Question: User: 5/8 by 10/11
1. **State the problem:** We need to multiply the fractions $\frac{5}{8}$ and $\frac{10}{11}$.
2. **Formula used:** To multiply two fractions $\frac{a}{b}$ and $\frac{c}{d}$, use the formula $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}.$$
3. **Apply the formula:** Multiply the numerators and denominators:
$$\frac{5}{8} \times \frac{10}{11} = \frac{5 \times 10}{8 \times 11} = \frac{50}{88}.$$
4. **Simplify the fraction:** Find the greatest common divisor (GCD) of $50$ and $88$, which is $2$.
5. **Cancel common factors:**
$$\frac{\cancel{50}^{25 \times 2}}{\cancel{88}^{44 \times 2}} = \frac{25}{44}.$$
6. **Final answer:** The product of $\frac{5}{8}$ and $\frac{10}{11}$ is $\frac{25}{44}$.