Question

In the following exercise,Perform the indicated operation, $\frac{{\displaystyle \frac{-4}{9}}}{{\displaystyle \frac{8}{21}}}$

Short answer

The simplified value of the expression is$\frac{-7}{6}$

Step-by-step solution

Step 1. Given information

The given expression is$\frac{{\displaystyle \frac{-4}{9}}}{{\displaystyle \frac{8}{21}}}$

Step 2. Perform division operation 

if $a,b,c,d$are numbers then $\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$

$$\begin{gathered} \frac{{\displaystyle \frac{-4}{9}}}{{\displaystyle \frac{8}{21}}}=\frac{-4}{9}\times \frac{21}{8} \\ =\frac{-1}{3}\times \frac{7}{2} \\ =\frac{-7}{6} \end{gathered}$$

Step 3. Conclusion

Hence, the value of the given expression is$\frac{-7}{6}$