Question

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

$\frac{\mathrm{x}}{28},\frac{5}{14}$

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, $\frac{\mathrm{x}}{28},\frac{5}{14}$

$$\begin{gathered} \Rightarrow \mathrm{x}\times 14=28\times 5 \\ \Rightarrow 14\mathrm{x}=140 \\ \Rightarrow \mathrm{x}=\frac{140}{14} \\ \Rightarrow \mathrm{x}=\frac{{\displaystyle \stackrel{10}{\cancel{140}}}}{\cancel{14}} \\ \Rightarrow \mathrm{x}=10 \end{gathered}$$

Hence, the value of $\mathrm{x}$ is $10$ i.e., $\frac{\mathrm{x}}{28},\frac{5}{14}$.