Question

If $\frac{9}{12}\times \frac{8}{11}\times \frac{-24}{27}\times \frac{33}{40}=\frac{-2}{m}$. Find $m$.

Answer 1

Let us solve the given expression $\frac{9}{12}\times \frac{8}{11}\times \frac{-24}{27}\times \frac{33}{40}=\frac{-2}{m}$ to find the value of $m$ as shown below:

$\frac{9}{12}\times \frac{8}{11}\times \frac{-24}{27}\times \frac{33}{40}=\frac{-2}{m}$

$\Rightarrow \frac{3}{4}\times \frac{8}{11}\times \frac{-8}{9}\times \frac{33}{40}=\frac{-2}{m}$

$\Rightarrow \frac{1}{1}\times \frac{2}{1}\times \frac{-1}{1}\times \frac{1}{5}=\frac{-2}{m}$

$\Rightarrow \frac{-2}{5}=\frac{-2}{m}$

$\Rightarrow m=-2\times \frac{5}{-2}$

$\Rightarrow m=5$

Hence, $m=5$.