Упр.191 Рабочая тетрадь №1 ГДЗ Мерзляк Полонский 6 класс (Математика)

1. Найдите значение выражения: а) $$\left(\frac{5}{6}-\frac{11}{14}\right):\frac{3}{7}$$; б) $$16:1\frac{11}{13}-1\frac{1}{4}:\frac{15}{58}$$; в) $$\left(8-1\frac{3}{13}:1\frac{17}{39}\right):5\frac{5}{14}$$.

1) $$\left(\frac{5}{6}-\frac{11}{14}\right):\frac{3}{7}$$

$$\frac{5}{6}-\frac{11}{14}=\frac{35}{42}-\frac{33}{42}=\frac{2}{42}=\frac{1}{21}$$
$$\frac{1}{21}:\frac{3}{7}=\frac{1}{21}\cdot\frac{7}{3}=\frac{1}{9}$$

2) $$16:1\frac{11}{13}-1\frac{1}{4}:\frac{15}{58}$$

$$16:1\frac{11}{13}=16:\frac{24}{13}=16\cdot\frac{13}{24}=\frac{2\cdot 13}{3}=\frac{26}{3}=8\frac{2}{3}$$
$$1\frac{1}{4}:\frac{15}{58}=\frac{5}{4}:\frac{15}{58}=\frac{5}{4}\cdot\frac{58}{15}=\frac{29}{6}=4\frac{5}{6}$$
$$8\frac{2}{3}-4\frac{5}{6}=8\frac{4}{6}-4\frac{5}{6}=7\frac{10}{6}-4\frac{5}{6}=3\frac{5}{6}$$

3) $$\left(8-1\frac{3}{13}:1\frac{17}{39}\right):5\frac{5}{14}$$

$$1\frac{3}{13}:1\frac{17}{39}=\frac{16}{13}:\frac{56}{39}=\frac{16}{13}\cdot\frac{39}{56}=\frac{16\cdot 39}{13\cdot 56}=\frac{2\cdot 3}{1\cdot 7}=\frac{6}{7}$$
$$8-\frac{6}{7}=7\frac{1}{7}$$
$$7\frac{1}{7}:5\frac{5}{14}=\frac{50}{7}:\frac{75}{14}=\frac{50}{7}\cdot\frac{14}{75}=\frac{50\cdot 14}{7\cdot 75}=\frac{2\cdot 2}{1\cdot 3}=\frac{4}{3}=1\frac{1}{3}$$

Ответ: 1) $$\frac{1}{9}$$; 2) $$3\frac{5}{6}$$; 3) $$1\frac{1}{3}$$.