1. **State the problem:** We need to find the quotient of $3 \frac{1}{3} \div \frac{1}{2}$ and express the answer as a mixed number in simplest form. 2. **Convert the mixed number to an improper fraction:** $$3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}$$ 3. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ 4. **Apply the rule:** $$\frac{10}{3} \div \frac{1}{2} = \frac{10}{3} \times \frac{2}{1} = \frac{10 \times 2}{3 \times 1} = \frac{20}{3}$$ 5. **Convert the improper fraction back to a mixed number:** Divide 20 by 3: $$20 \div 3 = 6 \text{ remainder } 2$$ So, $$\frac{20}{3} = 6 \frac{2}{3}$$ 6. **Final answer:** The quotient is $6 \frac{2}{3}$. The whole number part is **6**.