1) \(15\frac{5}{9} - 4\frac{2}{3} \cdot 3\frac{3}{8} = \frac{140}{9} - \frac{14}{3} \cdot \frac{27}{8} = \frac{140}{9} - \frac{378}{24} = \frac{140}{9} - \frac{63}{4} = \frac{560 - 567}{36} = \frac{-7}{36} \)
2) \(\frac{81}{88} \cdot (6\frac{1}{15} - 1\frac{2}{3}) = \frac{81}{88} \cdot (\frac{91}{15} - \frac{5}{3}) = \frac{81}{88} \cdot (\frac{91 - 25}{15}) = \frac{81}{88} \cdot \frac{66}{15} = \frac{81 \cdot 66}{88 \cdot 15} = \frac{5346}{1320} = \frac{99}{20} = 4\frac{19}{20}\)