№2. Найдите значение выражения: а) \(1\frac{5}{17} \cdot (7 - 2\frac{4}{11})\); б) \((4.2 : 1.2 - 1.05) \cdot 1.6\); в) \(\frac{36 \times 1\frac{1}{30}}{2.4}\); г) \(\frac{3}{11} \times (3\frac{2}{3} : 4\frac{1}{2})\); д) \((\frac{7}{18} + 0.3) : (3 - \frac{14}{15})\)

Решение:

1. а) \(1\frac{5}{17} \cdot (7 - 2\frac{4}{11}) = \frac{22}{17} \cdot (7 - \frac{26}{11}) = \frac{22}{17} \cdot (\frac{77 - 26}{11}) = \frac{22}{17} \cdot \frac{51}{11} = \frac{2 \times 11}{17} \cdot \frac{3 \times 17}{11} = 2 \times 3 = 6\)
2. б) \((4.2 : 1.2 - 1.05) \cdot 1.6 = (\frac{42}{10} : \frac{12}{10} - \frac{105}{100}) \cdot \frac{16}{10} = (\frac{42}{10} \times \frac{10}{12} - \frac{21}{20}) \cdot \frac{8}{5} = (\frac{42}{12} - \frac{21}{20}) \cdot \frac{8}{5} = (\frac{7}{2} - \frac{21}{20}) \cdot \frac{8}{5} = (\frac{70 - 21}{20}) \cdot \frac{8}{5} = \frac{49}{20} \cdot \frac{8}{5} = \frac{49 \times 8}{20 \times 5} = \frac{49 \times 2 \times 4}{5 \times 4 \times 5} = \frac{98}{25} = 3.92\)
3. в) \(\frac{36 \times 1\frac{1}{30}}{2.4} = \frac{36 \times \frac{31}{30}}{\frac{24}{10}} = \frac{\frac{36 \times 31}{30}}{\frac{12}{5}} = \frac{\frac{6 \times 6 \times 31}{5 \times 6}}{\frac{12}{5}} = \frac{\frac{6 \times 31}{5}}{\frac{12}{5}} = \frac{6 \times 31}{5} \times \frac{5}{12} = \frac{6 \times 31}{12} = \frac{31}{2} = 15.5\)
4. г) \(\frac{3}{11} \times (3\frac{2}{3} : 4\frac{1}{2}) = \frac{3}{11} \times (\frac{11}{3} : \frac{9}{2}) = \frac{3}{11} \times (\frac{11}{3} \times \frac{2}{9}) = \frac{3}{11} \times \frac{11 \times 2}{3 \times 9} = \frac{3 \times 11 \times 2}{11 \times 3 \times 9} = \frac{2}{9}\)
5. д) \((\frac{7}{18} + 0.3) : (3 - \frac{14}{15}) = (\frac{7}{18} + \frac{3}{10}) : (\frac{45 - 14}{15}) = (\frac{7 \times 5 + 3 \times 9}{90}) : \frac{31}{15} = (\frac{35 + 27}{90}) : \frac{31}{15} = \frac{62}{90} : \frac{31}{15} = \frac{31}{45} \times \frac{15}{31} = \frac{15}{45} = \frac{1}{3}\)

Ответ: а) 6; б) 3.92; в) 15.5; г) \(\frac{2}{9}\); д) \(\frac{1}{3}\).