Упр.118(стар учебник) ГДЗ Дорофеев Суворова 7 класс (Алгебра)

1. Вычислите: а) $$\frac{(2{,}8 : 2*4/5 (2*2/3))}{(1{,}6 : 1{,}3)}$$; б) $$\frac{(1{,}8 : 1*1/5 * 0{,}12)}{(0{,}27 : 2/7)}$$.

а)

$$\frac{2{,}8:2\frac{4}{5}\cdot 2\frac{2}{3}}{1{,}6:1{,}3} = \frac{\frac{28}{10}:\frac{14}{5}\cdot \frac{8}{3}}{\frac{16}{10}:\frac{13}{10}}$$

$$\frac{28}{10}:\frac{14}{5}=\frac{28}{10}\cdot \frac{5}{14}=1,\qquad 1\cdot \frac{8}{3}=\frac{8}{3}$$

$$\frac{16}{10}:\frac{13}{10}=\frac{16}{10}\cdot \frac{10}{13}=\frac{16}{13}$$

$$\frac{\frac{8}{3}}{\frac{16}{13}}=\frac{8}{3}\cdot \frac{13}{16}=\frac{13}{6}=2\frac{1}{6}$$

б)

$$\frac{1{,}8:1\frac{1}{5}\cdot 0{,}12}{0{,}27:\frac{2}{7}} = \frac{\frac{18}{10}:\frac{6}{5}\cdot \frac{12}{100}}{\frac{27}{100}:\frac{2}{7}}$$

$$\frac{18}{10}:\frac{6}{5}=\frac{18}{10}\cdot \frac{5}{6}=\frac{3}{2},\qquad \frac{3}{2}\cdot \frac{12}{100}=\frac{9}{50}$$

$$\frac{27}{100}:\frac{2}{7}=\frac{27}{100}\cdot \frac{7}{2}=\frac{189}{200}$$

$$\frac{\frac{9}{50}}{\frac{189}{200}}=\frac{9}{50}\cdot \frac{200}{189}=\frac{4}{21}$$

Ответ

а) $$2\frac{1}{6}$$; б) $$\frac{4}{21}$$.