1. **State the problem:** Multiply the mixed numbers $2 \frac{1}{2}$ and $3 \frac{1}{3}$. 2. **Convert mixed numbers to improper fractions:** $$2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$$ $$3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}$$ 3. **Multiply the improper fractions:** $$\frac{5}{2} \times \frac{10}{3} = \frac{5 \times 10}{2 \times 3} = \frac{50}{6}$$ 4. **Simplify the fraction:** $$\frac{50}{6} = \frac{\cancel{50}^{25} \times 2}{\cancel{6}^{3} \times 2} = \frac{25}{3}$$ 5. **Convert back to a mixed number:** Divide 25 by 3: $$25 \div 3 = 8 \text{ remainder } 1$$ So, $$\frac{25}{3} = 8 \frac{1}{3}$$ **Final answer:** $8 \frac{1}{3}$