Упр.80 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 6 класс (Математика)

1) 2 1/4 : 3/8 : 1/2; 3) (6 3/4 — 5 1/8 : 1 9/32) : 2 1/5;
2) 2 1/4 : (3/8 : 1/2) 4) (3 1/4 + 2 1/6) : 2 3/5 — 2/3 : 4/9.

1) $$2\frac{1}{4} : \frac{3}{8} : \frac{1}{2} = \frac{9}{4} : \frac{3}{8} : \frac{1}{2}$$

Выполним деление слева направо:

$$ \frac{9}{4} : \frac{3}{8} = \frac{9}{4}\cdot\frac{8}{3} = 6 $$
$$ 6 : \frac{1}{2} = 6\cdot 2 = 12 $$

2) $$2\frac{1}{4} : \left(\frac{3}{8} : \frac{1}{2}\right) = \frac{9}{4} : \left(\frac{3}{8}\cdot 2\right)$$

$$ \frac{3}{8} : \frac{1}{2} = \frac{3}{8}\cdot 2 = \frac{3}{4} $$
$$ \frac{9}{4} : \frac{3}{4} = \frac{9}{4}\cdot\frac{4}{3} = 3 $$

3) $$\left(6\frac{3}{4} — 5\frac{1}{8} : 1\frac{9}{32}\right) : 2\frac{1}{5}$$

$$ 6\frac{3}{4} = \frac{27}{4}, \quad 5\frac{1}{8} = \frac{41}{8}, \quad 1\frac{9}{32} = \frac{41}{32}, \quad 2\frac{1}{5} = \frac{11}{5} $$

$$ \frac{41}{8} : \frac{41}{32} = \frac{41}{8}\cdot\frac{32}{41} = 4 $$
$$ \frac{27}{4} — 4 = \frac{27}{4} — \frac{16}{4} = \frac{11}{4} $$
$$ \frac{11}{4} : \frac{11}{5} = \frac{11}{4}\cdot\frac{5}{11} = \frac{5}{4} = 1\frac{1}{4} $$

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

$$ 3\frac{1}{4} = \frac{13}{4}, \quad 2\frac{1}{6} = \frac{13}{6}, \quad 2\frac{3}{5} = \frac{13}{5} $$

$$ \frac{13}{4} + \frac{13}{6} = \frac{39}{12} + \frac{26}{12} = \frac{65}{12} $$
$$ \frac{65}{12} : \frac{13}{5} = \frac{65}{12}\cdot\frac{5}{13} = \frac{25}{12} $$
$$ \frac{2}{3} : \frac{4}{9} = \frac{2}{3}\cdot\frac{9}{4} = \frac{3}{2} $$
$$ \frac{25}{12} — \frac{3}{2} = \frac{25}{12} — \frac{18}{12} = \frac{7}{12} $$

Ответ

1) $$12$$; 2) $$3$$; 3) $$1\frac{1}{4}$$; 4) $$\frac{7}{12}$$.