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Simplify: $ \frac{-9}{42}+\left(\frac{-5}{21}\right)+\frac{3}{84}+\frac{1}{6} $.
Given:
\( \frac{-9}{42}+\left(\frac{-5}{21}\right)+\frac{3}{84}+\frac{1}{6} \).
To do:
We have to simplify \( \frac{-9}{42}+\left(\frac{-5}{21}\right)+\frac{3}{84}+\frac{1}{6} \).
Solution:
\( \frac{-9}{42}+\left(\frac{-5}{21}\right)+\frac{3}{84}+\frac{1}{6} \).
LCM of 42, 21, 84 and 6 $=84$.
$\frac{-9}{42}+\frac{-5}{21}+\frac{3}{84}+\frac{1}{6}=\frac{-9\times2+(-5\times4)+3\times1+1\times14}{84}$
$=\frac{-18-20+3+14}{84}$
$=\frac{-38+17}{84}$
$=\frac{-21}{84}$
$=\frac{-1}{4}$
Therefore,
$\frac{-9}{42}+\frac{-5}{21}+\frac{3}{84}+\frac{1}{6}=\frac{-1}{4}$.
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