О) (\(\frac{2}{15}+1\frac{7}{12}\))\(\cdot\)\(\frac{30}{103}\)-2:2\(\frac{1}{4}\)\(\cdot\)\(\frac{1}{32}\)\(\cdot\)\(\frac{9}{4}\)

Решение:

1. \( 1\frac{7}{12} = \frac{19}{12} \)
2. \( \frac{2}{15} + \frac{19}{12} = \frac{2\cdot4 + 19\cdot5}{60} = \frac{8+95}{60} = \frac{103}{60} \)
3. \( \frac{103}{60} \cdot \frac{30}{103} = \frac{103\cdot30}{60\cdot103} = \frac{1}{2} \)
4. \( 2\frac{1}{4} = \frac{9}{4} \)
5. \( 2 : \frac{9}{4} = 2 \cdot \frac{4}{9} = \frac{8}{9} \)
6. \( \frac{1}{2} - \frac{8}{9} \cdot \frac{1}{32} \cdot \frac{9}{4} = \frac{1}{2} - \frac{8\cdot1\cdot9}{9\cdot32\cdot4} = \frac{1}{2} - \frac{1\cdot1\cdot1}{1\cdot4\cdot4} = \frac{1}{2} - \frac{1}{16} \)
7. \( \frac{1}{2} - \frac{1}{16} = \frac{8}{16} - \frac{1}{16} = \frac{7}{16} \)

Ответ: \(\frac{7}{16}\)