Упр.68 ГДЗ Ткачёва 6 класс (Математика)

Выполнить действия:

1. $$\left(2\frac{1}{3}-\frac{1}{6}\cdot1\frac{4}{5}\right):3$$;
2. $$5\frac{1}{6}\cdot2-2\frac{11}{12}:1\frac{5}{9}$$;
3. $$\left(1\frac{1}{3}\right)^3+1\frac{2}{7}\cdot\left(1\frac{1}{3}\right)^2$$;
4. $$\left(1\frac{1}{5}\right)^2+7\frac{1}{7}:\left(1\frac{2}{3}\right)^3$$.

1) Преобразуем смешанные числа в неправильные дроби и выполняем действия по порядку:

$$\left(2\frac{1}{3}-\frac{1}{6}\cdot 1\frac{4}{5}\right):3$$
$$1\frac{4}{5}=\frac{9}{5}, \quad \frac{1}{6}\cdot \frac{9}{5}=\frac{9}{30}=\frac{3}{10}$$
$$2\frac{1}{3}=\frac{7}{3}, \quad \frac{7}{3}-\frac{3}{10}=\frac{70}{30}-\frac{9}{30}=\frac{61}{30}$$
$$\frac{61}{30}:3=\frac{61}{30}\cdot \frac{1}{3}=\frac{61}{90}$$

2)

$$5\frac{1}{6}\cdot 2-2\frac{11}{12}:1\frac{5}{9}$$
$$5\frac{1}{6}=\frac{31}{6}, \quad \frac{31}{6}\cdot 2=\frac{31}{3}=10\frac{1}{3}$$
$$2\frac{11}{12}=\frac{35}{12}, \quad 1\frac{5}{9}=\frac{14}{9}$$
$$\frac{35}{12}:\frac{14}{9}=\frac{35}{12}\cdot \frac{9}{14}=\frac{15}{8}=1\frac{7}{8}$$
$$10\frac{1}{3}-1\frac{7}{8}=10\frac{8}{24}-1\frac{21}{24}=9\frac{32}{24}-1\frac{21}{24}=8\frac{11}{24}$$

3)

$$\left(1\frac{1}{3}\right)^3+1\frac{2}{7}\cdot \left(1\frac{1}{3}\right)^2$$
$$1\frac{1}{3}=\frac{4}{3}, \quad 1\frac{2}{7}=\frac{9}{7}$$
$$\left(\frac{4}{3}\right)^3+\frac{9}{7}\cdot \left(\frac{4}{3}\right)^2 = \left(\frac{4}{3}\right)^2\left(\frac{4}{3}+\frac{9}{7}\right)$$
$$=\frac{16}{9}\left(\frac{28}{21}+\frac{27}{21}\right) =\frac{16}{9}\cdot \frac{55}{21} =\frac{880}{189} =4\frac{124}{189}$$

4)

$$\left(1\frac{1}{5}\right)^2+7\frac{1}{7}:\left(1\frac{2}{3}\right)^3$$
$$1\frac{1}{5}=\frac{6}{5}, \quad 7\frac{1}{7}=\frac{50}{7}, \quad 1\frac{2}{3}=\frac{5}{3}$$
$$\left(\frac{6}{5}\right)^2=\frac{36}{25}=1\frac{11}{25}$$
$$\left(\frac{5}{3}\right)^3=\frac{125}{27}$$
$$\frac{50}{7}:\frac{125}{27}=\frac{50}{7}\cdot \frac{27}{125}=\frac{54}{35}=1\frac{19}{35}$$
$$1\frac{11}{25}+1\frac{19}{35}=2\frac{172}{175}$$

Ответ

$$1)\ \frac{61}{90}; \quad 2)\ 8\frac{11}{24}; \quad 3)\ 4\frac{124}{189}; \quad 4)\ 2\frac{172}{175}$$