5.° Вычислите значение числового выражения:

Решение:

1. \( 14\frac{7}{15} - 3\frac{3}{23} \cdot \frac{23}{27} - 1\frac{1}{5} \cdot \frac{1}{6} = \frac{14 \cdot 15 + 7}{15} - \frac{3 \cdot 23 + 3}{23} \cdot \frac{23}{27} - \frac{1 \cdot 5 + 1}{5} \cdot \frac{1}{6} = \frac{217}{15} - \frac{72}{23} \cdot \frac{23}{27} - \frac{6}{5} \cdot \frac{1}{6} = \frac{217}{15} - \frac{72}{27} - \frac{6}{30} = \frac{217}{15} - \frac{8}{3} - \frac{1}{5} = \frac{217 - 40 - 3}{15} = \frac{174}{15} = \frac{58}{5} = 11\frac{3}{5} \)
2. \( \left(5\frac{8}{9} : 1\frac{17}{36} + 1\frac{1}{4}\right) \cdot \frac{5}{21} = \left(\frac{45+8}{9} : \frac{36+17}{36} + \frac{4+1}{4}\right) \cdot \frac{5}{21} = \left(\frac{53}{9} : \frac{53}{36} + \frac{5}{4}\right) \cdot \frac{5}{21} = \left(\frac{53}{9} \cdot \frac{36}{53} + \frac{5}{4}\right) \cdot \frac{5}{21} = \left(\frac{36}{9} + \frac{5}{4}\right) \cdot \frac{5}{21} = \left(4 + \frac{5}{4}\right) \cdot \frac{5}{21} = \left(\frac{16+5}{4}\right) \cdot \frac{5}{21} = \frac{21}{4} \cdot \frac{5}{21} = \frac{5}{4} = 1\frac{1}{4} \)
3. \( (-3,25 - 2,75) : (-0,6) + 0,8 \cdot (-7) = (-6) : (-0,6) + (-5,6) = 10 - 5,6 = 4,4 \)
4. \( \left(-1\frac{3}{8} - 2\frac{5}{12}\right) : 5\frac{5}{12} = \left(-\frac{11}{8} - \frac{29}{12}\right) : \frac{65}{12} = \left(-\frac{33}{24} - \frac{58}{24}\right) : \frac{65}{12} = \left(-\frac{91}{24}\right) : \frac{65}{12} = -\frac{91}{24} \cdot \frac{12}{65} = -\frac{91}{2 \cdot 65} = -\frac{7 \cdot 13}{2 \cdot 5 \cdot 13} = -\frac{7}{10} \)

Ответ: 1) \( 11\frac{3}{5} \); 2) \( 1\frac{1}{4} \); 3) 4,4; 4) \( -\frac{7}{10} \).