`1(1)/(3)+2(1)/(6)-3(1)/(9)=1div?`

Options

A. `7//18`
B. `18//7`
C. `16//7`
D. `7//8`

Explanation

To solve the equation \(1 \frac{1}{3} + 2 \frac{1}{6} - 3 \frac{1}{9} = 1 \div ?\), we will first simplify the left-hand side.

### Step-by-step Solution:

1. **Convert Mixed Numbers to Improper Fractions**:
- \(1 \frac{1}{3} = \frac{4}{3}\) (since \(1 \times 3 + 1 = 4\))
- \(2 \frac{1}{6} = \frac{13}{6}\) (since \(2 \times 6 + 1 = 13\))
- \(3 \frac{1}{9} = \frac{28}{9}\) (since \(3 \times 9 + 1 = 28\))

So, we can rewrite the equation as:
\[ \frac{4}{3} + \frac{13}{6} - \frac{28}{9} \]

2. **Find a Common Denominator**:
- The least common multiple (LCM) of the denominators \(3\), \(6\), and \(9\) is \(18\).

3. **Convert Each Fraction to Have the Common Denominator**:
- Convert \(\frac{4}{3}\) to \(\frac{24}{18}\) (multiply numerator and denominator by \(6\)).
- Convert \(\frac{13}{6}\) to \(\frac{39}{18}\) (multiply numerator and denominator by \(3\)).
- Convert \(\frac{28}{9}\) to \(\frac{56}{18}\) (multiply numerator and denominator by \(2\)).

Now, the equation looks like:
\[ \frac{24}{18} + \frac{39}{18} - \frac{56}{18} \]

4. **Combine the Fractions**:
- Combine the numerators:
\[ \frac{24 + 39 - 56}{18} = \frac{7}{18} \]

5. **Set the Left Side Equal to the Right Side**:
- Now we have:
\[ \frac{7}{18} = 1 \div ? \]
- This means:
\[ 1 = ? \times \frac{7}{18} \]

6. **Solve for the Question Mark**:
- Rearranging gives:
\[ ? = \frac{18}{7} \]

### Final Answer:
Thus, the value of the question mark is:
\[ \boxed{\frac{18}{7}} \]