Question

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

\[\frac{6}{7} + 1 + \frac{- 7}{9} + \frac{19}{21} + \frac{- 12}{7}\]

Answer 1

\[\frac{6}{7} + 1 + \frac{- 7}{9} + \frac{19}{21} + \frac{- 12}{7}\]
\[ = \frac{54}{63} + \frac{63}{63} + \frac{- 49}{63} + \frac{57}{63} + \frac{- 108}{63}\]
\[ = \frac{54 + 63 + ( - 49) + 57 + ( - 108)}{63}\]
\[ = \frac{54 + 63 - 49 + 57 - 108}{63}\]
\[ = \frac{17}{63}\]