Solve the following:$3\frac{1}{5} \div \frac{8}{27} - \frac{2}{21} \times \frac{7}{5}$.

Given :

The given expression is $3\frac{1}{5} \div \frac{8}{27} - \frac{2}{21} \times \frac{7}{5}$.

To do :

We have to solve the given expression.

Solution :

We know that, $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

 $3\frac{1}{5} \div \frac{8}{27} =  3\frac{1}{5} \times \frac{27}{8} $

$3\frac{1}{5} \div \frac{8}{27} -\frac{2}{21} \times \frac{7}{5} =\frac{3\times 5+1}{5} \div \frac{8}{27} -\frac{2}{21} \times \frac{7}{5} =\frac{15+1}{5} \div \frac{8}{27} -\frac{2}{21} \times \frac{7}{5} =\frac{16}{5} \times \frac{27}{8} -\frac{2}{21} \times \frac{7}{5} =\frac{2\times 27}{5\times 1} -\frac{2\times 1}{3\times 5} =\frac{54}{5} -\frac{2}{15} =\frac{54\times 3-2\times 1}{15} =\frac{162-2}{15} =\frac{160}{15} =\frac{32}{3}$

$ \frac{3 \times 5 +1}{5} = \frac{16}{5}$

$=  \frac{16}{5} \times \frac{27}{8} - \frac{2}{21} \times \frac{7}{5}$

$=  \frac{2}{5} \times \frac{27}{1} - \frac{2}{3} \times \frac{1}{5}$

$= \frac{2 \times 27}{5} - \frac{2}{3 \times 5}$

$=\frac{54}{5} - \frac{2}{15}$

$=\frac{54 \times 3}{5 \times 3} - \frac{2}{15} $ 

$= \frac{162}{15} - \frac{2}{15}$

$= \frac{162-2}{15}$

$=\frac{160}{15} =\frac{32}{3}$

Therefore, the value of the given expression is $\frac{32}{3}$.