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Using distributive property, solve$\frac{2}{3}\times\frac{1}{5}-\frac{4}{5}-\frac{2}{3}\times\frac{3}{5}$
Given :
The given expression is $\frac{2}{3}\times\frac{1}{5}-\frac{4}{5}-\frac{2}{3}\times\frac{3}{5}$.
To do :
We have to evaluate the given expression using the distributive property.
Solution :
$\frac{2}{3}\times\frac{1}{5}-\frac{4}{5}-\frac{2}{3}\times\frac{3}{5}=\frac{2}{3}(\frac{1}{5}-\frac{3}{5})-\frac{4}{5}$
$=\frac{2}{3}(\frac{1-3}{5})-\frac{4}{5}$
$= \frac{2}{3} (\frac{-2}{5})-\frac{4}{5}$
$= \frac{2\times(-2)}{3\times5}-\frac{4}{5}$
$= \frac{-4}{15}-\frac{4}{5}$
$=\frac{-4-4(3)}{15}$
$=\frac{-4-12}{15}$
$=\frac{-16}{15}$
Therefore, the value of $\frac{2}{3}\times\frac{1}{5}-\frac{4}{5}-\frac{2}{3}\times\frac{3}{5}$ is $\frac{-16}{15}$.
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