Упр.638 ГДЗ Зубарева Мордкович 6 класс ФГОС (Математика)

Задача

а) (2 5/6+1 7/9)•3 3/5+(2 5/6-1 7/9)•(-2 16/19);
б) (2 2/15+2 7/10) :1 2/27-(2 7/10-2 2/15) :2 3/7;
в) (1 1/12+1 5/8)•(-1 11/13)-(1 1/12-1 5/8)•1 7/26;
г) (1 2/9+1 7/12) :1 47/54+(1 2/9-1 7/12)•5 7/13.

Подробный ответ

а) Преобразуем смешанные числа в неправильные дроби и выполним действия по порядку:

$$ \left(2\frac{5}{6}+1\frac{7}{9}\right)\cdot 3\frac{3}{5}+\left(2\frac{5}{6}-1\frac{7}{9}\right)\cdot\left(-2\frac{16}{19}\right) $$
$$ =\left(2\frac{15}{18}+1\frac{14}{18}\right)\cdot\frac{18}{5}+\left(2\frac{15}{18}-1\frac{14}{18}\right)\cdot\left(-\frac{54}{19}\right) $$
$$ =3\frac{29}{18}\cdot\frac{18}{5}+1\frac{1}{18}\cdot\left(-\frac{54}{19}\right) $$
$$ =\frac{83}{18}\cdot\frac{18}{5}-\frac{19}{18}\cdot\frac{54}{19} =\frac{83}{5}-3 =16\frac{3}{5}-3 =13\frac{3}{5}. $$

б)

$$ \left(2\frac{2}{15}+2\frac{7}{10}\right):1\frac{2}{27}-\left(2\frac{7}{10}-2\frac{2}{15}\right):2\frac{3}{7} $$
$$ =\left(2\frac{4}{30}+2\frac{21}{30}\right):\frac{29}{27}-\left(2\frac{21}{30}-2\frac{4}{30}\right):\frac{17}{7} $$
$$ =4\frac{25}{30}:\frac{29}{27}-\frac{17}{30}:\frac{17}{7} =4\frac{5}{6}\cdot\frac{27}{29}-\frac{7}{30} $$
$$ =\frac{29}{6}\cdot\frac{27}{29}-\frac{7}{30} =\frac{27}{6}-\frac{7}{30} =\frac{9}{2}-\frac{7}{30} =4\frac{1}{2}-\frac{7}{30} =4\frac{15}{30}-\frac{7}{30} =4\frac{8}{30} =4\frac{4}{15}. $$

в)

$$ \left(1\frac{1}{12}+1\frac{5}{8}\right)\cdot\left(-1\frac{11}{13}\right)-\left(1\frac{1}{12}-1\frac{5}{8}\right)\cdot1\frac{7}{26} $$
$$ =\left(1\frac{2}{24}+1\frac{15}{24}\right)\cdot\left(-\frac{24}{13}\right)-\left(1\frac{2}{24}-1\frac{15}{24}\right)\cdot\frac{33}{26} $$
$$ =2\frac{17}{24}\cdot\left(-\frac{24}{13}\right)-\left(-\frac{13}{24}\right)\cdot\frac{33}{26} $$
$$ =-\frac{65}{24}\cdot\frac{24}{13}+\frac{13}{24}\cdot\frac{33}{26} =-5+\frac{1}{8}\cdot\frac{11}{2} =-5+\frac{11}{16} =-4\frac{5}{16}. $$

г)

$$ \left(1\frac{2}{9}+1\frac{7}{12}\right):1\frac{47}{54}+\left(1\frac{2}{9}-1\frac{7}{12}\right)\cdot5\frac{7}{13} $$
$$ =\left(1\frac{8}{36}+1\frac{21}{36}\right):\frac{101}{54}+\left(1\frac{8}{36}-1\frac{21}{36}\right)\cdot\frac{72}{13} $$
$$ =2\frac{29}{36}:\frac{101}{54}+\left(-\frac{13}{36}\right)\cdot\frac{72}{13} $$
$$ =\frac{101}{36}\cdot\frac{54}{101}-\frac{13}{36}\cdot\frac{72}{13} =\frac{54}{36}-\frac{72}{36} =\frac{3}{2}-2 =-\frac{1}{2}. $$