Упр.80 Вариант 4 Дидактические материалы ГДЗ Мерзляк Полонский 6 класс (Математика)

1) 5 1/3 : 8/9 : 1/3; 3) (8 5/7 — 6 5/6 : 1 5/36) : 4 3/4;
2) 5 1/3 : (8/9 : 1/3); 4) (2 5/6 + 2 2/9) : 3 1/4 — 2/7 : 1 2/7.

1) $$5\frac{1}{3} : \frac{8}{9} : \frac{1}{3}$$

$$ 5\frac{1}{3}=\frac{16}{3} $$
$$ \frac{16}{3}:\frac{8}{9}:\frac{1}{3} =\frac{16}{3}\cdot\frac{9}{8}\cdot 3 =\frac{16\cdot 9\cdot 3}{3\cdot 8\cdot 1} =18 $$

2) $$5\frac{1}{3} : \left(\frac{8}{9} : \frac{1}{3}\right)$$

$$ \frac{8}{9}:\frac{1}{3}=\frac{8}{9}\cdot 3=\frac{8}{3} $$
$$ 5\frac{1}{3}:\frac{8}{3}=\frac{16}{3}:\frac{8}{3}=\frac{16}{3}\cdot\frac{3}{8}=2 $$

3) $$\left(8\frac{5}{7}-6\frac{5}{6}:\,1\frac{5}{36}\right):4\frac{3}{4}$$

$$ 6\frac{5}{6}=\frac{41}{6}, \qquad 1\frac{5}{36}=\frac{41}{36}, \qquad 4\frac{3}{4}=\frac{19}{4} $$
$$ \frac{41}{6}:\frac{41}{36}=\frac{41}{6}\cdot\frac{36}{41}=6 $$
$$ 8\frac{5}{7}-6=2\frac{5}{7}=\frac{19}{7} $$
$$ \frac{19}{7}:\frac{19}{4}=\frac{19}{7}\cdot\frac{4}{19}=\frac{4}{7} $$

4) $$\left(2\frac{5}{6}+2\frac{2}{9}\right):3\frac{1}{4}-\frac{2}{7}:1\frac{2}{7}$$

$$ 2\frac{5}{6}=\frac{17}{6}, \qquad 2\frac{2}{9}=\frac{20}{9}, \qquad 3\frac{1}{4}=\frac{13}{4}, \qquad 1\frac{2}{7}=\frac{9}{7} $$
$$ \frac{17}{6}+\frac{20}{9}=\frac{51}{18}+\frac{40}{18}=\frac{91}{18} $$
$$ \frac{91}{18}:\frac{13}{4}=\frac{91}{18}\cdot\frac{4}{13}=\frac{14}{9} $$
$$ \frac{2}{7}:\frac{9}{7}=\frac{2}{7}\cdot\frac{7}{9}=\frac{2}{9} $$
$$ \frac{14}{9}-\frac{2}{9}=\frac{12}{9}=\frac{4}{3}=1\frac{1}{3} $$

Ответ

1) 18; 2) 2; 3) $$\frac{4}{7}$$; 4) $$1\frac{1}{3}$$.