1. **State the problem:** We need to calculate $2 \div 3 \frac{1}{2}$. 2. **Convert the mixed number to an improper fraction:** $$3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}$$ 3. **Rewrite the division as multiplication by the reciprocal:** $$2 \div \frac{7}{2} = 2 \times \frac{2}{7}$$ 4. **Multiply the numerators and denominators:** $$2 \times \frac{2}{7} = \frac{2 \times 2}{7} = \frac{4}{7}$$ 5. **Final answer:** $$2 \div 3 \frac{1}{2} = \frac{4}{7}$$ This means when you divide 2 by 3 and a half, the result is four sevenths.