Упр.2.294 ГДЗ Виленкин Жохов 6 класс Часть 1, Просвещение (Математика)

Вычислим по действиям.

а)

$$\frac{7}{16}\cdot\frac{4}{9}-1\frac{7}{15} = \frac{7\cdot4}{16\cdot9}-1\frac{7}{15} = \frac{7}{36}-1\frac{7}{15}$$

$$1\frac{7}{15}=\frac{22}{15}$$

$$\frac{7}{36}-\frac{22}{15} = \frac{35}{180}-\frac{264}{180} = -\frac{229}{180} = -1\frac{49}{180}$$

б)

$$\frac{8}{15}\cdot\left(2\frac{1}{2}\right)^2-\frac{5}{9} = \frac{8}{15}\cdot\left(\frac{5}{2}\right)^2-\frac{5}{9} = \frac{8}{15}\cdot\frac{25}{4}-\frac{5}{9}$$

$$\frac{8}{15}\cdot\frac{25}{4}=\frac{10}{3}$$

$$\frac{10}{3}-\frac{5}{9} = \frac{30}{9}-\frac{5}{9} = \frac{25}{9} = 2\frac{7}{9}$$

в)

$$\left(\left(1\frac{1}{6}\right)^2-\frac{7}{18}\right)\cdot2\frac{4}{7}-4\frac{2}{5} = \left(\left(\frac{7}{6}\right)^2-\frac{7}{18}\right)\cdot\frac{18}{7}-4\frac{2}{5}$$

$$\left(\frac{49}{36}-\frac{7}{18}\right)\cdot\frac{18}{7}-4\frac{2}{5} = \left(\frac{49}{36}-\frac{14}{36}\right)\cdot\frac{18}{7}-4\frac{2}{5} = \frac{35}{36}\cdot\frac{18}{7}-4\frac{2}{5}$$

$$\frac{35}{36}\cdot\frac{18}{7} = \frac{5}{2} = 2\frac{1}{2}$$

$$2\frac{1}{2}-4\frac{2}{5} = 2\frac{5}{10}-4\frac{4}{10} = 2{,}5-4{,}4 = -1{,}9$$

г)

$$\left(\frac{11}{16}+\frac{7}{24}-\frac{5}{12}\right)+\left(\frac{3}{4}\right)^2 = \left(\frac{33}{48}+\frac{14}{48}-\frac{20}{48}\right)+\frac{9}{16}$$

$$\frac{33}{48}+\frac{14}{48}-\frac{20}{48} = \frac{27}{48} = \frac{9}{16}$$

$$\frac{9}{16}+\frac{9}{16} = \frac{18}{16} = \frac{9}{8} = 1\frac{1}{8}$$

Ответ

а) $$-1\frac{49}{180}$$; б) $$2\frac{7}{9}$$; в) $$-1{,}9$$; г) $$1\frac{1}{8}$$.