1. **State the problem:** Solve the expressions for question 8 and question 9. 2. **Question 8:** Calculate $$\frac{5}{6} - \frac{3}{4} + \frac{5}{9}$$. 3. Find the common denominator for 6, 4, and 9, which is 36. 4. Convert each fraction: $$\frac{5}{6} = \frac{5 \times 6}{6 \times 6} = \frac{30}{36}$$ $$\frac{3}{4} = \frac{3 \times 9}{4 \times 9} = \frac{27}{36}$$ $$\frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36}$$ 5. Perform the operations: $$\frac{30}{36} - \frac{27}{36} + \frac{20}{36} = \frac{30 - 27 + 20}{36} = \frac{23}{36}$$ 6. **Answer for question 8:** $$\frac{23}{36}$$ 7. **Question 9:** Calculate $$\frac{5}{9} - \frac{1}{8} - \frac{1}{4}$$. 8. Find the common denominator for 9, 8, and 4, which is 72. 9. Convert each fraction: $$\frac{5}{9} = \frac{5 \times 8}{9 \times 8} = \frac{40}{72}$$ $$\frac{1}{8} = \frac{1 \times 9}{8 \times 9} = \frac{9}{72}$$ $$\frac{1}{4} = \frac{1 \times 18}{4 \times 18} = \frac{18}{72}$$ 10. Perform the operations: $$\frac{40}{72} - \frac{9}{72} - \frac{18}{72} = \frac{40 - 9 - 18}{72} = \frac{13}{72}$$ 11. **Answer for question 9:** $$\frac{13}{72}$$