State true or false. If the statements are correct, then state the property used.
`3215 times 311=311 times 3215`

Options

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

Answer

To determine whether the statement "3215 times 311 = 311 times 3215" is true or false, we can follow these steps:

### Step 1: Write down the equation
We need to check if:
\[ 3215 \times 311 = 311 \times 3215 \]

### Step 2: Calculate the left-hand side (LHS)
Now, let's calculate the left-hand side:
\[ 3215 \times 311 \]

Calculating this gives:
\[ 3215 \times 311 = 999865 \]

### Step 3: Calculate the right-hand side (RHS)
Next, we calculate the right-hand side:
\[ 311 \times 3215 \]

Calculating this gives:
\[ 311 \times 3215 = 999865 \]

### Step 4: Compare LHS and RHS
Now we compare the results from LHS and RHS:
- LHS = 999865
- RHS = 999865

Since both sides are equal:
\[ LHS = RHS \]

### Conclusion
The statement is **True**.

### Property Used
The property used here is the **Commutative Property of Multiplication**, which states that changing the order of the numbers being multiplied does not change the product. In mathematical terms, if \( A \) and \( B \) are any integers, then:
\[ A \times B = B \times A \]

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