What is the value of expression $2\frac{3}{10}-1\frac{7}{15}?$

The given expression is $2\frac{3}{10}-1\frac{7}{15}$.

The above expression can be written as,

$2\frac{3}{10}-1\frac{7}{15}=\frac{23}{10}-\frac{22}{15}$

To make the subtraction process easier, convert the given fractions to like fractions.

$\begin{array}{l}\frac{23}{10}\times \frac{3}{3}=\frac{69}{30}\\ \frac{22}{15}\times \frac{2}{2}=\frac{44}{30}\end{array}$

Determining the difference between the fractions, we get:

$\begin{array}{l}\frac{69}{30}-\frac{44}{30}\\ =\frac{25}{30}\\ =\frac{\mathbf{5}}{\mathbf{6}}\end{array}$

Thus, $2\frac{3}{10}-1\frac{7}{15}=\frac{\mathbf{5}}{\mathbf{6}}$