State true of false. If the statements are correct, then state the property used.
`12 times (11+21)=(12 times 11)+(12 times 21)`

Answer

To determine whether the statement \( 12 \times (11 + 21) = (12 \times 11) + (12 \times 21) \) is true or false, we can follow these steps:

### Step 1: Calculate \( 11 + 21 \)
First, we need to add the numbers inside the parentheses:
\[ 11 + 21 = 32 \]

### Step 2: Calculate \( 12 \times (11 + 21) \)
Now, we can substitute the sum back into the equation:
\[ 12 \times (11 + 21) = 12 \times 32 \]
Next, we calculate \( 12 \times 32 \):
\[ 12 \times 32 = 384 \]

### Step 3: Calculate \( (12 \times 11) + (12 \times 21) \)
Now, we will calculate each part of the right side of the equation:
1. Calculate \( 12 \times 11 \):
\[ 12 \times 11 = 132 \]
2. Calculate \( 12 \times 21 \):
\[ 12 \times 21 = 252 \]
3. Now, add these two results together:
\[ (12 \times 11) + (12 \times 21) = 132 + 252 \]
\[ 132 + 252 = 384 \]

### Step 4: Compare the Results
Now we compare both sides of the equation:
\[ 12 \times (11 + 21) = 384 \]
\[ (12 \times 11) + (12 \times 21) = 384 \]
Since both sides are equal, we conclude that the statement is true.

### Conclusion
The statement \( 12 \times (11 + 21) = (12 \times 11) + (12 \times 21) \) is **True**.

### Property Used
The property used in this statement is the **Distributive Property of Multiplication**.

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