Вопрос:

Вычислите: 29/4 : 5 * 4/5 - 3/4 * (3 - 1 19/30); 14/15 - 9/5 : (7 - 4 3/7) + 3/5; 11/14 + 8/15 : (4 - 2 26/27) - 1 1/10; 17/12 : 3 2/5 - 2/5 * (2 - 1 1/12); 7/30 + 9/8 : (4 - 3 7/22) - 1 5/6.

Фотография

Ответ ассистента

1. $\frac{29}{4} : 5 \cdot \frac{4}{5} - \frac{3}{4} \cdot \left( 3 - 1\frac{19}{30} \right) = \frac{29}{4} \cdot \frac{1}{5} \cdot \frac{4}{5} - \frac{3}{4} \cdot \left( 2\frac{30}{30} - 1\frac{19}{30} \right) = \frac{29 \cdot 1 \cdot 4}{4 \cdot 5 \cdot 5} - \frac{3}{4} \cdot 1\frac{11}{30} = \frac{29}{25} - \frac{3}{4} \cdot \frac{41}{30} = 1.16 - \frac{1 \cdot 41}{4 \cdot 10} = 1.16 - \frac{41}{40} = 1.16 - 1.025 = 0.135$ 2. $\frac{14}{15} - \frac{9}{5} : \left( 7 - 4\frac{3}{7} \right) + \frac{3}{5} = \frac{14}{15} - \frac{9}{5} : \left( 6\frac{7}{7} - 4\frac{3}{7} \right) + \frac{3}{5} = \frac{14}{15} - \frac{9}{5} : 2\frac{4}{7} + \frac{3}{5} = \frac{14}{15} - \frac{9}{5} : \frac{18}{7} + \frac{9}{15} = \frac{23}{15} - \frac{9}{5} \cdot \frac{7}{18} = \frac{23}{15} - \frac{1 \cdot 7}{5 \cdot 2} = \frac{23}{15} - \frac{7}{10} = \frac{46 - 21}{30} = \frac{25}{30} = \frac{5}{6}$ 3. $\frac{11}{14} + \frac{8}{15} : \left( 4 - 2\frac{26}{27} \right) - 1\frac{1}{10} = \frac{11}{14} + \frac{8}{15} : \left( 3\frac{27}{27} - 2\frac{26}{27} \right) - \frac{11}{10} = \frac{11}{14} + \frac{8}{15} : 1\frac{1}{27} - \frac{11}{10} = \frac{11}{14} + \frac{8}{15} : \frac{28}{27} - \frac{11}{10} = \frac{11}{14} + \frac{8 \cdot 27}{15 \cdot 28} - \frac{11}{10} = \frac{11}{14} + \frac{2 \cdot 9}{5 \cdot 7} - \frac{11}{10} = \frac{11}{14} + \frac{18}{35} - \frac{11}{10} = \frac{55 + 36}{70} - \frac{11}{10} = \frac{91}{70} - \frac{77}{70} = \frac{14}{70} = \frac{1}{5} = 0.2$ 4. $\frac{17}{12} : 3\frac{2}{5} - \frac{2}{5} \cdot \left( 2 - 1\frac{1}{12} \right) = \frac{17}{12} : \frac{17}{5} - \frac{2}{5} \cdot \frac{11}{12} = \frac{17 \cdot 5}{12 \cdot 17} - \frac{1 \cdot 11}{5 \cdot 6} = \frac{5}{12} - \frac{11}{30} = \frac{25 - 22}{60} = \frac{3}{60} = \frac{1}{20} = 0.05$ 5. $\frac{7}{30} + \frac{9}{8} : \left( 4 - 3\frac{7}{22} \right) - 1\frac{5}{6} = \frac{7}{30} + \frac{9}{8} : \frac{15}{22} - \frac{11}{6} = \frac{7}{30} + \frac{9 \cdot 22}{8 \cdot 15} - \frac{55}{30} = \frac{7 - 55}{30} + \frac{3 \cdot 11}{4 \cdot 5} = -\frac{48}{30} + \frac{33}{20} = -\frac{8}{5} + \frac{33}{20} = -\frac{32}{20} + \frac{33}{20} = \frac{1}{20} = 0.05$ **Ответы:** 1. $0.135$; 2. $\frac{5}{6}$; 3. $0.2$; 4. $0.05$; 5. $0.05$.

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