1. **State the problem:** Multiply the mixed numbers $1 \frac{3}{7}$ and $2 \frac{1}{5}$. 2. **Convert mixed numbers to improper fractions:** $1 \frac{3}{7} = \frac{1 \times 7 + 3}{7} = \frac{10}{7}$ $2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}$ 3. **Multiply the improper fractions:** $$\frac{10}{7} \times \frac{11}{5} = \frac{10 \times 11}{7 \times 5} = \frac{110}{35}$$ 4. **Simplify the fraction:** Find the greatest common divisor (GCD) of 110 and 35, which is 5. $$\frac{\cancel{110}^{22}}{\cancel{35}^{7}} = \frac{22}{7}$$ 5. **Convert back to a mixed number:** Divide 22 by 7: $22 \div 7 = 3$ remainder $1$, so $$3 \frac{1}{7}$$ **Final answer:** $$1 \frac{3}{7} \times 2 \frac{1}{5} = 3 \frac{1}{7}$$