1. **State the problem:** Verify if the equality \( \frac{5}{12} \times 2 \frac{2}{3} = \frac{5}{15} \times \frac{8^2}{3} = \frac{10}{9} \div \frac{1}{9} \) is correct. 2. **Convert mixed numbers and simplify:** - Convert \(2 \frac{2}{3}\) to an improper fraction: \(2 \frac{2}{3} = \frac{8}{3}\). 3. **Calculate the left side:** \[ \frac{5}{12} \times \frac{8}{3} = \frac{5 \times 8}{12 \times 3} = \frac{40}{36} = \frac{10}{9} \] 4. **Calculate the middle expression:** - Simplify \(\frac{5}{15} = \frac{1}{3}\). - Calculate \(8^2 = 64\). - So, \(\frac{5}{15} \times \frac{8^2}{3} = \frac{1}{3} \times \frac{64}{3} = \frac{64}{9}\). 5. **Calculate the right side:** \[ \frac{10}{9} \div \frac{1}{9} = \frac{10}{9} \times \frac{9}{1} = 10 \] 6. **Compare results:** - Left side: \(\frac{10}{9} \approx 1.111...\) - Middle expression: \(\frac{64}{9} \approx 7.111...\) - Right side: \(10\) 7. **Conclusion:** The expressions are not equal. Only the left side equals \(\frac{10}{9}\), the middle and right sides differ. **Final answer:** The equality is **not correct**.