Вопрос:

450. Найдите значение выражения:

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Ответ ассистента

1) $3\frac{3}{4} : \frac{3}{8} : 1\frac{3}{7} = \frac{15}{4} \cdot \frac{8}{3} : \frac{10}{7} = 10 : \frac{10}{7} = 10 \cdot \frac{7}{10} = 7$ 2) $3\frac{3}{4} : (\frac{3}{8} : 1\frac{3}{7}) = \frac{15}{4} : (\frac{3}{8} : \frac{10}{7}) = \frac{15}{4} : (\frac{3}{8} \cdot \frac{7}{10}) = \frac{15}{4} : \frac{21}{80} = \frac{15}{4} \cdot \frac{80}{21} = \frac{5 \cdot 20}{7} = \frac{100}{7} = 14\frac{2}{7}$ 3) $1\frac{7}{9} \cdot \frac{15}{32} : 1\frac{19}{36} = \frac{16}{9} \cdot \frac{15}{32} : \frac{55}{36} = (\frac{1}{3} \cdot \frac{5}{2}) : \frac{55}{36} = \frac{5}{6} \cdot \frac{36}{55} = \frac{1}{1} \cdot \frac{6}{11} = \frac{6}{11}$ 4) $1\frac{7}{9} \cdot (\frac{15}{32} : 1\frac{19}{36}) = \frac{16}{9} \cdot (\frac{15}{32} : \frac{55}{36}) = \frac{16}{9} \cdot (\frac{15}{32} \cdot \frac{36}{55}) = \frac{16}{9} \cdot (\frac{3}{8} \cdot \frac{9}{11}) = \frac{16}{9} \cdot \frac{27}{88} = \frac{2}{1} \cdot \frac{3}{11} = \frac{6}{11}$ 5) $3\frac{4}{7} : 1\frac{1}{7} \cdot \frac{2}{3} = \frac{25}{7} : \frac{8}{7} \cdot \frac{2}{3} = \frac{25}{7} \cdot \frac{7}{8} \cdot \frac{2}{3} = \frac{25}{8} \cdot \frac{2}{3} = \frac{25}{12} = 2\frac{1}{12}$ 6) $3\frac{4}{7} : (1\frac{1}{7} \cdot \frac{2}{3}) = \frac{25}{7} : (\frac{8}{7} \cdot \frac{2}{3}) = \frac{25}{7} : \frac{16}{21} = \frac{25}{7} \cdot \frac{21}{16} = \frac{25 \cdot 3}{16} = \frac{75}{16} = 4\frac{11}{16}$ 7) $(\frac{5}{12} + \frac{1}{8}) : \frac{3}{8} = (\frac{10}{24} + \frac{3}{24}) : \frac{3}{8} = \frac{13}{24} : \frac{3}{8} = \frac{13}{24} \cdot \frac{8}{3} = \frac{13}{9} = 1\frac{4}{9}$ 8) $\frac{5}{12} + \frac{1}{8} : \frac{3}{8} = \frac{5}{12} + (\frac{1}{8} \cdot \frac{8}{3}) = \frac{5}{12} + \frac{1}{3} = \frac{5}{12} + \frac{4}{12} = \frac{9}{12} = \frac{3}{4}$ 9) $2\frac{6}{7} : (\frac{5}{6} - \frac{9}{14}) = \frac{20}{7} : (\frac{35}{42} - \frac{27}{42}) = \frac{20}{7} : \frac{8}{42} = \frac{20}{7} : \frac{4}{21} = \frac{20}{7} \cdot \frac{21}{4} = 5 \cdot 3 = 15$ 10) $2\frac{6}{7} : \frac{5}{6} - \frac{9}{14} = (\frac{20}{7} \cdot \frac{6}{5}) - \frac{9}{14} = \frac{24}{7} - \frac{9}{14} = \frac{48}{14} - \frac{9}{14} = \frac{39}{14} = 2\frac{11}{14}$ 11) $2\frac{1}{4} : 1\frac{4}{11} - \frac{3}{8} : \frac{7}{8} = \frac{9}{4} : \frac{15}{11} - (\frac{3}{8} \cdot \frac{8}{7}) = (\frac{9}{4} \cdot \frac{11}{15}) - \frac{3}{7} = \frac{33}{20} - \frac{3}{7} = \frac{231 - 60}{140} = \frac{171}{140} = 1\frac{31}{140}$ 12) $(3\frac{1}{6} - 5\frac{1}{6} : 4\frac{2}{15}) \cdot \frac{3}{92} = (\frac{19}{6} - \frac{31}{6} : \frac{62}{15}) \cdot \frac{3}{92} = (\frac{19}{6} - (\frac{31}{6} \cdot \frac{15}{62})) \cdot \frac{3}{92} = (\frac{19}{6} - \frac{5}{4}) \cdot \frac{3}{92} = (\frac{38 - 15}{12}) \cdot \frac{3}{92} = \frac{23}{12} \cdot \frac{3}{92} = \frac{23}{4 \cdot 92} = \frac{23}{368} = \frac{1}{16}$

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