Question

By what rational number should $\frac{-8}{39}$ be multiplied to obtain $\frac{5}{26}$?

Answer 1

Let the required number be $x$.
Given condition is when $x$ multiplied by $\frac{-8}{39}$, the result is $\frac{5}{26}$.
So, $x\times \left(\frac{-8}{39}\right)=\left(\frac{5}{26}\right)$
$\Rightarrow x=\frac{5}{26}\times \frac{39}{-8}$
$=\frac{5\times 3}{2\times -8}$
$\Rightarrow x=\frac{15}{-16}\times \frac{-1}{-1}$
$\therefore x=\frac{-15}{16}$ is the required number.