a. \( \frac{11}{18}: \frac{4}{9}=x: \frac{3}{22} \)

To solve the proportion \( \frac{11}{18}: \frac{4}{9}=x: \frac{3}{22} \), we can first rewrite it in a more manageable form. This sets up the equation: \[ \frac{11}{18} \div \frac{4}{9} = \frac{x}{\frac{3}{22}} \] Calculating the left side, we multiply by the reciprocal of \( \frac{4}{9} \): \[ \frac{11}{18} \times \frac{9}{4} = \frac{11 \times 9}{18 \times 4} = \frac{99}{72} = \frac{11}{8} \] Now, we have: \[ \frac{11}{8} = \frac{x}{\frac{3}{22}} \] Cross-multiplying gives: \[ 11 \times \frac{3}{22} = 8x \] Which simplifies to: \[ \frac{33}{22} = 8x \] Thus: \[ x = \frac{33}{22 \times 8} \] Simplifying \(\frac{33}{176}\), we find: \[ x = \frac{33}{176} \] So, the solution to the problem is \( x = \frac{33}{176} \).