Question

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

\[\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}\]

Answer 1

\[ (\frac{3}{5} + \frac{9}{5}) + (\frac{- 7}{3} + \frac{7}{3}) + \frac{- 13}{15}\]
\[ = \left( \frac{3 + 9}{5} \right) + \left( \frac{- 7 + 7}{3} \right) + \frac{- 13}{15}\]
\[ = \frac{12}{5} + \frac{- 13}{15}\]
\[ = \frac{36 - 13}{15}\]
\[ = \frac{23}{15}\]