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