1. **State the problem:** Multiply the mixed numbers $1 \frac{6}{10}$ and $1 \frac{3}{10}$. 2. **Convert mixed numbers to improper fractions:** $1 \frac{6}{10} = \frac{10 \times 1 + 6}{10} = \frac{16}{10}$ $1 \frac{3}{10} = \frac{10 \times 1 + 3}{10} = \frac{13}{10}$ 3. **Multiply the improper fractions:** $$\frac{16}{10} \times \frac{13}{10} = \frac{16 \times 13}{10 \times 10} = \frac{208}{100}$$ 4. **Simplify the fraction:** Find the greatest common divisor (GCD) of 208 and 100, which is 4. $$\frac{\cancel{4} \times 52}{\cancel{4} \times 25} = \frac{52}{25}$$ 5. **Convert back to a mixed number:** Divide 52 by 25: $52 \div 25 = 2$ remainder $2$, so $$2 \frac{2}{25}$$ **Final answer:** $$1 \frac{6}{10} \times 1 \frac{3}{10} = 2 \frac{2}{25}$$