A student multiplied 3759 by 231 instead of multiplying by 213. How much was his product greater than the correct product?

Options

A. 67662
B. 66762
C. 22667
D. 27766

Answer

To find out how much greater the product of 3759 multiplied by 231 is compared to the product of 3759 multiplied by 213, we will follow these steps:

### Step 1: Calculate the incorrect product
First, we need to calculate the product of 3759 and 231.

\[ 3759 \times 231 \]

Calculating this step-by-step:

1. Multiply 3759 by 1 (the unit digit of 231):
\[ 3759 \times 1 = 3759 \]

2. Multiply 3759 by 3 (the tens digit of 231), and remember to shift one position to the left:
\[ 3759 \times 3 = 11277 \quad \text{(shift left gives 112770)} \]

3. Multiply 3759 by 2 (the hundreds digit of 231), and shift two positions to the left:
\[ 3759 \times 2 = 7518 \quad \text{(shift left gives 751800)} \]

4. Now, add these products together:
\[ 3759 + 112770 + 751800 = 866289 \]

So, the incorrect product is:
\[ 3759 \times 231 = 866289 \]

### Step 2: Calculate the correct product
Next, we calculate the correct product of 3759 and 213.

\[ 3759 \times 213 \]

Calculating this step-by-step:

1. Multiply 3759 by 3 (the unit digit of 213):
\[ 3759 \times 3 = 11277 \]

2. Multiply 3759 by 1 (the tens digit of 213), and shift one position to the left:
\[ 3759 \times 1 = 3759 \quad \text{(shift left gives 37590)} \]

3. Multiply 3759 by 2 (the hundreds digit of 213), and shift two positions to the left:
\[ 3759 \times 2 = 7518 \quad \text{(shift left gives 751800)} \]

4. Now, add these products together:
\[ 11277 + 37590 + 751800 = 799689 \]

So, the correct product is:
\[ 3759 \times 213 = 799689 \]

### Step 3: Find the difference
Now, we need to find out how much greater the incorrect product is than the correct product:

\[ 866289 - 799689 = 66600 \]

### Final Answer
The product of 3759 multiplied by 231 is greater than the product of 3759 multiplied by 213 by **66,600**.

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