State true of false. If the statements are correct, then state the property used.
`16 times (23-12)=(16 times 23)-(16 times 12)`

Answer

To determine whether the statement \( 16 \times (23 - 12) = (16 \times 23) - (16 \times 12) \) is true or false, we will evaluate both sides of the equation step by step.

### Step 1: Calculate the Left-Hand Side (LHS)
The LHS is given by:
\[ 16 \times (23 - 12) \]
First, we need to calculate \( 23 - 12 \):
\[ 23 - 12 = 11 \]
Now, substitute this back into the LHS:
\[ 16 \times 11 \]
Now, calculate \( 16 \times 11 \):
\[ 16 \times 11 = 176 \]
So, the LHS equals \( 176 \).

### Step 2: Calculate the Right-Hand Side (RHS)
The RHS is given by:
\[ (16 \times 23) - (16 \times 12) \]
First, calculate \( 16 \times 23 \):
\[ 16 \times 23 = 368 \]
Next, calculate \( 16 \times 12 \):
\[ 16 \times 12 = 192 \]
Now, substitute these values back into the RHS:
\[ 368 - 192 \]
Now, calculate \( 368 - 192 \):
\[ 368 - 192 = 176 \]
So, the RHS also equals \( 176 \).

### Step 3: Compare LHS and RHS
Now we compare both sides:
\[ LHS = 176 \quad \text{and} \quad RHS = 176 \]
Since both sides are equal, we conclude that the statement is true.

### Conclusion
The statement \( 16 \times (23 - 12) = (16 \times 23) - (16 \times 12) \) is **true**.

### Property Used
The property used in this statement is the **Distributive Property** of multiplication over subtraction.

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