Verify that 5 6 (-4 5 +-6 10 )= [5 6 (-4 5 ) ]+ [5 6 (-6 10 ) ]. - Vidyadip

Question

Verify that
$ \frac{5}{6} \times\left(-\frac{4}{5}+\frac{-6}{10}\right)=\left[\frac{5}{6} \times\left(\frac{-4}{5}\right)\right]+\left[\frac{5}{6} \times\left(\frac{-6}{10}\right)\right].$

✓

Answer

We have,
LHS $=\frac{5}{6} \times\left(-\frac{4}{5}+\frac{(-6)}{10}\right)=\frac{5}{6} \times\left(\frac{-8-6}{10}\right)$
$=\frac{5}{6} \times\left(\frac{-14}{10}\right)=\frac{-70}{60}=\frac{-7}{6}$
Also, RHS $=\left[\frac{5}{6} \times\left(\frac{-4}{5}\right)\right]+\left[\frac{5}{6} \times\left(\frac{-6}{10}\right)\right]$
$=\left(\frac{-20}{30}\right)+\left(\frac{-30}{60}\right)=\frac{-20}{30}-\frac{30}{60}$
$=\frac{-40-30}{60}=\frac{-70}{60}=\frac{-7}{6}$
Thus, LHS = RHS

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