Question

By what number should we multiply $\frac{-1}{6}$ so that the product may be $\frac{-23}{9}$?

Answer 1

Let x be the number by which we should multiply $\frac{-1}{6}\mathrm{to}\mathrm{get}\frac{-23}{9}.$
Then, according to the question, we have
$$\begin{gathered} \frac{-1}{6}\times x=\frac{-23}{9} \\ \Rightarrow x=\frac{-23}{9}\times (-6)=\frac{46}{3} \end{gathered}$$