valuate, correct to the nearest whole number \( \frac{1}{2}-\left(2 \frac{1}{2}+3\right) \div \frac{33}{2} \)

To evaluate the expression \( \frac{1}{2}-\left(2 \frac{1}{2}+3\right) \div \frac{33}{2} \), let's break it down step by step: 1. Convert \( 2 \frac{1}{2} \) to an improper fraction: \( 2 \frac{1}{2} = \frac{5}{2} \). 2. Now add \( \frac{5}{2} + 3 \) (which is \( 3 = \frac{6}{2} \)): \( \frac{5}{2} + \frac{6}{2} = \frac{11}{2} \). 3. Next, divide \( \frac{11}{2} \) by \( \frac{33}{2} \): \( \frac{11}{2} \div \frac{33}{2} = \frac{11}{2} \times \frac{2}{33} = \frac{11}{33} = \frac{1}{3} \). 4. Now substitute this back into the expression: \( \frac{1}{2} - \frac{1}{3} \). 5. Find a common denominator, which is 6: \( \frac{1}{2} = \frac{3}{6} \) and \( \frac{1}{3} = \frac{2}{6} \). 6. Now perform the subtraction: \( \frac{3}{6} - \frac{2}{6} = \frac{1}{6} \). 7. Finally, correcting to the nearest whole number, \( \frac{1}{6} \) rounds to 0. Thus, the final answer is \( 0 \).