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Find and explain the error in the following multiplication problem.

[tex]
\[
\begin{array}{r}
124 \\
\times 13 \\
\hline
372 \\
124 \\
\hline
496
\end{array}
\]
[/tex]

Choose the correct answer below:

A. The second partial product is incorrect. To find the second partial product, multiply 124 by 3 and not by 1.

B. The second partial product is incorrect. To find the second partial product, multiply 124 by 10 and not by 1.

C. The first partial product is incorrect. To find the first partial product, multiply 124 by 1 and not by 3.

D. The first partial product is incorrect. To find the first partial product, multiply 124 by 10 and not by 3.

Answer :

Let's go through the multiplication problem step by step and identify any errors:

### Problem Setup:
We want to multiply 124 by 13. In typical long multiplication, we multiply the top number by each digit of the bottom number and then sum the results, making sure to shift the placement as necessary.

### Provided Problem:
```
124
× 13
------
372
124
------
496
```

### Step-by-Step Analysis:

1. First Partial Product (Multiplying by 3):
- Here, you multiply 124 by 3 (the rightmost digit of the bottom number). This seems to be done correctly because:
[tex]\[
124 \times 3 = 372
\][/tex]
- So, the first partial product of 372 is correct.

2. Second Partial Product (Multiplying by 10):
- Normally, the next step is to multiply 124 by the next digit (which is 1) in the bottom number, but because this 1 is in the tens place, you actually multiply by 10.
- The given partial product is 124. However, we should have:
[tex]\[
124 \times 10 = 1240
\][/tex]
- Thus, the correct second partial product should be 1240, not 124.

### Error Identification:
There is an error in the second partial product. Instead of multiplying 124 by 1 directly, it should be multiplied by 10 (since the 1 is in the tens place).

### Conclusion:
The correct explanation for the error is: "The second partial product is incorrect. To find the second partial product, multiply 124 by 10 and not by 1." Therefore, the correct choice is B: "The second partial product is incorrect. To find the second partial product, multiply 124 by 10 and not by 1."

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