Question

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

$\frac{3}{7},\frac{\mathrm{x}}{42}$

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.

Since the given rational numbers are equivalent

So, $\frac{3}{7}=\frac{\mathrm{x}}{42}$

$\Rightarrow \frac{3}{7}\xcancel{=}\frac{\mathrm{x}}{42}$ [Cross multiplication]

$$\begin{gathered} \Rightarrow 3\times 42=7\times \mathrm{x} \\ \Rightarrow 126=7\mathrm{x} \\ \Rightarrow \frac{126}{7}=\mathrm{x} \\ \Rightarrow \mathrm{x}=\frac{{\displaystyle \stackrel{18}{\cancel{126}}}}{\cancel{7}} \\ \Rightarrow \mathrm{x}=18 \end{gathered}$$

Hence, the value of $\mathrm{x}$ is $18$.