14-(49 1/3:16-14:8 1/6)·7 / 1 17/18·(1 59/70+37/42+2 19/30)-10

Привет! Давай решим эти примеры по порядку. ### Решение примера б) $$\frac{14 - \left(49\frac{1}{3} : 16 - 14 : 8\frac{1}{6}\right) \cdot 7}{1\frac{17}{18} \cdot \left(1\frac{59}{70} + \frac{37}{42} + 2\frac{19}{30}\right) - 10}$$ 1. Числитель: - $49\frac{1}{3} : 16 = \frac{148}{3} : 16 = \frac{148}{3 \cdot 16} = \frac{37}{12} = 3\frac{1}{12}$ - $14 : 8\frac{1}{6} = 14 : \frac{49}{6} = 14 \cdot \frac{6}{49} = \frac{2 \cdot 6}{7} = \frac{12}{7} = 1\frac{5}{7}$ - $3\frac{1}{12} - 1\frac{5}{7} = \frac{37}{12} - \frac{12}{7} = \frac{259 - 144}{84} = \frac{115}{84} = 1\frac{31}{84}$ - $(1\frac{31}{84}) \cdot 7 = \frac{115}{84} \cdot 7 = \frac{115}{12} = 9\frac{7}{12}$ - $14 - 9\frac{7}{12} = 4\frac{5}{12}$ 2. Знаменатель: - $1\frac{59}{70} + \frac{37}{42} + 2\frac{19}{30} = \frac{129}{70} + \frac{37}{42} + \frac{79}{30}$ - Общий знаменатель 210: $\frac{387}{210} + \frac{185}{210} + \frac{553}{210} = \frac{1125}{210} = \frac{75}{14} = 5\frac{5}{14}$ - $1\frac{17}{18} \cdot \frac{75}{14} = \frac{35}{18} \cdot \frac{75}{14} = \frac{5 \cdot 25}{6 \cdot 2} = \frac{125}{12} = 10\frac{5}{12}$ - $10\frac{5}{12} - 10 = \frac{5}{12}$ 3. Итог: - $\frac{4\frac{5}{12}}{\frac{5}{12}} = \frac{53}{12} : \frac{5}{12} = \frac{53}{5} = 10,6$ **Ответ: 10,6** ### Решение примера в) $$\frac{12\frac{2}{3} - 63\frac{1}{3} : 5\frac{2}{11}}{2\frac{2}{3}}$$ 1. $63\frac{1}{3} : 5\frac{2}{11} = \frac{190}{3} : \frac{57}{11} = \frac{190}{3} \cdot \frac{11}{57} = \frac{10}{3} \cdot \frac{11}{3} = \frac{110}{9} = 12\frac{2}{9}$ 2. $12\frac{2}{3} - 12\frac{2}{9} = 12\frac{6}{9} - 12\frac{2}{9} = \frac{4}{9}$ 3. $\frac{4}{9} : 2\frac{2}{3} = \frac{4}{9} : \frac{8}{3} = \frac{4}{9} \cdot \frac{3}{8} = \frac{1}{3} \cdot \frac{1}{2} = \frac{1}{6}$ **Ответ: 1/6** ### Решение примера г) $$\left(7\frac{14}{45} : 7 - \frac{39}{40}\right) \cdot 7,2$$ 1. $7\frac{14}{45} : 7 = (7 + \frac{14}{45}) : 7 = 1 + \frac{14}{45 \cdot 7} = 1 + \frac{2}{45} = 1\frac{2}{45} = \frac{47}{45}$ 2. $\frac{47}{45} - \frac{39}{40} = \frac{47 \cdot 8 - 39 \cdot 9}{360} = \frac{376 - 351}{360} = \frac{25}{360} = \frac{5}{72}$ 3. $\frac{5}{72} \cdot 7,2 = \frac{5}{72} \cdot \frac{72}{10} = \frac{5}{10} = 0,5$ **Ответ: 0,5**