https://file.aiquickdraw.com/mathbot/file/17274591415133i5p0cd7.jpg

Let's work through the problem step by step. Here's how the missing blanks and reasons can be filled:

### Step-by-Step Solution:

1. **Step 1:**
   \[
   -5(0) = 0
   \]
   **Reason:**
   **Multiplication Property of Zero**  
   (Multiplying anything by 0 results in 0.)

2. **Step 2:**
   \[
   -5(-3 + 3) = 0
   \]
   **Reason:**
   **Additive Inverse Property**  
   (The sum of a number and its additive inverse is 0, so \(-3 + 3 = 0\).)

3. **Step 3:**
   \[
   -5(-3) + (-5)(3) = 0
   \]
   **Reason:**
   **Distributive Property**  
   (Distributing \(-5\) over the sum \((-3 + 3)\).)

4. **Step 4:**
   \[
   -5(-3) + (-15) = 0
   \]
   **Reason:**
   **Given**  
   (From the rule stated earlier, \(-5(3) = -15\).)

5. **Step 5:**
   \[
   -5(-3) = 15
   \]
   **Reason:**
   **Additive Inverse Property**  
   (To cancel \(-15\), we add \(15\) to both sides, so \(-5(-3) = 15\).)

### Final Answer:
The missing blanks should be filled as follows:

- **Blank 1**: \(3\) (in Step 2)
- **Reason in Step 1**: **Multiplication Property of Zero**
- **Reason in Step 3**: **Distributive Property**
- **Blank 2**: \(15\) (in Step 5)

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Would you like more details or have any questions?

Here are 5 questions to expand on this problem:
1. What is the additive inverse property, and how does it apply in algebra?
2. How does the distributive property work when multiplying negative numbers?
3. Why does multiplying two negative numbers result in a positive number?
4. What other properties of zero are useful in solving algebraic equations?
5. How can we apply similar steps to solve more complex equations?

**Tip:** Always keep properties like the distributive property, additive inverse, and zero property in mind when simplifying or solving equations. They can help break down more complicated expressions!

Solve for the missing blanks and reasons using properties of operations and the given rule: -5(3) = -15.

Learn how to solve for the missing blanks and reasons in the equation using properties of operations like the Additive Inverse Property and the Distributive Property. Suitable for students in Grades 6-8.

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