\begin{tabular}{l} Find three ratios that are equivalent to \( \frac{4}{5} \), \\ \( \square \) A. \( \frac{5}{6} \) \\ \( \square \) D. \( \frac{16}{20} \) \\ \( \square \mathrm{~B} . \frac{8}{10} \) \\ \( \square \mathrm{E} . \frac{20}{30} \) \\ \hline\end{tabular}

To determine which ratios are equivalent to \( \frac{4}{5} \), we'll simplify each option and compare it to \( \frac{4}{5} \). ### Given Ratios: - **A.** \( \frac{5}{6} \) - **B.** \( \frac{8}{10} \) - **D.** \( \frac{16}{20} \) - **E.** \( \frac{20}{30} \) ### Simplification and Comparison: 1. **Option A: \( \frac{5}{6} \)** - **Simplified Form:** \( \frac{5}{6} \) (already in simplest form) - **Comparison:** \( \frac{5}{6} \neq \frac{4}{5} \) 2. **Option B: \( \frac{8}{10} \)** - **Simplified Form:** \( \frac{8 \div 2}{10 \div 2} = \frac{4}{5} \) - **Comparison:** \( \frac{4}{5} = \frac{4}{5} \) ✔️ 3. **Option D: \( \frac{16}{20} \)** - **Simplified Form:** \( \frac{16 \div 4}{20 \div 4} = \frac{4}{5} \) - **Comparison:** \( \frac{4}{5} = \frac{4}{5} \) ✔️ 4. **Option E: \( \frac{20}{30} \)** - **Simplified Form:** \( \frac{20 \div 10}{30 \div 10} = \frac{2}{3} \) - **Comparison:** \( \frac{2}{3} \neq \frac{4}{5} \) ### Conclusion: The ratios that are equivalent to \( \frac{4}{5} \) are: - **B.** \( \frac{8}{10} \) - **D.** \( \frac{16}{20} \) **Note:** Although the problem asks for three equivalent ratios, based on the provided options, only two ratios (\( \frac{8}{10} \) and \( \frac{16}{20} \)) are equivalent to \( \frac{4}{5} \).