`(25xx22)xx25=25xx(22xx25)` is an example of ___ property .

Options

A. Commutative
B. Associative
C. Closure
D. Distributive

Answer

To solve the question `(25 x 22) x 25 = 25 x (22 x 25)` and identify the property it represents, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Expression**: We have the expression `(25 x 22) x 25` on the left side and `25 x (22 x 25)` on the right side.

2. **Understand the Components**: In both expressions, we can identify three components:
- First component: 25
- Second component: 22
- Third component: 25 (again)

3. **Apply the Associative Property**: The associative property states that when multiplying three or more numbers, the way in which the numbers are grouped does not change the product. This means we can group the numbers in any way and still get the same result.

4. **Group the Numbers**:
- In the left expression, we are grouping the first two numbers: `(25 x 22) x 25`.
- In the right expression, we are grouping the last two numbers: `25 x (22 x 25)`.

5. **Calculate Both Sides**:
- Left Side: Calculate `(25 x 22) x 25`.
- First, calculate `25 x 22 = 550`.
- Then, calculate `550 x 25 = 13750`.
- Right Side: Calculate `25 x (22 x 25)`.
- First, calculate `22 x 25 = 550`.
- Then, calculate `25 x 550 = 13750`.

6. **Compare the Results**: Both sides equal 13750, confirming that the expressions are equal.

7. **Conclusion**: Since the grouping of the numbers did not affect the final product, we conclude that this is an example of the **associative property** of multiplication.

### Final Answer:
The expression `(25 x 22) x 25 = 25 x (22 x 25)` is an example of the **associative property**.