Упр.1132 ГДЗ Мерзляк Полонский 6 класс (Математика)

Задача

1) (-3/14 — 8/21):20/21;
2) 3/8 : (-5/8) — (-2*1/4):(-1*4/11);
3) (-4*1/12 + 3*9/10) : 3*3/10;
4) (11/14 — 5/6) : (11/14 — 3/4).

Подробный ответ

1) $$\left(-\frac{3}{14}-\frac{8}{21}\right):\frac{20}{21}$$

$$ -\frac{3}{14}-\frac{8}{21}=-\frac{9}{42}-\frac{16}{42}=-\frac{25}{42} $$
$$ -\frac{25}{42}:\frac{20}{21}=-\frac{25}{42}\cdot\frac{21}{20}=-\frac{25}{40}=-\frac{5}{8} $$

2) $$\frac{3}{8}:\left(-\frac{5}{8}\right)-\left(-2\frac{1}{4}\right):\left(-1\frac{4}{11}\right)$$

$$ \frac{3}{8}:\left(-\frac{5}{8}\right)=\frac{3}{8}\cdot\left(-\frac{8}{5}\right)=-\frac{3}{5} $$
$$ -2\frac{1}{4}=-\frac{9}{4}, \qquad -1\frac{4}{11}=-\frac{15}{11} $$
$$ \left(-\frac{9}{4}\right):\left(-\frac{15}{11}\right)=\left(-\frac{9}{4}\right)\cdot\left(-\frac{11}{15}\right)=\frac{33}{20} $$
$$ -\frac{3}{5}-\frac{33}{20}=-\frac{12}{20}-\frac{33}{20}=-\frac{45}{20}=-\frac{9}{4}=-2\frac{1}{4} $$

3) $$\left(-4\frac{1}{12}+3\frac{9}{10}\right):3\frac{3}{10}$$

$$ -4\frac{1}{12}=-\frac{49}{12}, \qquad 3\frac{9}{10}=\frac{39}{10}, \qquad 3\frac{3}{10}=\frac{33}{10} $$
$$ -\frac{49}{12}+\frac{39}{10}=-\frac{245}{60}+\frac{234}{60}=-\frac{11}{60} $$
$$ -\frac{11}{60}:\frac{33}{10}=-\frac{11}{60}\cdot\frac{10}{33}=-\frac{1}{18} $$

4) $$\left(\frac{11}{14}-\frac{5}{6}\right):\left(\frac{11}{14}-\frac{3}{4}\right)$$

$$ \frac{11}{14}-\frac{5}{6}=\frac{33}{42}-\frac{35}{42}=-\frac{2}{42}=-\frac{1}{21} $$
$$ \frac{11}{14}-\frac{3}{4}=\frac{22}{28}-\frac{21}{28}=\frac{1}{28} $$
$$ -\frac{1}{21}:\frac{1}{28}=-\frac{1}{21}\cdot 28=-\frac{28}{21}=-\frac{4}{3}=-1\frac{1}{3} $$