Задание 105 Вариант 3 Самостоятельная работа ГДЗ Дидактические материалы Чесноков 6 класс (Математика)

а)

$$\left(4\frac{3}{8}\cdot 1\frac{2}{7}-3\frac{5}{14}\cdot 1\frac{10}{11}\right)\cdot 1\frac{1}{3}$$
$$4\frac{3}{8}\cdot 1\frac{2}{7}=\frac{35}{8}\cdot \frac{9}{7}=\frac{45}{8}=5\frac{5}{8}$$
$$3\frac{5}{14}\cdot 1\frac{10}{11}=\frac{47}{14}\cdot \frac{21}{11}=\frac{9}{2}=4\frac{1}{2}$$
$$5\frac{5}{8}-4\frac{1}{2}=1\frac{1}{8}$$
$$1\frac{1}{8}\cdot 1\frac{1}{3}=\frac{9}{8}\cdot \frac{4}{3}=\frac{3}{2}=1\frac{1}{2}$$

б)

$$\left(1\frac{7}{24}+2\frac{7}{30}\right)\cdot \frac{30}{47}-3\frac{5}{8}$$
$$1\frac{7}{24}+2\frac{7}{30}=1\frac{35}{120}+2\frac{28}{120}=3\frac{63}{120}=3\frac{21}{40}$$
$$3\frac{21}{40}\cdot \frac{30}{47}=\frac{141}{40}\cdot \frac{30}{47}=\frac{9}{4}=2\frac{1}{4}$$
$$2\frac{1}{4}-3\frac{5}{8}=2\frac{2}{8}-3\frac{5}{8}=-1\frac{3}{8}$$

в)

$$\left(2\frac{7}{30}-3\frac{1}{5}\cdot \frac{7}{12}\right)\cdot 3\frac{1}{2}$$
$$3\frac{1}{5}\cdot \frac{7}{12}=\frac{16}{5}\cdot \frac{7}{12}=\frac{28}{15}=1\frac{13}{15}$$
$$2\frac{7}{30}-1\frac{13}{15}=\frac{67}{30}-\frac{26}{30}=\frac{41}{30}=1\frac{11}{30}$$
$$1\frac{11}{30}\cdot 3\frac{1}{2}=\frac{41}{30}\cdot \frac{7}{2}=\frac{287}{60}=4\frac{47}{60}$$

г)

$$\left(3\frac{1}{3}-2\frac{7}{9}\right)^2\cdot \left(1\frac{1}{5}\right)^2$$
$$3\frac{1}{3}-2\frac{7}{9}=3\frac{3}{9}-2\frac{7}{9}=\frac{5}{9}$$
$$\left(\frac{5}{9}\right)^2=\frac{25}{81},\qquad \left(1\frac{1}{5}\right)^2=\left(\frac{6}{5}\right)^2=\frac{36}{25}$$
$$\frac{25}{81}\cdot \frac{36}{25}=\frac{4}{9}$$

д)

$$\left(6\frac{3}{8}-5\frac{7}{12}\right)\cdot 5\frac{1}{7}-3\frac{6}{7}$$
$$6\frac{3}{8}-5\frac{7}{12}=6\frac{9}{24}-5\frac{14}{24}=1\frac{19}{24}$$
$$1\frac{19}{24}\cdot 5\frac{1}{7}=\frac{43}{24}\cdot \frac{36}{7}=\frac{129}{14}=9\frac{3}{14}$$
$$9\frac{3}{14}-3\frac{6}{7}=9\frac{3}{14}-3\frac{12}{14}=5\frac{5}{14}$$

е)

$$7\cdot \left(\frac{1}{12}+\frac{1}{18}\right)\cdot \left(1\frac{3}{5}-\frac{4}{7}\right)$$
$$\frac{1}{12}+\frac{1}{18}=\frac{3}{36}+\frac{2}{36}=\frac{5}{36}$$
$$1\frac{3}{5}-\frac{4}{7}=1\frac{21}{35}-\frac{20}{35}=1\frac{1}{35}$$
$$7\cdot \frac{5}{36}=\frac{35}{36}$$
$$\frac{35}{36}\cdot 1\frac{1}{35}=\frac{35}{36}\cdot \frac{36}{35}=1$$

Ответ: а) $$1\frac{1}{2}$$; б) $$-1\frac{3}{8}$$; в) $$4\frac{47}{60}$$; г) $$\frac{4}{9}$$; д) $$5\frac{5}{14}$$; е) $$1$$.