Упр.1135 ГДЗ Никольский Потапов 6 класс (Математика)

а) 3 3/7•3 1/2 :(1 1/11-27/55);
б) (2 1/2 :10+10:2 1/2-2 1/6)•36/125;
в) 3 1/8 :((4 5/12-3 13/24)•4/7+(3 1/18-2 7/12)•1 10/17).

а) Преобразуем смешанные числа в неправильные дроби:

$$ 3\frac{3}{7}\cdot 3\frac{1}{2}:\left(1\frac{1}{11}-\frac{27}{55}\right) = \frac{24}{7}\cdot \frac{7}{2}:\left(\frac{12}{11}-\frac{27}{55}\right) $$

$$ \frac{12}{11}-\frac{27}{55}=\frac{60}{55}-\frac{27}{55}=\frac{33}{55}=\frac{3}{5} $$

$$ \frac{24}{7}\cdot \frac{7}{2}:\frac{3}{5} =12:\frac{3}{5} =12\cdot \frac{5}{3} =20 $$

б)

$$ \left(2\frac{1}{2}:10+10:2\frac{1}{2}-2\frac{1}{6}\right)\cdot \frac{36}{125} $$

$$ \left(\frac{5}{2}:10+10:\frac{5}{2}-2\frac{1}{6}\right)\cdot \frac{36}{125} = \left(\frac{5}{2}\cdot \frac{1}{10}+10\cdot \frac{2}{5}-2\frac{1}{6}\right)\cdot \frac{36}{125} $$

$$ \left(\frac{1}{4}+4-2\frac{1}{6}\right)\cdot \frac{36}{125} = \left(\frac{1}{4}+\frac{24}{6}-\frac{13}{6}\right)\cdot \frac{36}{125} = \left(\frac{1}{4}+\frac{11}{6}\right)\cdot \frac{36}{125} $$

$$ \frac{1}{4}+\frac{11}{6} = \frac{3}{12}+\frac{22}{12} = \frac{25}{12} $$

$$ \frac{25}{12}\cdot \frac{36}{125} = \frac{3}{1}\cdot \frac{1}{5} = \frac{3}{5} $$

в)

$$ 3\frac{1}{8}:\left(\left(4\frac{5}{12}-3\frac{13}{24}\right)\cdot \frac{4}{7} +\left(3\frac{1}{18}-2\frac{7}{12}\right)\cdot 1\frac{10}{17}\right) $$

$$ 3\frac{1}{8}=\frac{25}{8},\quad 4\frac{5}{12}=\frac{53}{12},\quad 3\frac{13}{24}=\frac{85}{24},\quad 3\frac{1}{18}=\frac{55}{18},\quad 2\frac{7}{12}=\frac{31}{12},\quad 1\frac{10}{17}=\frac{27}{17} $$

$$ \left(\frac{53}{12}-\frac{85}{24}\right)\cdot \frac{4}{7} = \left(\frac{106}{24}-\frac{85}{24}\right)\cdot \frac{4}{7} = \frac{21}{24}\cdot \frac{4}{7} = \frac{3}{4}\cdot \frac{4}{7} = \frac{3}{7} $$

$$ \left(\frac{55}{18}-\frac{31}{12}\right)\cdot \frac{27}{17} = \left(\frac{110}{36}-\frac{93}{36}\right)\cdot \frac{27}{17} = \frac{17}{36}\cdot \frac{27}{17} = \frac{3}{4} $$

Тогда

$$ \frac{25}{8}:\left(\frac{3}{7}+\frac{3}{4}\right) = \frac{25}{8}:\left(\frac{12}{28}+\frac{21}{28}\right) = \frac{25}{8}:\frac{33}{28} = \frac{25}{8}\cdot \frac{28}{33} = \frac{25\cdot 7}{2\cdot 33} = \frac{175}{66} $$

Ответ

а) 20; б) $$\frac{3}{5}$$; в) $$\frac{175}{66}$$.