Evaluate the following using properties for multiplication to simplify the multiplication.
`33 times 12`

Answer

To evaluate \( 33 \times 12 \) using properties of multiplication, we will use the distributive property. Here’s a step-by-step solution:

### Step 1: Break down the number 12
We can express 12 as the sum of 10 and 2:
\[ 12 = 10 + 2 \]

### Step 2: Apply the distributive property
Using the distributive property, we can rewrite the multiplication:
\[ 33 \times 12 = 33 \times (10 + 2) \]

### Step 3: Distribute 33 to both terms
Now, we will distribute 33 to both 10 and 2:
\[ 33 \times 12 = 33 \times 10 + 33 \times 2 \]

### Step 4: Calculate each multiplication
Now we calculate each part:
1. \( 33 \times 10 = 330 \)
2. \( 33 \times 2 = 66 \)

### Step 5: Add the results
Now we add the two results together:
\[ 330 + 66 = 396 \]

### Final Answer
Thus, the value of \( 33 \times 12 \) is \( 396 \).

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