On dividing 110111 by 11, the sum of the quotient and the remainder is

Options

A. 11011
B. 11001
C. 10101
D. 10011

Answer

To solve the problem of dividing 110111 by 11 and finding the sum of the quotient and the remainder, we can follow these steps:

### Step 1: Perform the Division
We need to divide 110111 by 11.

\[ 110111 \div 11 \]

### Step 2: Calculate the Quotient
When we perform the division, we find:

\[ 110111 \div 11 = 10010 \quad \text{(Quotient)} \]

### Step 3: Calculate the Remainder
To find the remainder, we can use the formula:

\[ \text{Remainder} = \text{Dividend} - (\text{Divisor} \times \text{Quotient}) \]

Substituting the values we have:

\[ \text{Remainder} = 110111 - (11 \times 10010) \]

Calculating \(11 \times 10010\):

\[ 11 \times 10010 = 110110 \]

Now substituting back to find the remainder:

\[ \text{Remainder} = 110111 - 110110 = 1 \]

### Step 4: Sum of Quotient and Remainder
Now we need to find the sum of the quotient and the remainder:

\[ \text{Sum} = \text{Quotient} + \text{Remainder} = 10010 + 1 = 10011 \]

### Final Answer
Thus, the sum of the quotient and the remainder when dividing 110111 by 11 is:

\[ \boxed{10011} \]

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