`2176 xx 316` = ?

Options

A. 687616
B. 768661
C. 687166
D. 786166

Answer

To solve the multiplication problem \( 2176 \times 316 \), we can break it down into simpler steps. Here’s a step-by-step solution:

### Step 1: Break Down the Numbers
We can break down \( 316 \) into \( 300 + 16 \). This makes the multiplication easier.

### Step 2: Distribute the Multiplication
Now we can distribute \( 2176 \) across the two parts of \( 316 \):
\[ 2176 \times 316 = 2176 \times (300 + 16) \]
This can be rewritten as:
\[ 2176 \times 300 + 2176 \times 16 \]

### Step 3: Calculate \( 2176 \times 300 \)
To calculate \( 2176 \times 300 \):
\[ 2176 \times 300 = 2176 \times 3 \times 100 \]
First, calculate \( 2176 \times 3 \):
\[ 2176 \times 3 = 6528 \]
Now multiply by \( 100 \):
\[ 6528 \times 100 = 652800 \]

### Step 4: Calculate \( 2176 \times 16 \)
Next, calculate \( 2176 \times 16 \):
\[ 2176 \times 16 = 2176 \times (10 + 6) = 2176 \times 10 + 2176 \times 6 \]
Calculating \( 2176 \times 10 \):
\[ 2176 \times 10 = 21760 \]
Now calculate \( 2176 \times 6 \):
\[ 2176 \times 6 = 13056 \]
Now add these two results together:
\[ 21760 + 13056 = 34816 \]

### Step 5: Combine the Results
Now we can combine the results from Step 3 and Step 4:
\[ 652800 + 34816 \]
To add these, align the numbers:
```
652800
+ 34816
---------
687616
```

### Final Answer
Thus, the result of \( 2176 \times 316 \) is \( 687616 \).

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