Solve the following equation :
`11 -: 3 + (1)/(9) - 5 xx 6 (1 xx (1)/(6) ) =?`

Options

A. `(-11)/(9)`
B. `(11)/(9)`
C. `(11)/(8)`
D. `(-1)/(9)`

Answer

To solve the equation \( 11 -: 3 + \frac{1}{9} - 5 \times 6 \times (1 \times \frac{1}{6}) \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Rewrite the equation**:
\[ \frac{11}{3} + \frac{1}{9} - 5 \times 6 \times \left(1 \times \frac{1}{6}\right) \]

2. **Calculate the multiplication inside the parentheses**:
\[ 1 \times \frac{1}{6} = \frac{1}{6} \]
So the equation now becomes:
\[ \frac{11}{3} + \frac{1}{9} - 5 \times 6 \times \frac{1}{6} \]

3. **Simplify \(5 \times 6 \times \frac{1}{6}\)**:
\[ 5 \times 6 = 30 \]
\[ 30 \times \frac{1}{6} = 5 \]
Now the equation is:
\[ \frac{11}{3} + \frac{1}{9} - 5 \]

4. **Convert \(5\) into a fraction with a common denominator**:
The common denominator for \(3\) and \(9\) is \(9\). So, convert \(5\):
\[ 5 = \frac{45}{9} \]
Now the equation is:
\[ \frac{11}{3} + \frac{1}{9} - \frac{45}{9} \]

5. **Convert \(\frac{11}{3}\) to have a denominator of \(9\)**:
\[ \frac{11}{3} = \frac{11 \times 3}{3 \times 3} = \frac{33}{9} \]
Now the equation is:
\[ \frac{33}{9} + \frac{1}{9} - \frac{45}{9} \]

6. **Combine the fractions**:
\[ \frac{33 + 1 - 45}{9} = \frac{34 - 45}{9} = \frac{-11}{9} \]

### Final Answer:
\[ \frac{-11}{9} \]