1. **State the problem:** Multiply the mixed numbers $4 \frac{1}{2}$ and $1 \frac{2}{5}$ and express the answer as a simplified fraction. 2. **Convert mixed numbers to improper fractions:** - $4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{9}{2}$ - $1 \frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{7}{5}$ 3. **Multiply the improper fractions:** $$\frac{9}{2} \times \frac{7}{5} = \frac{9 \times 7}{2 \times 5} = \frac{63}{10}$$ 4. **Simplify the fraction if possible:** - $\frac{63}{10}$ is already in simplest form because 63 and 10 have no common factors other than 1. 5. **Final answer:** $$\boxed{\frac{63}{10}}$$ This fraction can also be expressed as the mixed number $6 \frac{3}{10}$, but since the problem asks for a fraction, $\frac{63}{10}$ is the correct final answer.