Operations on Mixed Numbers

Example :

$\begin{array}{l}3\frac{2}{5}+4\frac{1}{5}=\frac{17}{5}+\frac{21}{5}\\ =\frac{\left(17+21\right)}{5}\\ =\frac{38}{5}\text{ or }7\frac{3}{5}\end{array}$

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:

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

Example :

$\begin{array}{l}9\frac{1}{6}-5\frac{2}{6}=\frac{55}{6}-\frac{32}{6}\\ =\frac{55-32}{6}\\ =\frac{23}{6}\text{ or }3\frac{5}{6}\end{array}$

Example :

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

Example :

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

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

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