Решение

1) $$14\frac{7}{15}-3\frac{3}{23} \cdot \frac{23}{27}-1\frac{1}{5} \cdot \frac{1}{6} = \frac{217}{15}-\frac{72}{23} \cdot \frac{23}{27}-\frac{6}{5} \cdot \frac{1}{6} = \frac{217}{15}-\frac{8}{3}-\frac{1}{5} = \frac{217}{15}-\frac{40}{15}-\frac{3}{15} = \frac{217-40-3}{15}=\frac{174}{15} = \frac{58}{5}=11\frac{3}{5}$$

Ответ: $$11\frac{3}{5}$$

2) $$\left(5\frac{8}{9}:1\frac{17}{36}+1\frac{1}{4}\right) \cdot \frac{5}{21} = \left(\frac{53}{9}:\frac{53}{36}+\frac{5}{4}\right) \cdot \frac{5}{21} = \left(\frac{53}{9} \cdot \frac{36}{53}+\frac{5}{4}\right) \cdot \frac{5}{21} = \left(4+\frac{5}{4}\right) \cdot \frac{5}{21} = \frac{21}{4} \cdot \frac{5}{21}=\frac{5}{4}=1\frac{1}{4}$$

Ответ: $$1\frac{1}{4}$$

3) $$(-3,25 -2,75): (-0,6) +0,8\cdot (-7) = -6:(-0,6) + 0,8\cdot (-7) = 10 - 5,6 = 4,4$$

Ответ: $$4,4$$

4) $$\left(-1\frac{3}{8}-2\frac{5}{12}\right):5\frac{5}{12} = \left(-\frac{11}{8}-\frac{29}{12}\right):\frac{65}{12} = \left(-\frac{33}{24}-\frac{58}{24}\right):\frac{65}{12} = \left(-\frac{91}{24}\right):\frac{65}{12} = -\frac{91}{24} \cdot \frac{12}{65} = -\frac{91}{2} \cdot \frac{1}{65} = -\frac{7}{2} \cdot \frac{1}{5} = -\frac{7}{10} = -0,7$$

Ответ: $$-0,7$$