The image shows four mathematical equations, and the task is to select the property of real numbers that justifies each equation. Here’s how to identify the properties:

1. $0 \cdot (c + 9) = 0 \cdot c + 0 \cdot 9$

   • This is the Distributive Property, which states that $a \cdot (b + c) = a \cdot b + a \cdot c$.

2. $\frac{1}{5} \cdot 5 = 1$

   • This is the Multiplicative Inverse Property, which states that $a \cdot \frac{1}{a} = 1$, assuming $a \neq 0$.

3. $(8 + a) + 2 = 8 + (a + 2)$

   • This is the Associative Property of Addition, which states that $(a + b) + c = a + (b + c)$.

4. $4 + (-4) = 0$

   • This is the Additive Inverse Property, which states that $a + (-a) = 0$.

Would you like further details on these properties, or do you have any questions?

Here are 5 relative questions for you:

1. What is the Commutative Property of addition or multiplication?
2. Can you provide another example of the Distributive Property in a different context?
3. What is the Additive Identity Property?
4. How do the Associative and Commutative properties differ?
5. Why is the Multiplicative Inverse important in solving equations?

Tip: Always check whether you are dealing with addition or multiplication when determining the property, as many properties apply differently depending on the operation.