Упр.267 ГДЗ Ткачёва 6 класс (Математика)

Задача

1) 3/35 + 1 5/14 + (2 1/6 — 9/14) : (4/7)^2;
2) (4/5)^2 : (7/15 + 2 1/3) + (2/9 + 1 5/12) · 2 4/7.

Подробный ответ

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,

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