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 $\frac{2}{3}\times\frac{1}{5}-\frac{4}{5}-\frac{2}{3}\times\frac{3}{5}$.

$\frac{2}{3}\times\frac{1}{5}-\frac{4}{5}-\frac{2}{3}\times\frac{3}{5}=\frac{2}{3}(\frac{1}{5}-\frac{3}{5})-\frac{4}{5}$

$=\frac{2}{3}(\frac{1-3}{5})-\frac{4}{5}$

$= \frac{2}{3} (\frac{-2}{5})-\frac{4}{5}$

$= \frac{2\times(-2)}{3\times5}-\frac{4}{5}$

$= \frac{-4}{15}-\frac{4}{5}$

$=\frac{-4-4(3)}{15}$

$=\frac{-4-12}{15}$

$=\frac{-16}{15}$

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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Updated on: 10-Oct-2022

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