d) \( \left(\frac{2}{11}+\frac{1}{2} \div \frac{11}{6}\right) \)

To evaluate the expression: \[ \left(\frac{2}{11} + \frac{1}{2} \div \frac{11}{6}\right) \] Let's break it down step by step. ### Step 1: Address the Division First, handle the division operation within the parentheses: \[ \frac{1}{2} \div \frac{11}{6} \] Dividing by a fraction is the same as multiplying by its reciprocal. Therefore: \[ \frac{1}{2} \div \frac{11}{6} = \frac{1}{2} \times \frac{6}{11} \] Multiply the numerators and the denominators: \[ \frac{1 \times 6}{2 \times 11} = \frac{6}{22} \] Simplify the fraction by dividing numerator and denominator by 2: \[ \frac{6}{22} = \frac{3}{11} \] ### Step 2: Add the Result to \(\frac{2}{11}\) Now, add \(\frac{2}{11}\) to the result from Step 1: \[ \frac{2}{11} + \frac{3}{11} \] Since the denominators are the same, add the numerators directly: \[ \frac{2 + 3}{11} = \frac{5}{11} \] ### Final Answer \[ \frac{5}{11} \]