Упр.1141 ГДЗ Никольский Потапов 6 класс (Математика)

Задача

а) (20:2 2/15+25 5/7 :2 2/35)/(20 7/9 :4 2/5-5/9);
б) (6 3/4 :9+24:6/7-1/9 :4/21)/(53 2/3-22 14/15 :2 2/3).

Подробный ответ

а) Преобразуем смешанные числа в неправильные дроби и выполняем деление на дробь как умножение на обратную:

$$ \frac{20:2\frac{2}{15}+25\frac{5}{7}:2\frac{2}{35}}{20\frac{7}{9}:4\frac{2}{5}-\frac{5}{9}} = \frac{20:\frac{32}{15}+\frac{180}{7}:\frac{72}{35}}{\frac{187}{9}:\frac{22}{5}-\frac{5}{9}} $$

$$ 20:\frac{32}{15}=20\cdot\frac{15}{32}=\frac{75}{8}, \qquad \frac{180}{7}:\frac{72}{35}=\frac{180}{7}\cdot\frac{35}{72}=\frac{25}{2} $$

$$ \frac{75}{8}+\frac{25}{2}=\frac{75}{8}+\frac{100}{8}=\frac{175}{8} $$

$$ \frac{187}{9}:\frac{22}{5}-\frac{5}{9} = \frac{187}{9}\cdot\frac{5}{22}-\frac{5}{9} = \frac{85}{18}-\frac{5}{9} = \frac{85}{18}-\frac{10}{18} = \frac{75}{18} $$

$$ \frac{\frac{175}{8}}{\frac{75}{18}} = \frac{175}{8}\cdot\frac{18}{75} = \frac{7\cdot 9}{4\cdot 3} = \frac{21}{4} = 5\frac{1}{4} $$

б) Аналогично преобразуем выражение:

$$ \frac{6\frac{3}{4}:9+24: \frac{6}{7}-\frac{1}{9}:\frac{4}{21}}{53\frac{2}{3}-22\frac{14}{15}:2\frac{2}{3}} = \frac{\frac{27}{4}:9+24:\frac{6}{7}-\frac{1}{9}:\frac{4}{21}}{53\frac{2}{3}-\frac{344}{15}:\frac{8}{3}} $$

$$ \frac{27}{4}:9=\frac{27}{4}\cdot\frac{1}{9}=\frac{3}{4}, \qquad 24:\frac{6}{7}=24\cdot\frac{7}{6}=28, \qquad \frac{1}{9}:\frac{4}{21}=\frac{1}{9}\cdot\frac{21}{4}=\frac{7}{12} $$

$$ \frac{3}{4}+28-\frac{7}{12} = \frac{9}{12}+\frac{336}{12}-\frac{7}{12} = \frac{338}{12} = \frac{169}{6} $$

$$ 53\frac{2}{3}-\frac{344}{15}:\frac{8}{3} = 53\frac{2}{3}-\frac{344}{15}\cdot\frac{3}{8} = 53\frac{2}{3}-\frac{43}{5} = 53\frac{10}{15}-8\frac{9}{15} = 45\frac{1}{15} = \frac{676}{15} $$

$$ \frac{\frac{169}{6}}{\frac{676}{15}} = \frac{169}{6}\cdot\frac{15}{676} = \frac{1}{2}\cdot\frac{5}{4} = \frac{5}{8} $$