question_answer

Find

(a) \[\frac{-3}{7}+\frac{2}{3}\]

(b) \[\frac{-5}{6}+\frac{-3}{11}\]

Answer:

(a) Given, \[\frac{-3}{7}+\frac{2}{3}\]

\[\because \]LCM of 7 and 3 = 21

So,\[\frac{-3}{7}=\frac{-3\times 3}{7\times 3}=\frac{-9}{21}\,\,and\,\,\frac{2}{3}=\frac{2\times 7}{3\times 7}=\frac{14}{21}\]

\[\therefore \]\[\frac{-3}{7}+\frac{2}{3}=\frac{-9}{21}+\frac{14}{21}=\frac{-9+14}{21}=\frac{5}{21}\]

(b) Given, \[\frac{-5}{6}+\frac{-3}{11}\]

\[\because \] LCM of 6 and 11 = 66

\[\therefore \]\[\frac{-5}{6}=\frac{-25\times 11}{6\times 11}=\frac{-55}{66}\,\,and\,\,\frac{-3}{11}=\frac{-3\times 6}{6\times 11}=\frac{-18}{66}\]

Now,\[\frac{-5}{6}+\frac{-3}{11}=\frac{-55}{66}+\frac{-18}{66}=\frac{-55(-18)}{66}\]

\[=\frac{-55-18}{66}=\frac{-73}{66}\]