  6. Write it as a mixed number

    5 ÷ 4 = 1 remainder 1

    5/4 = 1 1/4

Answer: 5/4

Open this example in the calculator

As a decimal the answer is 1.25; the fraction to decimal calculator shows that division, and the decimal to fraction calculator goes the other way. For a fraction whose top or bottom is itself a fraction, use the complex fraction calculator.

Fraction strips cut into quarters: 2 3/4 is 11 quarters, 1 1/2 is 6 quarters, and the difference is 5 quarters, which is 1 1/4.
With quarters as the common denominator, 11 quarters take away 6 quarters leaves 5 quarters.

Fraction practice question

Work out 2/3 + 3/4. Give the answer as a mixed number.

Check your answer

Answer: 17/12

  1. Find the least common denominator

    LCM(3, 4) = 12

    This is the smallest number that both denominators divide into.

  2. Rewrite both fractions over 12

    2/3 = 2 × 4/3 × 4 = 8/12

    3/4 = 3 × 3/4 × 3 = 9/12

    Multiplying the top and the bottom by the same number does not change the value.

  3. Add the numerators

    8/12 + 9/12 = 8 + 9/12 = 17/12

    The denominator stays the same.

  4. Simplify

    17/12 is already in lowest terms

    17 and 12 share no common factor other than 1.

  5. Write it as a mixed number

    17 ÷ 12 = 1 remainder 5

    17/12 = 1 5/12

Open this question in the calculator

Fraction Calculator: FAQ

How do you add fractions with different denominators?

Find the least common denominator, rewrite both fractions with it, then add the numerators and keep the denominator. For 1/2 + 1/3 the common denominator is 6, so the sum is 3/6 + 2/6 = 5/6.

How do you multiply fractions?

Multiply the numerators together and the denominators together, then simplify. 3/4 × 2/9 = 6/36 = 1/6. You do not need a common denominator to multiply.

How do you divide fractions?

Flip the second fraction and multiply. 3/4 ÷ 3/8 becomes 3/4 × 8/3 = 24/12 = 2. The flipped fraction is called the reciprocal.

How do you simplify a fraction?

Divide the numerator and the denominator by their greatest common divisor. For 18/24 the greatest common divisor is 6, so 18/24 = 3/4. When the only common factor is 1, the fraction is already in lowest terms.

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

Multiply the whole number by the denominator and add the numerator. That is the new numerator, over the same denominator. 2 3/4 = (2 × 4 + 3)/4 = 11/4.

How do I use the fraction calculator with whole numbers or negative fractions?

For a whole number, fill in the Whole box and leave the numerator and denominator empty. For a negative fraction, put a minus sign in front of the whole number or the numerator.

Sources

More in Arithmetic