1. The problem is to multiply the mixed numbers $4 \frac{1}{5}$ and $4 \frac{1}{2}$. 2. First, convert the mixed numbers to improper fractions. $$4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5}$$ $$4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2}$$ 3. Multiply the improper fractions: $$\frac{21}{5} \times \frac{9}{2} = \frac{21 \times 9}{5 \times 2} = \frac{189}{10}$$ 4. Simplify the fraction if possible. Here, $189$ and $10$ have no common factors other than 1, so the fraction is already in simplest form. 5. Convert the improper fraction back to a mixed number: $$\frac{189}{10} = 18 \frac{9}{10}$$ because $189 \div 10 = 18$ remainder $9$. Final answer: $18 \frac{9}{10}$