Упр.8.121 ГДЗ Дорофеев Шарыгин 5 класс (Математика)

Вычислите: а) $$17:\left(\frac{3}{5}+\frac{1}{4}\right)+\left(\frac{7}{8}-\frac{1}{4}\right)\cdot\left(\frac{4}{5}\right)^2$$; б) $$70:\left(\frac{5}{8}+\frac{5}{6}\right)+\left(3\frac{1}{9}-\frac{1}{3}\right)\cdot\left(\frac{3}{10}\right)^2$$.

а) Преобразуем дроби в скобках:

$$17 : \left(\frac{3}{5}+\frac{1}{4}\right)+\left(\frac{7}{8}-\frac{1}{4}\right)\cdot\left(\frac{4}{5}\right)^2$$
$$\frac{3}{5}+\frac{1}{4}=\frac{12}{20}+\frac{5}{20}=\frac{17}{20}$$
$$\frac{7}{8}-\frac{1}{4}=\frac{7}{8}-\frac{2}{8}=\frac{5}{8}$$
$$\left(\frac{4}{5}\right)^2=\frac{16}{25}$$
Тогда
$$17:\frac{17}{20}+\frac{5}{8}\cdot\frac{16}{25}$$
$$17:\frac{17}{20}=17\cdot\frac{20}{17}=20$$
$$\frac{5}{8}\cdot\frac{16}{25}=\frac{2}{5}$$
$$20+\frac{2}{5}=20\frac{2}{5}$$

б)

$$70 : \left(\frac{5}{8}+\frac{5}{6}\right)+\left(3\frac{1}{9}-\frac{1}{3}\right)\cdot\left(\frac{3}{10}\right)^2$$
$$\frac{5}{8}+\frac{5}{6}=\frac{15}{24}+\frac{20}{24}=\frac{35}{24}$$
$$3\frac{1}{9}=\frac{28}{9}, \qquad \frac{28}{9}-\frac{1}{3}=\frac{28}{9}-\frac{3}{9}=\frac{25}{9}$$
$$\left(\frac{3}{10}\right)^2=\frac{9}{100}$$
Тогда
$$70:\frac{35}{24}+\frac{25}{9}\cdot\frac{9}{100}$$
$$70:\frac{35}{24}=70\cdot\frac{24}{35}=2\cdot 24=48$$
$$\frac{25}{9}\cdot\frac{9}{100}=\frac{1}{4}$$
$$48+\frac{1}{4}=48\frac{1}{4}$$

Ответ

а) $$20\frac{2}{5}$$;
б) $$48\frac{1}{4}$$.