To add \(-3\) and \(-17\), we can use the properties of operations, particularly the property of addition which states that adding two negative numbers results in a more negative number.
So, we can add \(-3\) and \(-17\):
\[ (-3) + (-17) = -(3 + 17) \]
Now, we calculate \(3 + 17\):
\[ 3 + 17 = 20 \]
Thus,
\[ (-3) + (-17) = -20 \]
Therefore, \((-3) + (-17) = -20\).