Question

Express each of the following as a rational number of the form \[\frac{p}{q}:\] 

\[\frac{- 7}{4} + \frac{5}{3} + \frac{- 1}{2} + \frac{- 5}{6} + 2\]

Answer 1

\[\frac{- 7}{4} + \frac{5}{3} + \frac{- 1}{2} + \frac{- 5}{6} + 2\]
\[ = \frac{- 21}{12} + \frac{20}{12} + \frac{- 6}{12} + \frac{- 10}{12} + \frac{24}{12}\]
\[ = \frac{( - 21) + 20 + ( - 6) + ( - 10) + 24}{12}\]
\[ = \frac{- 21 + 20 - 6 - 10 + 24}{12}\]
\[ = \frac{7}{12}\]