Fractions Calculator

Use this calculator to solve arithmetic problems with fractions. You can also switch tabs to convert an improper fraction to the mixed form, or vice versa.

A mixed number (or mixed fraction) is a fraction of the form c ⁿ/_d, where c, n and d are integers and n < d. For example, 2 ³/₄. It is therefore the sum of a whole number and a proper fraction.

To perform an elementary operation on two mixed fractions, we first need to convert them to improper fractions. For example, given \(1 {1 \over 2}\) and \(2 {1 \over 3}\), we convert both fractions to the following improper fractions: \( {3 \over 2}\) and \( {7 \over 3}\). Next, we perform one of the operations.

Addition

To add two fractions, make sure that their denominators are the same. For example, to add \({1 \over 2}\) and \( {1 \over 3}\), both fraction's denominator should be equal to 6.

example: \({3 \over 6} + {2 \over 6} = {5 \over 6}\).

The general formula for adding two fractions with different denominators is: \({n_1 \over d_1} + {n_2 \over d_2} = {n_1 \cdot d_2 \over d_1 \cdot d_2} + {n_2 \cdot d_1 \over d_2 \cdot d_1 } = {n_1 \cdot d_2 + n_2 \cdot d_1 \over d_1 \cdot d_2}\)

Substraction

Substraction is the opposite of addition, so the formula is almost the same:

\({n_1 \over d_1} + {n_2 \over d_2} = {n_1 \cdot d_2 \over d_1 \cdot d_2} - {n_2 \cdot d_1 \over d_2 \cdot d_1 } = {n_1 \cdot d_2 - n_2 \cdot d_1 \over d_1 \cdot d_2}\)

Multiplication

To perform multiplication, multiply the nominator of the first fraction with the nominator of the other fraction, then multiply the denominator of the first fraction with the denomiantor of the other fraction:

\({n_1 \over d_1} \times {n_2 \over d_2} = {n_1 \cdot n_1 \over d_1 \cdot d_2} \)

Division

Division is the opposite of multiplication, so we do the opposite: multiply the nominator of the first fraction with the denominator of the other fraction, then multiply the nominator of the second fraction with the denomiantor of the other fraction:

\({n_1 \over d_1} \div {n_2 \over d_2} = {n_1 \cdot d_2 \over d_1 \cdot n_2} \)

Another method is just to swap the numerator of the second fraction with the denominator, and then perform multiplication:

\({n_1 \over d_1} \div {n_2 \over d_2} = {n_1 \over d_1} \times{d_2 \over n_2} = {n_1 \cdot d_2 \over d_1 \cdot n_2} \)