https://file.aiquickdraw.com/mathbot/file/1727537593048pyx8pc36.jpg

Let's analyze each equation in the image and identify the missing number along with the corresponding property of multiplication.

### Analyzing the Equations:
1. **Equation (a):** \(\_\_ \times 9 = 9 \times 2\)
   - This uses the **Commutative Property of Multiplication**, which states that changing the order of multiplication does not change the result.
   - Missing number: **2**.
   - Property: **Commutative Property**.

2. **Equation (b):** \(\_\_ \times 2 = 0\)
   - This uses the **Zero Property of Multiplication**, which states that any number multiplied by zero is zero.
   - Missing number: **0**.
   - Property: **Zero Property**.

3. **Equation (c):** \(\_\_ \times (5 \times 7) = (4 \times 5) \times 7\)
   - This uses the **Associative Property of Multiplication**, which states that changing the grouping of numbers does not affect the product.
   - Missing number: **4**.
   - Property: **Associative Property**.

4. **Equation (d):** \(\_\_ \times 9 = 9\)
   - This uses the **Identity Property of Multiplication**, which states that any number multiplied by 1 remains unchanged.
   - Missing number: **1**.
   - Property: **Identity Property**.

### Final Answers:
1. **(a)** \( 2 \times 9 = 9 \times 2 \) - **Commutative Property**
2. **(b)** \( 0 \times 2 = 0 \) - **Zero Property**
3. **(c)** \( 4 \times (5 \times 7) = (4 \times 5) \times 7 \) - **Associative Property**
4. **(d)** \( 1 \times 9 = 9 \) - **Identity Property**

Would you like a detailed explanation for any specific property or have any other questions?

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### Related Questions:
1. What is the Commutative Property of Multiplication?
2. How does the Zero Property differ from the Identity Property in multiplication?
3. Can the Associative Property be applied to addition as well?
4. What are some real-world examples of the Identity Property in use?
5. Why is understanding multiplication properties important?

### Tip:
Always try to identify the pattern or property being used when analyzing equations, as it helps in quickly filling in missing values and understanding the underlying rules.

Fill in the blanks and choose the property of multiplication used for the following equations:
1. __ × 9 = 9 × 2
2. __ × 2 = 0
3. __ × (5 × 7) = (4 × 5) × 7
4. __ × 9 = 9

Learn to identify the properties of multiplication, including commutative, associative, zero, and identity properties. Solve equations such as __ × 9 = 9 × 2 and __ × 2 = 0 by filling in the blanks and selecting the correct property. Suitable for Grade 5-6 students.

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