Упр.83 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 6 класс (Математика)

Вычислите значение выражения:

1. 1) $$\left(3\frac{2}{3}+1\frac{3}{4}\right):\left(6\frac{7}{12}-2\frac{1}{4}\right)\cdot 0{,}8$$; 2) $$\left(4\frac{2}{5}:1\frac{3}{5}+2\frac{4}{7}-8\frac{1}{2}:14\right):\left(2\frac{3}{8}-1\frac{11}{14}\right)$$.

1) $$\left(3\frac{2}{3}+1\frac{3}{4}\right):\left(6\frac{7}{12}-2\frac{1}{4}\right)\cdot 0{,}8$$

$$3\frac{2}{3}+1\frac{3}{4}=3\frac{8}{12}+1\frac{9}{12}=4\frac{17}{12}=5\frac{5}{12}$$
$$6\frac{7}{12}-2\frac{1}{4}=6\frac{7}{12}-2\frac{3}{12}=4\frac{4}{12}=4\frac{1}{3}$$
$$5\frac{5}{12}:4\frac{1}{3}=\frac{65}{12}:\frac{13}{3}=\frac{65}{12}\cdot\frac{3}{13}=\frac{5}{4}$$
$$\frac{5}{4}\cdot 0{,}8=\frac{5}{4}\cdot\frac{8}{10}=\frac{5}{4}\cdot\frac{4}{5}=1$$

Ответ: 1.

2) $$\left(4\frac{2}{5}:1\frac{3}{5}+2\frac{4}{7}-8\frac{1}{2}:14\right):\left(2\frac{3}{8}-1\frac{11}{14}\right)$$

$$4\frac{2}{5}:1\frac{3}{5}=\frac{22}{5}:\frac{8}{5}=\frac{22}{5}\cdot\frac{5}{8}=\frac{11}{4}$$
$$8\frac{1}{2}:14=\frac{17}{2}:14=\frac{17}{2}\cdot\frac{1}{14}=\frac{17}{28}$$
$$2\frac{3}{7}+\frac{11}{4}-\frac{17}{28}=2\frac{21}{28}+2\frac{16}{28}-\frac{17}{28}=4\frac{37}{28}-\frac{17}{28}=4\frac{20}{28}=4\frac{5}{7}$$
$$2\frac{3}{8}-1\frac{11}{14}=2\frac{21}{56}-1\frac{44}{56}=1\frac{77}{56}-1\frac{44}{56}=\frac{33}{56}$$
$$4\frac{5}{7}:\frac{33}{56}=\frac{33}{7}:\frac{33}{56}=\frac{33}{7}\cdot\frac{56}{33}=8$$

Ответ: 8.