Упр.451 ГДЗ Мерзляк Полонский 6 класс (Математика)

1. Найдите значение выражения:
   1) $$12 : 3\frac{3}{8} — 1\frac{1}{4} : \frac{15}{32};$$
   2) $$1\frac{31}{35} : \left(2\frac{8}{9} — 1\frac{19}{45}\right);$$
   3) $$\left(1\frac{1}{35} : \frac{4}{5} — 1\frac{8}{35}\right) \cdot 3\frac{1}{3};$$
   4) $$\left(7 — 1\frac{5}{9} : \frac{7}{24}\right) : \frac{20}{27}.$$

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)

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

Ответ

1) $$2\frac{2}{9}$$; 2) $$1\frac{13}{35}$$; 3) $$\frac{4}{21}$$; 4) $$2\frac{1}{4}$$.