What whole number is nearest to 457 which is divisible by 11?

Options

A. 450
B. 451
C. 460
D. 462

Answer

To find the whole number nearest to 457 that is divisible by 11, we can follow these steps:

### Step 1: Divide 457 by 11
First, we need to divide 457 by 11 to find out how many times 11 fits into 457.

\[ 457 \div 11 = 41 \quad \text{(quotient)} \]
\[ 41 \times 11 = 451 \quad \text{(product)} \]

### Step 2: Calculate the Remainder
Now, we will calculate the remainder when we divide 457 by 11.

\[ 457 - 451 = 6 \quad \text{(remainder)} \]

### Step 3: Find the Nearest Whole Numbers
Next, we will find the two whole numbers that are divisible by 11, which are closest to 457. We can do this by subtracting the remainder from 457 and adding the difference needed to reach the next multiple of 11.

1. **Lower number**:
\[ 457 - 6 = 451 \]

2. **Upper number**:
\[ 457 + (11 - 6) = 457 + 5 = 462 \]

### Step 4: Compare the Two Numbers
Now we will compare which of the two numbers (451 and 462) is closer to 457.

- The difference between 457 and 451:
\[ 457 - 451 = 6 \]

- The difference between 457 and 462:
\[ 462 - 457 = 5 \]

### Step 5: Determine the Nearest Whole Number
Since 462 is closer to 457 than 451 is, we conclude that the nearest whole number to 457 that is divisible by 11 is:

\[ \text{Answer: } 462 \]

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