Question

Simplify.

$\frac{-{\displaystyle \frac{4}{5}}}{2}$

Short answer

The value of the given expression is $-\frac{{\displaystyle 2}}{5}$.

Step-by-step solution

Step 1. Given information

Consider the expression.

$\frac{-{\displaystyle \frac{4}{5}}}{2}$

Step 2. Rewrite the given expression as division. 

$\frac{-{\displaystyle \frac{4}{5}}}{2}=-\frac{{\displaystyle 4}}{5}÷2$

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

$\frac{-{\displaystyle \frac{4}{5}}}{2}=\left(-\frac{{\displaystyle 4}}{5}\right)·\frac{1}{2}$

Step 4.  Determine the sign of the product and then simplify.

The sign of the product are different. So, the product will be negative.

$\begin{array}{rcl}\frac{-{\displaystyle \frac{4}{5}}}{2}& =& -\frac{{\displaystyle 4}}{5}·\frac{1}{2}\\ & =& -\frac{2·\cancel{2}}{5}·\frac{1}{\cancel{2}}\\ & =& -\frac{2}{5}\end{array}$

Hence, the value is $-\frac{2}{5}$.