Question

The reciprocal of$\left(\frac{2}{5}\right)\times \left(\frac{-4}{9}\right)$is _____

Answer 1

Step-1: Find the product of $\left(\frac{2}{5}\right)\times \left(\frac{-4}{9}\right)$

$\left(\frac{2}{5}\right)\times \left(\frac{-4}{9}\right)$$=\frac{2\times (-4)}{5\times 9}=\frac{-8}{45}$

Step-2: Find the reciprocal of $\frac{-8}{45}$

Reciprocal of $\frac{-8}{45}$$=\frac{1}{\left({\displaystyle \frac{-8}{45}}\right)}=1\times \frac{-45}{8}=\frac{-45}{8}$

Hence, the reciprocal of $\left(\frac{2}{5}\right)\times \left(\frac{-4}{9}\right)$is $\frac{-45}{8}$.