Question

Which of the given pairs of rational numbers are equivalent?

$\frac{10}{21},\frac{50}{105}$

Answer 1

By multiplying the numerator and denominator of a rational number by the same non zero integer, we obtain another rational number equivalent to the given rational number is called equivalent rational number.

Or 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,

$$\begin{gathered} \frac{10}{21},\frac{50}{105} \\ 10\times 105=21\times 50 \\ 1050=1050 \end{gathered}$$

So it is an equivalent pair.

Hence, Yes they are equivalent rational number.