1. **State the problem:** Multiply the mixed numbers $2 \frac{5}{7}$ and $1 \frac{1}{5}$ and write the answer as a mixed number in simplest form. 2. **Convert mixed numbers to improper fractions:** - $2 \frac{5}{7} = \frac{2 \times 7 + 5}{7} = \frac{14 + 5}{7} = \frac{19}{7}$ - $1 \frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{5 + 1}{5} = \frac{6}{5}$ 3. **Multiply the improper fractions:** $$\frac{19}{7} \times \frac{6}{5} = \frac{19 \times 6}{7 \times 5} = \frac{114}{35}$$ 4. **Convert the product back to a mixed number:** Divide 114 by 35: - $114 \div 35 = 3$ remainder $9$ - So, $\frac{114}{35} = 3 \frac{9}{35}$ 5. **Simplify the fraction if possible:** - The fraction $\frac{9}{35}$ cannot be simplified further because 9 and 35 have no common factors other than 1. **Final answer:** $$2 \frac{5}{7} \times 1 \frac{1}{5} = 3 \frac{9}{35}$$