Select all of the equations that are true. \( 16 \div \frac{3}{4}=16 \times \frac{4}{3} \) \( 10 \div \frac{3}{8}=\frac{1}{10} \times \frac{3}{8} \) \( 12 \div 4=12 \times \frac{1}{4} \) \( 15 \div \frac{3}{5}=15 \times \frac{5}{3} \) \( 18 \div \frac{4}{7}=\frac{1}{18} \times \frac{4}{7} \)

Let's evaluate each equation one by one to determine which are true. 1. **Equation:** \( 16 \div \frac{3}{4} = 16 \times \frac{4}{3} \) **Left Side:** \[ 16 \div \frac{3}{4} = 16 \times \frac{4}{3} = \frac{16 \times 4}{3} = \frac{64}{3} \] **Right Side:** \[ 16 \times \frac{4}{3} = \frac{16 \times 4}{3} = \frac{64}{3} \] **Conclusion:** True. 2. **Equation:** \( 10 \div \frac{3}{8} = \frac{1}{10} \times \frac{3}{8} \) **Left Side:** \[ 10 \div \frac{3}{8} = 10 \times \frac{8}{3} = \frac{80}{3} \] **Right Side:** \[ \frac{1}{10} \times \frac{3}{8} = \frac{3}{80} \] **Conclusion:** False. 3. **Equation:** \( 12 \div 4 = 12 \times \frac{1}{4} \) **Left Side:** \[ 12 \div 4 = 3 \] **Right Side:** \[ 12 \times \frac{1}{4} = 3 \] **Conclusion:** True. 4. **Equation:** \( 15 \div \frac{3}{5} = 15 \times \frac{5}{3} \) **Left Side:** \[ 15 \div \frac{3}{5} = 15 \times \frac{5}{3} = \frac{15 \times 5}{3} = 25 \] **Right Side:** \[ 15 \times \frac{5}{3} = \frac{15 \times 5}{3} = 25 \] **Conclusion:** True. 5. **Equation:** \( 18 \div \frac{4}{7} = \frac{1}{18} \times \frac{4}{7} \) **Left Side:** \[ 18 \div \frac{4}{7} = 18 \times \frac{7}{4} = \frac{18 \times 7}{4} = \frac{126}{4} = 31.5 \] **Right Side:** \[ \frac{1}{18} \times \frac{4}{7} = \frac{4}{126} = \frac{2}{63} \] **Conclusion:** False. **Final Results:** The true equations are: - \( 16 \div \frac{3}{4} = 16 \times \frac{4}{3} \) - \( 12 \div 4 = 12 \times \frac{1}{4} \) - \( 15 \div \frac{3}{5} = 15 \times \frac{5}{3} \)