Find the approximate value of `18 xx 82.`

Options

A. 1300
B. 1400
C. 1500
D. 1600

Answer

To find the approximate value of \( 18 \times 82 \), we can follow these steps:

### Step 1: Simplify the Multiplication
We can rewrite \( 18 \) as \( 20 - 2 \). Thus, we have:
\[ 18 \times 82 = (20 - 2) \times 82 \]

### Step 2: Apply the Distributive Property
Using the distributive property, we can expand the expression:
\[ (20 - 2) \times 82 = 20 \times 82 - 2 \times 82 \]

### Step 3: Calculate \( 20 \times 82 \)
Now, calculate \( 20 \times 82 \):
\[ 20 \times 82 = 1640 \]

### Step 4: Calculate \( 2 \times 82 \)
Next, calculate \( 2 \times 82 \):
\[ 2 \times 82 = 164 \]

### Step 5: Subtract the Two Results
Now we subtract the result from Step 4 from the result in Step 3:
\[ 1640 - 164 = 1476 \]

### Step 6: Round to the Nearest Hundred for Approximation
To find the approximate value, we round \( 1476 \) to the nearest hundred. The digit in the tens place is \( 7 \), which is greater than \( 5 \). Therefore, we round up:
\[ 1476 \approx 1500 \]

### Final Answer
The approximate value of \( 18 \times 82 \) is \( 1500 \).

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