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Simplify: $ \left(\frac{3}{5} \times \frac{-15}{21}\right)+\left(\frac{-9}{14} \div \frac{45}{28}\right)-\left(\frac{2}{3} \times \frac{30}{12}\right) $
Given:
\( \left(\frac{3}{5} \times \frac{-15}{21}\right)+\left(\frac{-9}{14} \div \frac{45}{28}\right)-\left(\frac{2}{3} \times \frac{30}{12}\right) \)
To do:
We have to simplify the given expression.
Solution:
\( \left(\frac{3}{5} \times \frac{-15}{21}\right)+\left(\frac{-9}{14} \div \frac{45}{28}\right)-\left(\frac{2}{3} \times \frac{30}{12}\right) \)
$=\frac{1\times-3}{1\times7}+\frac{-9}{14}\times\frac{28}{45}-\frac{1\times10}{1\times6}$
$=\frac{-3}{7}+\frac{-1\times2}{1\times5}-\frac{10}{6}$
$=-\frac{3}{7}-\frac{2}{5}-\frac{5}{3}$
$=-(\frac{3}{7}+\frac{2}{5}+\frac{5}{3})$
$=-(\frac{3\times15+2\times21+5\times35}{105})$
$= -\frac{45+42+175}{105}$
$=-\frac{262}{105}$
Therefore,
\( \left(\frac{3}{5} \times \frac{-15}{21}\right)+\left(\frac{-9}{14} \div \frac{45}{28}\right)-\left(\frac{2}{3} \times \frac{30}{12}\right) \)$=-\frac{262}{105}$.
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