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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} $
$ \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 $\frac{32}{3}$.