И) \(3\frac{1}{4}+2\frac{1}{6}\):\(\frac{3}{5}\)-2\(\frac{2}{3}\)\(\cdot\)2\(\frac{1}{4}\)+5\(\frac{1}{6}\)

Решение:

1. \( 3\frac{1}{4} = \frac{13}{4} \), \( 2\frac{1}{6} = \frac{13}{6} \)
2. \( \frac{13}{4} + \frac{13}{6} = \frac{13\cdot3 + 13\cdot2}{12} = \frac{39+26}{12} = \frac{65}{12} \)
3. \( \frac{65}{12} : \frac{3}{5} = \frac{65}{12} \cdot \frac{5}{3} = \frac{325}{36} \)
4. \( 2\frac{2}{3} = \frac{8}{3} \), \( 2\frac{1}{4} = \frac{9}{4} \)
5. \( \frac{8}{3} \cdot \frac{9}{4} = \frac{8\cdot9}{3\cdot4} = \frac{72}{12} = 6 \)
6. \( \frac{325}{36} - 6 + 5\frac{1}{6} = \frac{325}{36} - \frac{216}{36} + \frac{31}{6} = \frac{325-216}{36} + \frac{31\cdot6}{36} = \frac{109}{36} + \frac{186}{36} = \frac{295}{36} \)

Ответ: \(\frac{295}{36}\)