The image is related to the Distributive Property in mathematics. Let me analyze the exercises and provide the solutions step-by-step:

Exercises on the Distributive Property:

1. Simplify $2(a - \frac{1}{2}c)$ by using the Distributive Property: $2(a - \frac{1}{2}c) = 2a - 2 \times \frac{1}{2}c = 2a - c$

2. Simplify $\frac{4}{3}(x + 6)$ by using the Distributive Property: $\frac{4}{3}(x + 6) = \frac{4}{3}x + \frac{4}{3} \times 6 = \frac{4}{3}x + 8$

3. Simplify $\frac{2}{3}(6x - 9)$ by using the Distributive Property: $\frac{2}{3}(6x - 9) = \frac{2}{3} \times 6x - \frac{2}{3} \times 9 = 4x - 6$

4. Simplify $\frac{3}{2}(6x - 9)$ by using the Distributive Property: $\frac{3}{2}(6x - 9) = \frac{3}{2} \times 6x - \frac{3}{2} \times 9 = 9x - \frac{27}{2}$

Summary of Results:

1. $2(a - \frac{1}{2}c) = 2a - c$
2. $\frac{4}{3}(x + 6) = \frac{4}{3}x + 8$
3. $\frac{2}{3}(6x - 9) = 4x - 6$
4. $\frac{3}{2}(6x - 9) = 9x - \frac{27}{2}$

Would you like a more detailed explanation or any additional questions answered?

5 Related Questions:

1. How can the Distributive Property be applied when dealing with negative numbers?
2. How would you distribute if there were multiple terms inside the parentheses?
3. What is the reverse process of the Distributive Property called?
4. How does the Distributive Property apply to algebraic expressions with variables on both sides?
5. Can the Distributive Property be used with division?

Tip:

When using the Distributive Property, always ensure you multiply each term inside the parentheses by the factor outside to avoid mistakes.