The smallest number that must be added to 803642 in order to obtain a multiple of 11 is

Options

A. a) 1
B. b) 4
C. c) 7
D. d) 9

Answer

To find the smallest number that must be added to 803642 in order to obtain a multiple of 11, we can follow these steps:

### Step 1: Divide 803642 by 11
First, we need to divide the number 803642 by 11 to find the remainder.

\[ 803642 \div 11 = 73058 \quad \text{(quotient)} \]
\[ 803642 - (73058 \times 11) = 803642 - 803638 = 4 \quad \text{(remainder)} \]

### Step 2: Determine the amount to add
Since the remainder is 4, we need to find out how much more we need to add to make it a multiple of 11. A multiple of 11 can be obtained by subtracting the remainder from 11.

\[ 11 - 4 = 7 \]

### Step 3: Add the result to the original number
Now, we add this result to the original number to find the new multiple of 11.

\[ 803642 + 7 = 803649 \]

### Conclusion
Thus, the smallest number that must be added to 803642 to obtain a multiple of 11 is **7**.

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