A student multiplied 2736 by 35 instead of 53. How much was his answer smaller than the correct one?

Options

A. 41040
B. 24624
C. 49248
D. 20520

Answer

To solve the problem step by step, we need to find the difference between the correct multiplication (2736 multiplied by 53) and the incorrect multiplication (2736 multiplied by 35).

### Step 1: Calculate the correct answer (2736 multiplied by 53)
We start by multiplying 2736 by 53.

\[ 2736 \times 53 \]

To perform this multiplication, we can break it down:

\[ 2736 \times 53 = 2736 \times (50 + 3) = (2736 \times 50) + (2736 \times 3) \]

Calculating each part:

1. **Calculating \(2736 \times 50\)**:
\[ 2736 \times 50 = 136800 \]

2. **Calculating \(2736 \times 3\)**:
\[ 2736 \times 3 = 8208 \]

Now, we add these two results together:

\[ 136800 + 8208 = 144008 \]

### Step 2: Calculate the incorrect answer (2736 multiplied by 35)
Now, we calculate the incorrect multiplication:

\[ 2736 \times 35 \]

Again, we can break it down:

\[ 2736 \times 35 = 2736 \times (30 + 5) = (2736 \times 30) + (2736 \times 5) \]

Calculating each part:

1. **Calculating \(2736 \times 30\)**:
\[ 2736 \times 30 = 82080 \]

2. **Calculating \(2736 \times 5\)**:
\[ 2736 \times 5 = 13680 \]

Now, we add these two results together:

\[ 82080 + 13680 = 95760 \]

### Step 3: Find the difference between the correct and incorrect answers
Now, we find out how much smaller the incorrect answer is compared to the correct answer:

\[ 144008 - 95760 \]

Calculating this difference:

\[ 144008 - 95760 = 48248 \]

### Final Answer
The student's answer was **48248** smaller than the correct answer.

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