Question

Re-arrange suitably and find the sum in each of the following:

\[\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}\]

Answer 1

\[ (\frac{4}{13} - \frac{8}{13} + \frac{9}{13}) + \frac{- 5}{8}\]
\[ = \left( \frac{4 - 8 + 9}{13} \right) + \frac{- 5}{8}\]
\[ = \frac{5}{13} + \frac{- 5}{8}\]
\[ = \frac{40 - 65}{104}\]
\[ = \frac{- 25}{104}\]