During a trip to the mall, you spend \( \frac{7}{11} \) of your money on clothes and \( \frac{1}{2} \) of the remainder on food. What fraction of your money did you spend on food? Express your answer in lowest terms.

1. Let the total amount of money be \(1\). 2. The fraction spent on clothes is \(\frac{7}{11}\), so the amount remaining is \[ 1 - \frac{7}{11} = \frac{11}{11} - \frac{7}{11} = \frac{4}{11}. \] 3. Then, you spend \(\frac{1}{2}\) of the remaining amount on food. Therefore, the fraction of your total money spent on food is \[ \frac{1}{2} \times \frac{4}{11} = \frac{4}{22}. \] 4. Simplify the fraction \(\frac{4}{22}\) by dividing both the numerator and the denominator by \(2\): \[ \frac{4}{22} = \frac{2}{11}. \] Thus, you spent \(\frac{2}{11}\) of your total money on food.