What will come in place of the question mark (?) in the following questions ?
`1 1/3+2 1/6-3 1/9=1-?`

Options

A. `5 2/7`
B. `2 1/3`
C. `3 1/3`
D. `11/18`

Answer

To solve the equation \( 1 \frac{1}{3} + 2 \frac{1}{6} - 3 \frac{1}{9} = 1 - ? \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \( 1 \frac{1}{3} \) to an improper fraction:
\[ 1 \frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3} \]

2. Convert \( 2 \frac{1}{6} \) to an improper fraction:
\[ 2 \frac{1}{6} = \frac{6 \times 2 + 1}{6} = \frac{13}{6} \]

3. Convert \( 3 \frac{1}{9} \) to an improper fraction:
\[ 3 \frac{1}{9} = \frac{9 \times 3 + 1}{9} = \frac{28}{9} \]

### Step 2: Substitute the Improper Fractions into the Equation
Now substitute these improper fractions back into the equation:
\[ \frac{4}{3} + \frac{13}{6} - \frac{28}{9} = 1 - ? \]

### Step 3: Find the Least Common Multiple (LCM)
To add and subtract these fractions, we need to find the LCM of the denominators \( 3, 6, \) and \( 9 \):
- The LCM of \( 3, 6, \) and \( 9 \) is \( 18 \).

### Step 4: Convert Each Fraction to Have the Same Denominator
1. Convert \( \frac{4}{3} \):
\[ \frac{4}{3} = \frac{4 \times 6}{3 \times 6} = \frac{24}{18} \]

2. Convert \( \frac{13}{6} \):
\[ \frac{13}{6} = \frac{13 \times 3}{6 \times 3} = \frac{39}{18} \]

3. Convert \( \frac{28}{9} \):
\[ \frac{28}{9} = \frac{28 \times 2}{9 \times 2} = \frac{56}{18} \]

### Step 5: Combine the Fractions
Now we can combine the fractions:
\[ \frac{24}{18} + \frac{39}{18} - \frac{56}{18} = \frac{(24 + 39 - 56)}{18} = \frac{7}{18} \]

### Step 6: Set Up the Equation
Now we have:
\[ \frac{7}{18} = 1 - ? \]

### Step 7: Solve for ?
Rearranging gives:
\[ ? = 1 - \frac{7}{18} \]

### Step 8: Convert 1 to a Fraction with the Same Denominator
Convert \( 1 \) to a fraction:
\[ 1 = \frac{18}{18} \]

### Step 9: Perform the Subtraction
Now subtract:
\[ ? = \frac{18}{18} - \frac{7}{18} = \frac{11}{18} \]

### Final Answer
Thus, the value that comes in place of the question mark (?) is:
\[ \boxed{\frac{11}{18}} \]