question_answer

Simplify: \[\frac{5}{3}+\frac{11}{2}+\frac{-9}{4}+\frac{-8}{3}+\frac{-7}{2}\]

Answer:

\[\frac{5}{3}+\frac{11}{2}+\frac{-9}{4}+\frac{-8}{3}+\frac{-7}{2}=\left( \frac{5}{3}+\frac{-8}{3} \right)+\left( \frac{11}{2}+\frac{-7}{2} \right)+\left( \frac{-9}{4} \right)\]\[=\frac{5+(-8)}{3}+\frac{11+(-7)}{2}+\frac{-9}{4}\]

\[=-\frac{3}{3}+\frac{4}{2}+\frac{-9}{4}\]

\[=1+\frac{(-9)}{4}\]

\[=\frac{1\times 4+(-9)}{4}=\frac{4-9}{4}\]

\[=\frac{-5}{4}.\]