11—3:(5—6-31—2)

To solve the expression \( 11 - 3 : (5 - 6 - 31 - 2) \), we first need to interpret the notation correctly. In mathematical operations, the colon (:) often represents division, so we will treat it as \( 11 - \frac{3}{(5 - 6 - 31 - 2)} \). Let's break it down step-by-step: 1. **Evaluate the expression inside the parentheses:** \[ 5 - 6 - 31 - 2 \] Performing the operations from left to right: \[ 5 - 6 = -1 \] \[ -1 - 31 = -32 \] \[ -32 - 2 = -34 \] So, the expression inside the parentheses evaluates to \(-34\). 2. **Now substitute back into the expression:** \[ 11 - \frac{3}{-34} \] 3. **Calculate the division:** \[ \frac{3}{-34} = -\frac{3}{34} \] 4. **Finally, perform the subtraction:** \[ 11 - \left(-\frac{3}{34}\right) = 11 + \frac{3}{34} \] To add these, convert \(11\) into a fraction with a denominator of \(34\): \[ 11 = \frac{374}{34} \] Now, add: \[ \frac{374}{34} + \frac{3}{34} = \frac{377}{34} \] Thus, the final answer is: \[ \frac{377}{34} \] or approximately \(11.09\) if you require a decimal. If you format it as a mixed number, it would be \(11 \frac{3}{34}\).