Question

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

\[\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}\]

Answer 1

\[(\frac{1}{8} + \frac{- 5}{16}) + (\frac{5}{12} + \frac{7}{12}) + (\frac{2}{7} + \frac{9}{7})\]
\[ = (\frac{2 - 5}{16}) + (\frac{5 + 7}{12}) + (\frac{2 + 9}{7})\]
\[ = \frac{- 3}{16} + \frac{12}{12} + \frac{11}{7}\]
\[ = \frac{- 63 + 336 + 528}{336}\]
\[ = \frac{801}{336}\]
\[ = \frac{267}{112}\]