Question

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

\[\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}\]

Answer 1

\[\text{We have:}\]
\[ \frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}\]
\[ = (\frac{4}{7} + \frac{- 13}{7}) + (\frac{- 8}{9}) + \frac{17}{21}\]
\[ = \left( \frac{4 - 13}{7} \right) + \left( \frac{- 8}{9} \right) + \frac{17}{21}\]
\[ = \frac{- 9}{7} + \frac{- 8}{9} + \frac{17}{21}\]
\[ = \frac{- 81 - 56 + 51}{63}\]
\[ = \frac{- 86}{63}\]