Question

Mark the correct alternative in each of the following:

If $-\frac{3}{8}$ and $\frac{x}{-24}$ are equivalent rational numbers, then x =

(a) 3 (b) 6 (c) 9 (d) 12

Answer 1

It is given that the rational numbers $-\frac{3}{8}$ and $\frac{x}{-24}$ are equivalent rational numbers.

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

$$\begin{gathered} \therefore \frac{x}{-24}=-\frac{3}{8} \\ \Rightarrow x\times 8=-3\times \left(-24\right)\left(\frac{a}{b}=\frac{c}{d}\Rightarrow ad=bc\right) \\ \Rightarrow 8x=72 \\ \Rightarrow \frac{8x}{8}=\frac{72}{8}\left(\mathrm{Dividing}\mathrm{both}\mathrm{sides}\mathrm{by}8\right) \\ \Rightarrow x=9 \end{gathered}$$

Hence, the correct answer is option (c).