Question

If $(-24{)}^{-1}$ is divided by $-\frac{1}{m}$, then the quotient is $3^{-1}$. The value of $m$ is

Answer 1

Let the required number be $x$.

$\therefore (-24{)}^{-1}÷x=3^{-1}$

$\Rightarrow \frac{(-24{)}^{-1}}{x}=3^{-1}$

$\Rightarrow \frac{\frac{1}{-24}}{x}=\frac{1}{3}$ ...$[\because a^{-1}=\frac{1}{a}]$

$\Rightarrow \frac{1}{-24x}=\frac{1}{3}$

$\Rightarrow 3=-24x$

$\Rightarrow x=\frac{3}{-24}$

$\Rightarrow x=\frac{-3}{24}=-\frac{1}{8}$