Question

Multiply:

$\frac{3}{7}$ by $\frac{21}{81}$

Answer 1

We know, $\mathrm{Product}\mathrm{of}\mathrm{two}\mathrm{rational}\mathrm{numbers}=\frac{\mathrm{Product}\mathrm{of}\mathrm{their}\mathrm{numerators}}{\mathrm{Product}\mathrm{of}\mathrm{their}\mathrm{denominators}}$

So, $\frac{3}{7}$ by $\frac{21}{81}$

$$\begin{gathered} =\frac{3}{7}\times \frac{21}{81} \\ =\frac{3\times 21}{7\times 81} \\ =\frac{\cancel{3}\times {\displaystyle \stackrel{3}{\cancel{21}}}}{\cancel{7}\times {\displaystyle \underset{27}{\cancel{81}}}} \\ =\frac{\cancel{3}}{{\displaystyle \underset{9}{\cancel{27}}}} \\ =\frac{1}{9} \end{gathered}$$

Hence, $\frac{3}{7}$ by $\frac{21}{81}$ is $\frac{1}{9}$.