Задание 105 Вариант 2 Самостоятельная работа ГДЗ Дидактические материалы Чесноков 6 класс (Математика)

а) $$\left(6\frac{1}{8}\cdot1\frac{2}{7}-2\frac{11}{14}\cdot1\frac{8}{13}\right)\cdot1\frac{3}{5}=5\frac{2}{5}$$

$$6\frac{1}{8}\cdot1\frac{2}{7}=\frac{49}{8}\cdot\frac{9}{7}=\frac{63}{8}=7\frac{7}{8}$$
$$2\frac{11}{14}\cdot1\frac{8}{13}=\frac{39}{14}\cdot\frac{21}{13}=\frac{9}{2}=4\frac{1}{2}$$
$$7\frac{7}{8}-4\frac{1}{2}=3\frac{3}{8}$$
$$3\frac{3}{8}\cdot1\frac{3}{5}=\frac{27}{8}\cdot\frac{8}{5}=\frac{27}{5}=5\frac{2}{5}$$

б) $$\left(2\frac{7}{15}+1\frac{7}{12}\right)\cdot1\frac{1}{9}-1\frac{7}{8}=2\frac{5}{8}$$

$$2\frac{7}{15}+1\frac{7}{12}=2\frac{28}{60}+1\frac{35}{60}=3\frac{63}{60}=4\frac{3}{60}=4\frac{1}{20}$$
$$4\frac{1}{20}\cdot1\frac{1}{9}=\frac{81}{20}\cdot\frac{10}{9}=\frac{9}{2}=4\frac{1}{2}$$
$$4\frac{1}{2}-1\frac{7}{8}=4\frac{4}{8}-1\frac{7}{8}=2\frac{5}{8}$$

в) $$\left(4\frac{3}{10}-3\frac{3}{5}\cdot1\frac{5}{12}\right)\cdot3\frac{5}{6}=2\frac{1}{3}$$

$$3\frac{3}{5}\cdot1\frac{5}{12}=\frac{18}{5}\cdot\frac{17}{12}=\frac{51}{10}=5\frac{1}{10}$$
$$4\frac{3}{10}-5\frac{1}{10}=3\frac{13}{10}-5\frac{1}{10}=2\frac{8}{10}=2\frac{4}{5}$$
$$2\frac{4}{5}\cdot3\frac{5}{6}=\frac{14}{5}\cdot\frac{23}{6}=\frac{7}{3}=2\frac{1}{3}$$

г) $$\left(4\frac{1}{3}-3\frac{4}{9}\right)^2\cdot\left(2\frac{1}{4}\right)^2=4$$

$$2\frac{1}{4}=\frac{9}{4},\qquad \left(2\frac{1}{4}\right)^2=\left(\frac{9}{4}\right)^2=\frac{81}{16}$$
$$4\frac{1}{3}-3\frac{4}{9}=4\frac{3}{9}-3\frac{4}{9}=\frac{8}{9}$$
$$\left(\frac{8}{9}\right)^2=\frac{64}{81}$$
$$\frac{64}{81}\cdot\frac{81}{16}=4$$

д) $$\left(5\frac{8}{15}-4\frac{7}{10}\right)\cdot2\frac{2}{3}-\frac{5}{9}=1\frac{2}{3}$$

$$5\frac{8}{15}-4\frac{7}{10}=5\frac{16}{30}-4\frac{21}{30}=4\frac{46}{30}-4\frac{21}{30}=\frac{25}{30}=\frac{5}{6}$$
$$\frac{5}{6}\cdot2\frac{2}{3}=\frac{5}{6}\cdot\frac{8}{3}=\frac{20}{9}=2\frac{2}{9}$$
$$2\frac{2}{9}-\frac{5}{9}=1\frac{1}{9}$$

е) $$\left(\frac{5}{24}+\frac{5}{16}\right)\cdot3\left(1\frac{2}{3}-\frac{3}{5}\right)\cdot4\frac{4}{5}=1$$

$$\frac{5}{24}+\frac{5}{16}=\frac{10}{48}+\frac{15}{48}=\frac{25}{48}$$
$$1\frac{2}{3}-\frac{3}{5}=1\frac{10}{15}-\frac{9}{15}=1\frac{1}{15}$$
$$\frac{25}{48}\cdot1\frac{1}{15}=\frac{25}{48}\cdot\frac{16}{15}=\frac{5}{9}$$
$$\frac{5}{9}\cdot4\frac{4}{5}=\frac{5}{9}\cdot\frac{24}{5}=1$$

Ответ: а) $$5\frac{2}{5}$$; б) $$2\frac{5}{8}$$; в) $$2\frac{1}{3}$$; г) $$4$$; д) $$1\frac{2}{3}$$; е) $$1$$.