Упр.561 ГДЗ Никольский Потапов 6 класс (Математика)

Задача

а) -3/4 :5/6+15/16•2/5-1:1/9;
б) 2:(-3/5)+3/5 :2-3/2 :6+6:3/2;
в) 11/4 :(2/5-3/2)+(3/4+5/6) :(-25/8);
г) (2/15+19/12)•30/103-(1:9/4)•(-9/16).

Подробный ответ

а)

$$ -\frac{3}{4}:\frac{5}{6}+\frac{15}{16}\cdot\frac{2}{5}-1:\frac{1}{9} = -\frac{3}{4}\cdot\frac{6}{5}+\frac{15}{16}\cdot\frac{2}{5}-1\cdot 9 $$
$$ = -\frac{18}{20}+\frac{30}{80}-9 = -\frac{9}{10}+\frac{3}{8}-9 $$
$$ = \frac{-36+15-360}{40} = -\frac{381}{40} = -9\frac{21}{40} $$

б)

$$ 2:\left(-\frac{3}{5}\right)+\frac{3}{5}:2-\frac{3}{2}:6+6:\frac{3}{2} = 2\cdot\left(-\frac{5}{3}\right)+\frac{3}{5}\cdot\frac{1}{2}-\frac{3}{2}\cdot\frac{1}{6}+6\cdot\frac{2}{3} $$
$$ = -\frac{10}{3}+\frac{3}{10}-\frac{1}{4}+4 = -3\frac{1}{3}+\frac{3}{10}-\frac{1}{4}+4 $$
$$ = \frac{-40+9-15+120}{120} = \frac{74}{120} = \frac{43}{60} $$

в)

$$ \frac{11}{4}:\left(\frac{2}{5}-\frac{3}{2}\right)+\left(\frac{3}{4}+\frac{5}{6}\right):\left(-\frac{25}{8}\right) $$
$$ = \frac{11}{4}:\left(\frac{4-15}{10}\right)+\frac{9+10}{12}\cdot\left(-\frac{8}{25}\right) = \frac{11}{4}:\left(-\frac{11}{10}\right)+\frac{19}{12}\cdot\left(-\frac{8}{25}\right) $$
$$ = \frac{11}{4}\cdot\frac{10}{-11}-\frac{19\cdot 8}{12\cdot 25} = -\frac{5}{2}-\frac{38}{75} $$
$$ = \frac{-375-76}{150} = -\frac{451}{150} = -3\frac{1}{150} $$

г)

$$ \left(\frac{2}{15}+\frac{19}{12}\right)\cdot\frac{30}{103}-\left(1:\frac{9}{4}\right)\cdot\left(-\frac{9}{16}\right) $$
$$ = \frac{8+95}{60}\cdot\frac{30}{103}-\left(1\cdot\frac{4}{9}\right)\cdot\left(-\frac{9}{16}\right) = \frac{103}{60}\cdot\frac{30}{103}+\frac{4}{9}\cdot\frac{9}{16} $$
$$ = \frac{1}{2}+\frac{1}{4} = \frac{3}{4} $$