1. Calculate $-\frac{2}{7} + \frac{9}{7}$. Since denominators are the same, add numerators: $$-\frac{2}{7} + \frac{9}{7} = \frac{-2 + 9}{7} = \frac{7}{7} = 1$$ 2. Calculate $\frac{2}{9} - \frac{8}{9}$. Same denominator, subtract numerators: $$\frac{2}{9} - \frac{8}{9} = \frac{2 - 8}{9} = \frac{-6}{9} = \frac{\cancel{-6}}{\cancel{9}} = -\frac{2}{3}$$ 3. Calculate $\frac{5}{16} + \frac{7}{4}$. Find common denominator: 16. Convert $\frac{7}{4} = \frac{7 \times 4}{4 \times 4} = \frac{28}{16}$. Add: $$\frac{5}{16} + \frac{28}{16} = \frac{5 + 28}{16} = \frac{33}{16}$$ 4. Calculate $\frac{9}{32} - \frac{5}{8}$. Common denominator: 32. Convert $\frac{5}{8} = \frac{5 \times 4}{8 \times 4} = \frac{20}{32}$. Subtract: $$\frac{9}{32} - \frac{20}{32} = \frac{9 - 20}{32} = \frac{-11}{32}$$ 5. Calculate $\frac{12}{5} = \frac{11}{20}$. Check equality by cross-multiplying: $$12 \times 20 = 240, \quad 11 \times 5 = 55$$ Since $240 \neq 55$, the fractions are not equal. 6. Calculate $\frac{13}{64} = \frac{5}{8}$. Cross-multiply: $$13 \times 8 = 104, \quad 5 \times 64 = 320$$ Since $104 \neq 320$, fractions are not equal. 7. Calculate $-\frac{17}{-36} = -\frac{5}{-9}$. Simplify signs: $$-\frac{17}{-36} = \frac{17}{36}, \quad -\frac{5}{-9} = \frac{5}{9}$$ Check equality: $$17 \times 9 = 153, \quad 5 \times 36 = 180$$ Not equal. 8. Calculate $\frac{9}{40} = \frac{2}{5}$. Cross-multiply: $$9 \times 5 = 45, \quad 2 \times 40 = 80$$ Not equal. Final answers: 1. $1$ 2. $-\frac{2}{3}$ 3. $\frac{33}{16}$ 4. $-\frac{11}{32}$ 5. Not equal 6. Not equal 7. Not equal 8. Not equal