Question

By what number should (−3)⁻¹ be multiplied so that the product becomes 6⁻¹?

Answer 1

Let the number be $x$.

$\therefore$ ${\left(-3\right)}^{-1}\times x={\left(6\right)}^{-1}$
$$\begin{gathered} \Rightarrow \frac{1}{-3}\times x=\frac{1}{6} \\ \Rightarrow \frac{1\times -1}{-3\times -1}\times x=\frac{1}{6} \\ \therefore \frac{-x}{3}=\frac{1}{6} \\ \mathrm{On}\mathrm{cross}\mathrm{multiplying}: \\ -x\times 6=1\times 3 \\ \Rightarrow -6x=3 \\ \Rightarrow 6x=-3 \\ \therefore x=\frac{-3}{6}=\frac{-1}{2} \end{gathered}$$