1. Multiply each expression by distributing the factor outside the parentheses. 2. For problem 1: Multiply 5 by each term inside the parentheses: $$5(y - 6) = 5y - 30$$ 3. For problem 2: Multiply -4 by each term inside the parentheses: $$-4(x - 3y - 8) = -4x + 12y + 32$$ 4. For problem 3: Multiply \frac{3}{4} by each term inside the parentheses: $$\frac{3}{4}(4a - 8b - 40) = \frac{3}{4} \times 4a - \frac{3}{4} \times 8b - \frac{3}{4} \times 40 = 3a - 6b - 30$$ 5. For problem 4: Multiply 2 by each term inside the parentheses: $$2\left(6x - \frac{1}{2}y - \frac{7}{2}\right) = 12x - y - 7$$ 6. For problem 5: Multiply -\frac{3}{5} by each term inside the parentheses: $$-\frac{3}{5}\left(\frac{5}{9}a - \frac{10}{27}\right) = -\frac{3}{5} \times \frac{5}{9}a + \frac{3}{5} \times \frac{10}{27} = -\cancel{\frac{3}{5}} \times \cancel{\frac{5}{9}}a + \frac{3}{5} \times \frac{10}{27} = -\frac{1}{3}a + \frac{2}{9}$$ 7. For problem 6: Multiply -1.6 by each term inside the parentheses: $$-1.6(3.4 - 8x - 7y) = -1.6 \times 3.4 + 1.6 \times 8x + 1.6 \times 7y = -5.44 + 12.8x + 11.2y$$ 8. Find the reciprocal of each number or expression (flip numerator and denominator): 9. Problem 7: Reciprocal of -12 is $$-\frac{1}{12}$$ 10. Problem 8: Convert mixed number 3 \frac{1}{5} to improper fraction $$\frac{16}{5}$$, reciprocal is $$\frac{5}{16}$$ 11. Problem 9: Reciprocal of -0.7 (which is -\frac{7}{10}) is $$-\frac{10}{7}$$ 12. Problem 10: Reciprocal of $$\frac{a}{b}$$ is $$\frac{b}{a}$$ 13. Problem 11: Reciprocal of $$\frac{l}{m}$$ is $$\frac{m}{l}$$ 14. Problem 12: Reciprocal of $$\frac{2x}{5y}$$ is $$\frac{5y}{2x}$$ Final answers: 1. $$5y - 30$$ 2. $$-4x + 12y + 32$$ 3. $$3a - 6b - 30$$ 4. $$12x - y - 7$$ 5. $$-\frac{1}{3}a + \frac{2}{9}$$ 6. $$-5.44 + 12.8x + 11.2y$$ 7. $$-\frac{1}{12}$$ 8. $$\frac{5}{16}$$ 9. $$-\frac{10}{7}$$ 10. $$\frac{b}{a}$$ 11. $$\frac{m}{l}$$ 12. $$\frac{5y}{2x}$$