Simplify: $\frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}$.

Given: $\frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}$.

To do: To simplify: $\frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}$.

Solution:

$\frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}$

$=-\frac{2\times3}{5\times7}-\frac{1\times3}{6\times2}+\frac{1\times2}{14\times5}$

$=-\frac{6}{35}-\frac{3}{12}+\frac{2}{70}$

$=-\frac{6\times12}{35\times12}-\frac{3\times35}{12\times35}+\frac{2\times6}{70\times6}$

$=-\frac{72}{420}-\frac{105}{420}+\frac{12}{420}$

$=\frac{-72-105+12}{420}$

$=\frac{-165}{420}$

$=-\frac{165}{420}$

$=-\frac{3}{4}$

Thus, $\frac{2}{5} \times\left(-\frac{3}{7}\right)-\frac{1}{6} \times \frac{3}{2}+\frac{1}{14} \times \frac{2}{5}=-\frac{3}{4}$.

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Updated on: 10-Oct-2022

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