1. **State the problem:** Multiply the fractions and mixed numbers given. We will solve the first problem: $\frac{5}{6} \times 1 \frac{1}{10}$. 2. **Convert mixed numbers to improper fractions:** $$1 \frac{1}{10} = \frac{10 \times 1 + 1}{10} = \frac{11}{10}$$ 3. **Multiply the fractions:** $$\frac{5}{6} \times \frac{11}{10} = \frac{5 \times 11}{6 \times 10} = \frac{55}{60}$$ 4. **Simplify the fraction:** Find the greatest common divisor (GCD) of 55 and 60, which is 5. $$\frac{\cancel{5} \times 11}{\cancel{5} \times 12} = \frac{11}{12}$$ 5. **Final answer:** $$\frac{5}{6} \times 1 \frac{1}{10} = \frac{11}{12}$$ This means when you multiply $\frac{5}{6}$ by $1 \frac{1}{10}$, the product is $\frac{11}{12}$.