Question

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

\[\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}\]

Answer 1

\[\text{We have:}\]
\[\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}\]
\[ = (\frac{3}{7} + \frac{- 11}{7}) + (\frac{- 4}{9} + \frac{7}{9})\]
\[ = \left( \frac{3 - 11}{7} \right) + \left( \frac{- 4 + 7}{9} \right)\]
\[ = \frac{- 8}{7} + \frac{3}{9}\]
\[ = \frac{- 72 + 21}{63}\]
\[ = \frac{- 51}{63}\]
\[ = \frac{- 17}{21}\]