Упр.937 ГДЗ Никольский Потапов 5 класс (Математика)

Задача

а) (1/2 : 3/4 — 4/9) : 3/5; б) 1/2 : 3/8 — 4/9 : 3/5;
в) 3/5 : (9/10 — 3/5 · 8/9); г) 3/5 : 9/10 — 3/5 · 8/9.

Подробный ответ

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

$$\frac{1}{2}:\frac{3}{4}=\frac{1}{2}\cdot\frac{4}{3}=\frac{2}{3}$$
$$\frac{2}{3}-\frac{4}{9}=\frac{6}{9}-\frac{4}{9}=\frac{2}{9}$$
$$\frac{2}{9}:\frac{3}{5}=\frac{2}{9}\cdot\frac{5}{3}=\frac{10}{27}$$

б) $$\frac{1}{2}:\frac{3}{8}-\frac{4}{9}:\frac{3}{5}$$

$$\frac{1}{2}:\frac{3}{8}=\frac{1}{2}\cdot\frac{8}{3}=\frac{4}{3}$$
$$\frac{4}{9}:\frac{3}{5}=\frac{4}{9}\cdot\frac{5}{3}=\frac{20}{27}$$
$$\frac{4}{3}-\frac{20}{27}=\frac{36}{27}-\frac{20}{27}=\frac{16}{27}$$

в) $$\frac{3}{5}:\left(\frac{9}{10}-\frac{3}{5}\cdot\frac{8}{9}\right)$$

$$\frac{3}{5}\cdot\frac{8}{9}=\frac{24}{45}=\frac{8}{15}$$
$$\frac{9}{10}-\frac{8}{15}=\frac{27}{30}-\frac{16}{30}=\frac{11}{30}$$
$$\frac{3}{5}:\frac{11}{30}=\frac{3}{5}\cdot\frac{30}{11}=\frac{18}{11}$$

г) $$\frac{3}{5}:\frac{9}{10}-\frac{3}{5}\cdot\frac{8}{9}$$

$$\frac{3}{5}:\frac{9}{10}=\frac{3}{5}\cdot\frac{10}{9}=\frac{2}{3}$$
$$\frac{3}{5}\cdot\frac{8}{9}=\frac{8}{15}$$
$$\frac{2}{3}-\frac{8}{15}=\frac{10}{15}-\frac{8}{15}=\frac{2}{15}$$