Упр.80 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 6 класс (Математика)

1) 4 1/5 : 7/15 : 1/3; 3) (5 8/9 : 1 17/36 + 1 1/4) : 4 1/5;
2) 4 1/5 : (7/15 : 1/3); 4) (2 1/4 + 4 5/6) : 3 2/5 — 3/4 : 3/5.

1) $$4 \frac{1}{5} : \frac{7}{15} : \frac{1}{3}$$

$$ 4 \frac{1}{5} = \frac{21}{5} $$
$$ \frac{21}{5} : \frac{7}{15} : \frac{1}{3} = \frac{21}{5} \cdot \frac{15}{7} \cdot 3 = \frac{21 \cdot 15 \cdot 3}{5 \cdot 7} = 27 $$

2) $$4 \frac{1}{5} : \left(\frac{7}{15} : \frac{1}{3}\right)$$

$$ 4 \frac{1}{5} = \frac{21}{5} $$
$$ \frac{7}{15} : \frac{1}{3} = \frac{7}{15} \cdot 3 = \frac{7}{5} $$
$$ \frac{21}{5} : \frac{7}{5} = \frac{21}{5} \cdot \frac{5}{7} = 3 $$

3) $$\left(5 \frac{8}{9} : 1 \frac{17}{36} + 1 \frac{1}{4}\right) : 4 \frac{1}{5}$$

$$ 5 \frac{8}{9} = \frac{53}{9}, \quad 1 \frac{17}{36} = \frac{53}{36}, \quad 1 \frac{1}{4} = \frac{5}{4}, \quad 4 \frac{1}{5} = \frac{21}{5} $$
$$ \left(\frac{53}{9} : \frac{53}{36} + \frac{5}{4}\right) : \frac{21}{5} = \left(\frac{53}{9} \cdot \frac{36}{53} + \frac{5}{4}\right) : \frac{21}{5} $$
$$ = \left(4 + \frac{5}{4}\right) : \frac{21}{5} = \frac{21}{4} : \frac{21}{5} = \frac{21}{4} \cdot \frac{5}{21} = \frac{5}{4} = 1 \frac{1}{4} $$

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

$$ 2 \frac{1}{4} = \frac{9}{4}, \quad 4 \frac{5}{6} = \frac{29}{6}, \quad 3 \frac{2}{5} = \frac{17}{5} $$
$$ \left(\frac{9}{4} + \frac{29}{6}\right) : \frac{17}{5} — \frac{3}{4} : \frac{3}{5} = \left(\frac{27}{12} + \frac{58}{12}\right) : \frac{17}{5} — \frac{3}{4} \cdot \frac{5}{3} $$
$$ = \frac{85}{12} : \frac{17}{5} — \frac{5}{4} = \frac{85}{12} \cdot \frac{5}{17} — \frac{5}{4} = \frac{25}{12} — \frac{15}{12} = \frac{10}{12} = \frac{5}{6} $$

Ответ

1) 27; 2) 3; 3) $$1 \frac{1}{4}$$; 4) $$\frac{5}{6}$$.