Question

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

\[\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}\]

Answer 1

\[\text{We have}:\]
\[\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}\]
\[ = (\frac{2}{5} + \frac{- 4}{5}) + (\frac{7}{3}+ \frac{- 1}{3})\]
\[ = \left( \frac{2 - 4}{5} \right) + \left( \frac{7 - 1}{3} \right)\]
\[ = \frac{- 2}{5} + \frac{6}{3}\]
\[ = \frac{- 6 + 30}{15}\]
\[ = \frac{24}{15}\]
\[ = \frac{8}{5}\]