Упр.267 ГДЗ Ткачёва 6 класс (Математика)

Вычислить:

1. $$\frac{3}{35}+1\frac{5}{14}+\left(2\frac{1}{6}-\frac{9}{14}\right):\left(\frac{4}{7}\right)^2$$;
2. $$\left(\frac{4}{5}\right)^2:\left(\frac{7}{15}+2\frac{1}{3}\right)+\left(\frac{2}{9}+1\frac{5}{12}\right)\cdot2\frac{4}{7}$$.

1) Вычислим по действиям:

$$\left(\frac{4}{7}\right)^2=\frac{16}{49}$$
$$2\frac{1}{6}-\frac{9}{14}=2\frac{7}{42}-\frac{27}{42}=1\frac{22}{42}=1\frac{11}{21}$$
$$1\frac{11}{21}:\frac{16}{49}= \frac{32}{21}\cdot\frac{49}{16}=\frac{2\cdot 7}{3\cdot 1}=\frac{14}{3}=4\frac{2}{3}$$
$$\frac{3}{35}+1\frac{5}{14}=\frac{3}{35}+1\frac{25}{70}=1\frac{31}{70}$$
$$1\frac{31}{70}+4\frac{2}{3}=1\frac{93}{210}+4\frac{140}{210}=5\frac{233}{210}=6\frac{23}{210}$$

Значит,

$$\frac{3}{35}+1\frac{5}{14}+\left(2\frac{1}{6}-\frac{9}{14}\right):\left(\frac{4}{7}\right)^2=6\frac{23}{210}$$

2) Аналогично:

$$\left(\frac{4}{5}\right)^2=\frac{16}{25}$$
$$\frac{7}{15}+2\frac{1}{3}=\frac{7}{15}+2\frac{5}{15}=2\frac{12}{15}=2\frac{4}{5}$$
$$\frac{16}{25}:2\frac{4}{5}=\frac{16}{25}:\frac{14}{5}=\frac{16}{25}\cdot\frac{5}{14}=\frac{8}{35}$$
$$\frac{2}{9}+1\frac{5}{12}=\frac{8}{36}+1\frac{15}{36}=1\frac{23}{36}$$
$$1\frac{23}{36}\cdot 2\frac{4}{7}=\frac{59}{36}\cdot\frac{18}{7}=\frac{59\cdot 1}{2\cdot 7}=\frac{59}{14}=4\frac{3}{14}$$
$$\frac{8}{35}+4\frac{3}{14}=\frac{16}{70}+4\frac{15}{70}=4\frac{31}{70}$$

Следовательно,

$$\left(\frac{4}{5}\right)^2:\left(\frac{7}{15}+2\frac{1}{3}\right)+\left(\frac{2}{9}+1\frac{5}{12}\right)\cdot 2\frac{4}{7}=4\frac{31}{70}$$

Ответ

1) $$6\frac{23}{210}$$
2) $$4\frac{31}{70}$$