Operations on Mixed Numbers

To add the mixed numbers, first convert each mixed number to an improper fraction. Then add the improper fractions and write the answer in simplest form.

Example :

Note: You can use another method to add the mixed numbers. First, add the whole number parts and then add the fraction parts separately. Then write the answer in simplest form. For example:

$\begin{array}{l}3\frac{2}{5}+4\frac{1}{5}=\left(3+4\right)+\left(\frac{2}{5}+\frac{1}{5}\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=7+\frac{2+1}{5}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=7+\frac{3}{5}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=7\frac{3}{5}\end{array}$

Subtracting Mixed Numbers

To subtract the mixed numbers, first rewrite each mixed number as an improper fraction. Then subtract the improper fractions and write the answer in simplest form.

Example :

Multiplying Mixed Numbers

To multiply the mixed numbers, first rewrite each mixed number as an improper fraction. Then multiply the improper fractions and write the result in simplest form.

Example :

$\begin{array}{l}2\frac{2}{3}\cdot 3\frac{1}{5}=\frac{8}{3}\cdot \frac{16}{5}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{128}{15}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=8\frac{8}{15}\end{array}$

Dividing Mixed Numbers

To divide the mixed numbers, first rewrite each mixed number as an improper fraction. Then to divide the improper fractions, multiply the first fraction by the multiplicative inverse of the second fraction.

Example :

$3\frac{1}{2}÷4\frac{2}{3}=\frac{7}{2}÷\frac{14}{3}$

The multiplicative inverse of $\frac{14}{3}$ is $\frac{3}{14}$.

$\begin{array}{l}=\frac{7}{2}\cdot \frac{3}{14}\\ =\frac{21}{28}\\ =\frac{3}{4}\end{array}$