Question

Mark the correct alternative in each of the following:

If the rational numbers $\frac{-2}{3}$ and $\frac{4}{x}$ represent a pair of equivalent rational numbers, then x =

(a) 6 (b) −6 (c) 3 (d) −3

Answer 1

It is given that the rational numbers $\frac{-2}{3}$ and $\frac{4}{x}$ represent a pair of equivalent rational numbers.

We know that the values of two equivalent rational numbers is equal.

$$\begin{gathered} \therefore \frac{-2}{3}=\frac{4}{x} \\ \Rightarrow -2\times x=4\times 3\left(\frac{a}{b}=\frac{c}{d}\Rightarrow ad=bc\right) \\ \Rightarrow -2x=12 \\ \Rightarrow \frac{-2x}{-2}=\frac{12}{-2}\left(\mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}-2\right) \\ \Rightarrow x=-6 \end{gathered}$$

Hence, the correct answer is option (b).