Question

Simplify and reduce to a simple fraction: $\left(\frac{4}{5}\right)÷\left(\frac{7}{15}\right)\times \left(\frac{8}{9}\right)$

Answer 1

Given: $\left(\frac{4}{5}\right)÷\left(\frac{7}{15}\right)\times \left(\frac{8}{9}\right)$

$$\begin{gathered} =\left(\frac{4}{\cancel{5}}\right)\times \left(\frac{{\cancel{15}}^{\cancel{3}}}{7}\right)\times \left(\frac{8}{{\cancel{9}}_3}\right)[\because \frac{\mathrm{a}}{\mathrm{b}}÷\frac{\mathrm{c}}{\mathrm{d}}=\frac{\mathrm{a}}{\mathrm{b}}\times \frac{\mathrm{d}}{\mathrm{c}}] \\ =\frac{4\times 8}{7\times 3} \end{gathered}$$

$=\frac{32}{21}$

Hence, $\left(\frac{4}{5}\right)÷\left(\frac{7}{15}\right)\times \left(\frac{8}{9}\right)=\frac{32}{21}$