38. \(3 \frac{1}{2} - 2 \frac{3}{4}\) \(\cdot\) \(1 \frac{1}{6} - \frac{1}{12}\)

1. Calculate first parenthesis: $$3 \frac{1}{2} - 2 \frac{3}{4} = \frac{7}{2} - \frac{11}{4} = \frac{14}{4} - \frac{11}{4} = \frac{3}{4}$$.
2. Calculate second parenthesis: $$1 \frac{1}{6} - \frac{1}{12} = \frac{7}{6} - \frac{1}{12} = \frac{14}{12} - \frac{1}{12} = \frac{13}{12}$$.
3. Multiply results: $$\frac{3}{4} \cdot \frac{13}{12} = \frac{3 \cdot 13}{4 \cdot 12} = \frac{39}{48} = \frac{13}{16}$$.