To find out how many gallons of lemonade each person would get if 3 people share \( 6 \frac{1}{2} \) gallons equally, we first need to convert \( 6 \frac{1}{2} \) to an improper fraction.
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Convert \( 6 \frac{1}{2} \) to an improper fraction: \[ 6 \frac{1}{2} = 6 + \frac{1}{2} = \frac{12}{2} + \frac{1}{2} = \frac{13}{2} \]
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Now, divide \( \frac{13}{2} \) by 3 to find out how much lemonade each person gets: \[ \frac{13}{2} \div 3 = \frac{13}{2} \times \frac{1}{3} = \frac{13}{6} \]
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Converting \( \frac{13}{6} \) back to a mixed number (if desired): \[ \frac{13}{6} = 2 \frac{1}{6} \]
So, each person would get \( \frac{13}{6} \) gallons of lemonade, or 2 \( \frac{1}{6} \) gallons.
Thus, the answer is: \[ \frac{13}{6} \text{ gallons of lemonade.} \]