-3,6+81:(-9)*1 1/18

To solve the expression \(-3 + 6 + 81 \div (-9) \times 1 \frac{1}{18}\), we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. Convert the mixed number: \(1 \frac{1}{18}\) can be converted to an improper fraction: \[ 1 \frac{1}{18} = \frac{18}{18} + \frac{1}{18} = \frac{19}{18} \]

2. Rewrite the expression: The expression is now: \[ -3 + 6 + 81 \div (-9) \times \frac{19}{18} \]

3. Perform the division: \[ 81 \div (-9) = -9 \]

4. Now substitute back: The expression becomes: \[ -3 + 6 - 9 \times \frac{19}{18} \]

5. Perform the multiplication: \[ -9 \times \frac{19}{18} = -\frac{171}{18} \]

6. Convert \(-3\) and \(6\) to fractions with the same denominator of \(18\): \[ -3 = -\frac{54}{18}, \quad 6 = \frac{108}{18} \]

7. Now rewrite the expression again: \[ -\frac{54}{18} + \frac{108}{18} - \frac{171}{18} \]

8. Combine the fractions: \[ \frac{-54 + 108 - 171}{18} = \frac{-117}{18} \]

9. Simplify: \[ \frac{-117}{18} = -\frac{39}{6} = -\frac{13}{2} \] (Divide numerator and denominator by 3)

Thus, the final result of the expression is: \[ -\frac{13}{2} \]

Or approximately \(-6.5\).