Question

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

$\frac{-5}{9},\frac{10}{\mathrm{x}}$

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, $\frac{-5}{9},\frac{10}{\mathrm{x}}$

$$\begin{gathered} \Rightarrow -5\times \mathrm{x}=9\times 10 \\ \Rightarrow -5\mathrm{x}=90 \\ \Rightarrow \mathrm{x}=\frac{90}{-5} \\ \Rightarrow \mathrm{x}=\frac{{\displaystyle \stackrel{18}{\cancel{90}}}}{-\cancel{5}} \\ \Rightarrow \mathrm{x}=-18 \end{gathered}$$

Hence, the value of $\mathrm{x}$ is $-18$ i.e., $\frac{-5}{9},\frac{10}{-18}$