Question

Simplify.

$\frac{{\displaystyle \frac{5}{3}}}{10}$

Short answer

The value of the given expression is $\frac{1}{6}$.

Step-by-step solution

Step 1. Given information

Consider the expression.

$\frac{{\displaystyle \frac{5}{3}}}{10}$

Step 2. Rewrite the given expression as division.

$\frac{{\displaystyle \frac{5}{3}}}{10}=\frac{5}{3}÷10$

Step 3. Apply the Fraction Division Formula:ab÷cd=ab·dc, where b≠0, c≠0, and d≠0.

$\begin{array}{rcl}\frac{{\displaystyle \frac{5}{3}}}{10}& =& \frac{5}{3}·\frac{1}{10}\\ & =& \frac{\cancel{5}}{3}·\frac{1}{2·\cancel{5}}\\ & =& \frac{1}{6}\end{array}$

Hence, the value is $\begin{array}{rcl}& & \frac{1}{6}\end{array}$.