Упр.12 Повторение ГДЗ Мордкович Семенов 7 класс (Алгебра)

1. Найдите значение выражения:
   
   а) $$\frac{\left(\frac{5}{12}-\frac{2}{3}\right)\cdot 0{,}2^2}{5{,}7-5\frac{3}{4}}$$;
   
   б) $$\frac{-2\frac{1}{40}+1{,}125}{0{,}3^2\cdot\left(\frac{8}{15}-\frac{4}{5}\right)}$$.

а)

$$\frac{\left(\frac{5}{12}-\frac{2}{3}\right)\cdot 0{,}2^2}{5{,}7-5\frac{3}{4}} = \frac{\left(\frac{5}{12}-\frac{8}{12}\right)\cdot 0{,}04}{5{,}7-5{,}75} = \frac{-\frac{3}{12}\cdot 0{,}04}{-0{,}05}$$

$$\frac{-\frac{1}{4}\cdot 0{,}04}{-0{,}05} = \frac{-0{,}01}{-0{,}05} = 0{,}2$$

б)

$$\frac{-2\frac{1}{40}+1{,}125}{0{,}3^2\cdot\left(\frac{8}{15}-\frac{4}{5}\right)} = \frac{-\frac{81}{40}+\frac{9}{8}}{0{,}09\cdot\left(\frac{8}{15}-\frac{12}{15}\right)} = \frac{-\frac{81}{40}+\frac{45}{40}}{0{,}09\cdot\left(-\frac{4}{15}\right)}$$

$$= \frac{-\frac{36}{40}}{-\frac{0{,}36}{15}} = \frac{36}{40}\cdot\frac{15}{0{,}36} = \frac{9}{10}\cdot\frac{1500}{36} = 37{,}5$$

Ответ

а) $$0{,}2$$; б) $$37{,}5$$.