Вопрос:

341. Найдите значение выражения: 1) (11/18 - 4/9) * 3/16; 2) 11/18 - 4/9 * 3/16; 3) 1 3/5 * (3/4 + 1 3/8); 4) 1 3/5 * 3/4 + 1 3/8; 5) 13 4/5 - 3 1/5 * 3 3/4; 6) 1 3/25 * 2 1/7 - 2 1/9 * 27/190; 7) 4 7/12 * 1 3/11 + 1 1/15 * 45/64; 8) (8 - 2 1/7 * 3 1/9) * 27/44; 9) (4/5 + 4/7) * (7 11/12 - 5 7/9); 10) 4/5 + 4/7 * (7 11/12 - 5 7/9)

Ответ:

1) \((\frac{11}{18} - \frac{4}{9}) \cdot \frac{3}{16} = (\frac{11}{18} - \frac{8}{18}) \cdot \frac{3}{16} = \frac{3}{18} \cdot \frac{3}{16} = \frac{1}{6} \cdot \frac{3}{16} = \frac{1}{32}\) 2) \(\frac{11}{18} - \frac{4}{9} \cdot \frac{3}{16} = \frac{11}{18} - \frac{1}{12} = \frac{22}{36} - \frac{3}{36} = \frac{19}{36}\) 3) \(1 \frac{3}{5} \cdot (\frac{3}{4} + 1 \frac{3}{8}) = \frac{8}{5} \cdot (\frac{6}{8} + \frac{11}{8}) = \frac{8}{5} \cdot \frac{17}{8} = \frac{17}{5} = 3 \frac{2}{5}\) 4) \(1 \frac{3}{5} \cdot \frac{3}{4} + 1 \frac{3}{8} = \frac{8}{5} \cdot \frac{3}{4} + \frac{11}{8} = \frac{6}{5} + \frac{11}{8} = \frac{48}{40} + \frac{55}{40} = \frac{103}{40} = 2 \frac{23}{40}\) 5) \(13 \frac{4}{5} - 3 \frac{1}{5} \cdot 3 \frac{3}{4} = \frac{69}{5} - \frac{16}{5} \cdot \frac{15}{4} = \frac{69}{5} - \frac{4 \cdot 3}{1 \cdot 1} = \frac{69}{5} - 12 = \frac{69}{5} - \frac{60}{5} = \frac{9}{5} = 1 \frac{4}{5}\) 6) \(1 \frac{3}{25} \cdot 2 \frac{1}{7} - 2 \frac{1}{9} \cdot \frac{27}{190} = \frac{28}{25} \cdot \frac{15}{7} - \frac{19}{9} \cdot \frac{27}{190} = \frac{4 \cdot 3}{5 \cdot 1} - \frac{1 \cdot 3}{1 \cdot 10} = \frac{12}{5} - \frac{3}{10} = \frac{24}{10} - \frac{3}{10} = \frac{21}{10} = 2 \frac{1}{10}\) 7) \(4 \frac{7}{12} \cdot 1 \frac{3}{11} + 1 \frac{1}{15} \cdot \frac{45}{64} = \frac{55}{12} \cdot \frac{14}{11} + \frac{16}{15} \cdot \frac{45}{64} = \frac{5 \cdot 7}{6 \cdot 1} + \frac{1 \cdot 3}{1 \cdot 4} = \frac{35}{6} + \frac{3}{4} = \frac{70}{12} + \frac{9}{12} = \frac{79}{12} = 6 \frac{7}{12}\) 8) \((8 - 2 \frac{1}{7} \cdot 3 \frac{1}{9}) \cdot \frac{27}{44} = (8 - \frac{15}{7} \cdot \frac{28}{9}) \cdot \frac{27}{44} = (8 - \frac{5 \cdot 4}{1 \cdot 3}) \cdot \frac{27}{44} = (8 - \frac{20}{3}) \cdot \frac{27}{44} = (\frac{24}{3} - \frac{20}{3}) \cdot \frac{27}{44} = \frac{4}{3} \cdot \frac{27}{44} = \frac{1 \cdot 9}{1 \cdot 11} = \frac{9}{11}\) 9) \((\frac{4}{5} + \frac{4}{7}) \cdot (7 \frac{11}{12} - 5 \frac{7}{9}) = (\frac{28}{35} + \frac{20}{35}) \cdot (\frac{95}{12} - \frac{52}{9}) = \frac{48}{35} \cdot (\frac{285}{36} - \frac{208}{36}) = \frac{48}{35} \cdot \frac{77}{36} = \frac{4 \cdot 11}{5 \cdot 3} = \frac{44}{15} = 2 \frac{14}{15}\) 10) \(\frac{4}{5} + \frac{4}{7} \cdot (7 \frac{11}{12} - 5 \frac{7}{9}) = \frac{4}{5} + \frac{4}{7} \cdot (\frac{95}{12} - \frac{52}{9}) = \frac{4}{5} + \frac{4}{7} \cdot (\frac{285}{36} - \frac{208}{36}) = \frac{4}{5} + \frac{4}{7} \cdot \frac{77}{36} = \frac{4}{5} + \frac{4 \cdot 11}{1 \cdot 36} = \frac{4}{5} + \frac{11}{9} = \frac{36}{45} + \frac{55}{45} = \frac{91}{45} = 2 \frac{1}{45}\) Ответ: 1) 1/32 2) 19/36 3) 3 2/5 4) 2 23/40 5) 1 4/5 6) 2 1/10 7) 6 7/12 8) 9/11 9) 2 14/15 10) 2 1/45
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