Question

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

\[\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}\]

Answer 1

\[\text{We have:}\]
\[\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}\]
\[ = (\frac{2}{5} + \frac{4}{5}) + (+\frac{8}{3} + \frac{- 2}{3}) + \frac{- 11}{15}\]
\[ = \left( \frac{2 + 4}{5} \right) + \left( \frac{8 - 2}{3} \right) + \frac{- 11}{15}\]
\[ = \frac{6}{5} + \frac{6}{3} + \frac{- 11}{15}\]
\[ = \frac{18 + 30 - 11}{15}\]
\[ = \frac{37}{15}\]