Упр.8.150 ГДЗ Дорофеев Шарыгин 5 класс (Математика)

Вычислите:

• а) $$\frac{8}{9}\cdot\frac{3}{4}-\left(\frac{5}{6}-\frac{1}{4}\right)$$;
• в) $$\left(\frac{2}{5}-\frac{2}{7}\right):\frac{2}{7}\cdot\frac{2}{5}$$;
• б) $$\frac{3}{5}+\frac{4}{5}\cdot\frac{3}{7}+\frac{6}{7}$$;
• г) $$\left(\frac{5}{6}-\frac{3}{10}\right):\left(\frac{3}{10}+\frac{2}{15}\right)$$.

а) $$\frac{8}{9}\cdot\frac{3}{4}-\left(\frac{5}{6}-\frac{1}{4}\right)$$

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

$$\frac{5}{6}-\frac{1}{4}=\frac{10}{12}-\frac{3}{12}=\frac{7}{12}$$

$$\frac{2}{3}-\frac{7}{12}=\frac{8}{12}-\frac{7}{12}=\frac{1}{12}$$

б) $$\frac{3}{5}+\frac{4}{5}\cdot\frac{3}{7}+\frac{6}{7}$$

$$\frac{4}{5}\cdot\frac{3}{7}=\frac{12}{35}$$

$$\frac{3}{5}=\frac{21}{35},\qquad \frac{6}{7}=\frac{30}{35}$$

$$\frac{21}{35}+\frac{12}{35}+\frac{30}{35}=\frac{63}{35}=\frac{9}{5}=1\frac{4}{5}$$

в) $$\left(\frac{2}{5}-\frac{2}{7}\right):\frac{2}{7}\cdot\frac{2}{5}$$

$$\frac{2}{5}-\frac{2}{7}=\frac{14}{35}-\frac{10}{35}=\frac{4}{35}$$

$$\frac{4}{35}:\frac{2}{7}\cdot\frac{2}{5}=\frac{4}{35}\cdot\frac{7}{2}\cdot\frac{2}{5}$$

$$\frac{4}{35}\cdot\frac{7}{2}\cdot\frac{2}{5}=\frac{4}{25}$$

г) $$\left(\frac{5}{6}-\frac{3}{10}\right):\left(\frac{3}{10}+\frac{2}{15}\right)$$

$$\frac{5}{6}-\frac{3}{10}=\frac{25}{30}-\frac{9}{30}=\frac{16}{30}$$

$$\frac{3}{10}+\frac{2}{15}=\frac{9}{30}+\frac{4}{30}=\frac{13}{30}$$

$$\frac{16}{30}:\frac{13}{30}=\frac{16}{30}\cdot\frac{30}{13}=\frac{16}{13}=1\frac{3}{13}$$

Ответ

а) $$\frac{1}{12}$$; б) $$1\frac{4}{5}$$; в) $$\frac{4}{25}$$; г) $$1\frac{3}{13}$$.