To find out how many gallons of lemonade each person would get when 3 people share \(6 \frac{1}{2}\) gallons of lemonade equally, first convert \(6 \frac{1}{2}\) into an improper fraction.
\[ 6 \frac{1}{2} = 6 + \frac{1}{2} = \frac{12}{2} + \frac{1}{2} = \frac{13}{2} \text{ gallons} \]
Now, divide this amount by 3:
\[ \text{Amount per person} = \frac{13}{2} \div 3 = \frac{13}{2} \times \frac{1}{3} = \frac{13}{6} \]
To convert \(\frac{13}{6}\) into a mixed number, divide 13 by 6:
\[ 13 \div 6 = 2 \quad \text{with a remainder of } 1 \]
So,
\[ \frac{13}{6} = 2 \frac{1}{6} \text{ gallons} \]
Therefore, each person would get \(\mathbf{2 \frac{1}{6}}\) of a gallon of lemonade.