Упр.388 Часть 2 ГДЗ Дорофеев Петерсон 6 класс (Математика)

1) 0,9:(3 2/7•2,8-2,79+7,2:2 4/7+2,79);
2) (15,04•2,5-2,4•(85,24-84,24:1,2))/(0,047•16,9-0,9•0,047).

1) Преобразуем выражение в скобках:

$$ 0{,}9:(3\tfrac{2}{7}\cdot 2{,}8-2{,}79+7{,}2:2\tfrac{4}{7}+2{,}79) $$
$$ =0{,}9:\left(\frac{23}{7}\cdot\frac{28}{10}+\frac{72}{10}:\frac{18}{7}+(2{,}79-2{,}79)\right) $$
$$ =0{,}9:\left(\frac{23}{1}\cdot\frac{2}{5}+\frac{36}{5}\cdot\frac{7}{18}\right) =0{,}9:\left(\frac{46}{5}+\frac{14}{5}\right) $$
$$ =0{,}9:\frac{60}{5}=0{,}9:12. $$

$$ 0{,}9:12=\frac{9}{10}:\,12=\frac{9}{120}=\frac{3}{40}=0{,}075. $$

2) Упростим числитель и знаменатель дроби:

$$ \frac{15{,}04\cdot 2{,}5-2{,}4\cdot(85{,}24-84{,}24:1{,}2)}{0{,}047\cdot 16{,}9-0{,}9\cdot 0{,}047} $$
$$ =\frac{15{,}04\cdot 2{,}5-2{,}4\cdot(85{,}24-70{,}2)}{0{,}047\cdot(16{,}9-0{,}9)} $$
$$ =\frac{15{,}04\cdot 2{,}5-2{,}4\cdot 15{,}04}{0{,}047\cdot 16} $$
$$ =\frac{15{,}04\cdot(2{,}5-2{,}4)}{0{,}047\cdot 16} =\frac{15{,}04\cdot 0{,}1}{0{,}047\cdot 16}. $$

$$ \frac{15{,}04\cdot 0{,}1}{0{,}047\cdot 16} =\frac{1{,}504}{0{,}752} =\frac{1504}{752} =2. $$

Ответ

1) $$0{,}075$$; 2) $$2$$.