State true or false. If the statements are correct, then state the property used.
`(412 times 216) times 187=412 times (216 times 187)`

Options

A. True; commutative property of multiplication
B. True; associative property of multiplication
C. False
D. True; distributive property of multiplication over addition

Answer

To determine whether the statement `(412 times 216) times 187 = 412 times (216 times 187)` is true or false, we will analyze it step by step.

### Step 1: Understand the Expression
We have two expressions:
1. `(412 × 216) × 187`
2. `412 × (216 × 187)`

### Step 2: Calculate Each Expression
Let's calculate both expressions to see if they yield the same result.

**For the first expression:**
- Calculate `412 × 216`
- Then multiply the result by `187`.

**For the second expression:**
- Calculate `216 × 187`
- Then multiply `412` by the result.

### Step 3: Check if Both Results are Equal
After calculating both expressions, we will compare the results.

### Step 4: Conclusion
If both expressions yield the same result, then the statement is true. If they do not yield the same result, then the statement is false.

### Step 5: Identify the Property Used
If the statement is true, we will identify the property used in this operation. In this case, we are using the **Associative Property of Multiplication**, which states that the way in which numbers are grouped in multiplication does not change the product.

### Final Answer
The statement `(412 times 216) times 187 = 412 times (216 times 187)` is **True**. The property used is the **Associative Property of Multiplication**.

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