Question

Find the value of $\mathrm{x}$ if the pairs of the rational numbers given below are equivalent:

$\frac{15}{\mathrm{x}},\frac{-6}{16}$

Answer 1

If $\frac{\mathrm{p}}{\mathrm{q}}$ is a rational number , then $\frac{\mathrm{p}\times \mathrm{k}}{\mathrm{q}\times \mathrm{k}}$ is its equivalent rational number, where $\mathrm{k}$ is a non zero integer.

So, let us use cross multiplication method, $\frac{15}{\mathrm{x}},\frac{-6}{16}$

$$\begin{gathered} \Rightarrow 15\times 16=\mathrm{x}\times (-6) \\ \Rightarrow -6\mathrm{x}=240 \\ \Rightarrow \mathrm{x}=\frac{240}{-6} \\ \Rightarrow \mathrm{x}=\frac{{\displaystyle \stackrel{18}{\cancel{240}}}}{-\cancel{6}} \\ \Rightarrow \mathrm{x}=-40 \end{gathered}$$

Hence, the value of $\mathrm{x}$ is $-40$ i.e., $\frac{15}{-40},\frac{-6}{16}$