To find the sum of \( p \) and \( q \), where \( p = \frac{3}{4} \) and \( q = -\frac{11}{4} \), we can add these two fractions together:
\[ p + q = \frac{3}{4} + \left(-\frac{11}{4}\right) \]
Since both fractions have the same denominator, we can combine them directly:
\[ p + q = \frac{3 - 11}{4} = \frac{-8}{4} \]
Now, we simplify \( \frac{-8}{4} \):
\[ \frac{-8}{4} = -2 \]
Thus, the sum of \( p \) and \( q \) is \( -2 \).
The answer is \(-2\).