Упр.451 ГДЗ Мерзляк Полонский 6 класс (Математика)

Задача

1) 12:3*3/8?1*1/4: 15/32 ;
2) 1*31/35:(2? 8/9:1*19/45) ;
3) (1*1/35: 4/5?1*8/35)*3*1/3 ;
4) (7?1*5/9: 7/24): 20/27.

Подробный ответ

1) Преобразуем смешанные числа в неправильные дроби и выполняем действия по порядку:

$$ 12:3\frac{3}{8}-1\frac{1}{4}:\frac{15}{32} =12:\frac{27}{8}-\frac{5}{4}:\frac{15}{32} =12\cdot\frac{8}{27}-\frac{5}{4}\cdot\frac{32}{15} $$
$$ =4\frac{8}{9}-\frac{8}{3} =\frac{44}{9}-\frac{24}{9} =\frac{20}{9} =2\frac{2}{9} $$

2)

$$ 1\frac{31}{35}:\left(2-\frac{8}{9}:1\frac{19}{45}\right) =\frac{66}{35}:\left(2-\frac{8}{9}:\frac{64}{45}\right) $$
$$ =\frac{66}{35}:\left(2-\frac{8}{9}\cdot\frac{45}{64}\right) =\frac{66}{35}:\left(2-\frac{5}{8}\right) $$
$$ =\frac{66}{35}:1\frac{3}{8} =\frac{66}{35}:\frac{11}{8} =\frac{66}{35}\cdot\frac{8}{11} =\frac{48}{35} =1\frac{13}{35} $$

3)

$$ \left(1\frac{1}{35}:\frac{4}{5}-1\frac{8}{35}\right)\cdot 3\frac{1}{3} =\left(\frac{36}{35}\cdot\frac{5}{4}-\frac{43}{35}\right)\cdot\frac{10}{3} $$
$$ =\left(\frac{9}{7}-1\frac{8}{35}\right)\cdot\frac{10}{3} =\left(1\frac{2}{7}-1\frac{8}{35}\right)\cdot\frac{10}{3} $$
$$ =\left(1\frac{10}{35}-1\frac{8}{35}\right)\cdot\frac{10}{3} =\frac{2}{35}\cdot\frac{10}{3} =\frac{4}{21} $$

4)

$$ \left(7-1\frac{5}{9}:\frac{7}{24}\right):\frac{20}{27} =\left(7-\frac{14}{9}\cdot\frac{24}{7}\right):\frac{20}{27} $$
$$ =\left(7-\frac{2}{3}\cdot 8\right):\frac{20}{27} =\left(7-\frac{16}{3}\right):\frac{20}{27} $$
$$ =\left(6\frac{3}{3}-5\frac{1}{3}\right):\frac{20}{27} =1\frac{2}{3}:\frac{20}{27} =\frac{5}{3}\cdot\frac{27}{20} =\frac{9}{4} =2\frac{1}{4} $$