1. The problem asks to divide 3 by 2 and a half. 2. First, convert 2 and a half to an improper fraction: 2 and a half = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}. 3. Now, divide 3 by \frac{5}{2} which is the same as multiplying 3 by the reciprocal of \frac{5}{2}. 4. The reciprocal of \frac{5}{2} is \frac{2}{5}. 5. So, 3 \div \frac{5}{2} = 3 \times \frac{2}{5} = \frac{3 \times 2}{5} = \frac{6}{5}. 6. \frac{6}{5} is an improper fraction and can be written as 1 \frac{1}{5}. 7. Therefore, 3 divided by 2 and a half equals \frac{6}{5} or 1 \frac{1}{5}.