Question

If $\frac{2}{7}$ and $\frac{a}{21}$ are equivalent fractions, then what is the value of $a$ ?

Answer 1

We get equivalent fractions when we multiply or divide the numerator and denominator of a fraction by the same number.

We see that the denominator of $\frac{a}{21}$ is thrice that of $\frac{2}{7}$ i.e. $7\times 3=21$.

Thus, the numerator of $\frac{2}{7}$ should also be multiplied by 3, in order to have $\frac{2}{7}$ equivalent to $\frac{a}{21}$ .

$\frac{2}{7}\times \frac{3}{3}=\frac{6}{21}$

On comparing $\frac{a}{21}$ and $\frac{6}{21}$, we get

$a=6$