Упр.10 Повторение ГДЗ Мордкович Семенов 7 класс (Алгебра)

Задача

а) (0,56 : 1,4 — 2 2/3 : 2 2/15) · (-6/17);
б) (-4,1 + 5,67 — 9,57) · (-1/2)^4;
в) (-0,72 : 2,4 + 8 4/7 · 4,2) : (-1 4/7);
г) (-1/4)^3 : (-1,3 + 3,8 — 3 1/8).

Подробный ответ

а)

$$ (0{,}56 : 1{,}4 — 2\tfrac{2}{3} : 2\tfrac{2}{15})\cdot\left(-\tfrac{6}{17}\right) $$
$$ 0{,}56 : 1{,}4 = 0{,}4,\qquad 2\tfrac{2}{3}=\tfrac{8}{3},\qquad 2\tfrac{2}{15}=\tfrac{32}{15} $$
$$ \tfrac{8}{3} : \tfrac{32}{15}=\tfrac{8}{3}\cdot\tfrac{15}{32}=\tfrac{5}{4}=1{,}25 $$
$$ 0{,}4-1{,}25=-0{,}85=-\tfrac{17}{20} $$
$$ -\tfrac{17}{20}\cdot\left(-\tfrac{6}{17}\right)=\tfrac{6}{20}=\tfrac{3}{10}=0{,}3 $$

б)

$$ (-4{,}1+5{,}67-9{,}57)\cdot\left(-\tfrac{1}{2}\right)^4 $$
$$ -4{,}1+5{,}67-9{,}57=-8 $$
$$ \left(-\tfrac{1}{2}\right)^4=\tfrac{1}{16} $$
$$ -8\cdot\tfrac{1}{16}=-\tfrac{1}{2}=-0{,}5 $$

в)

$$ (-0{,}72:2{,}4+8\tfrac{4}{7}\cdot4{,}2):\left(-1\tfrac{4}{7}\right) $$
$$ -0{,}72:2{,}4=-0{,}3,\qquad 8\tfrac{4}{7}=\tfrac{60}{7},\qquad 4{,}2=\tfrac{21}{5} $$
$$ \tfrac{60}{7}\cdot4{,}2=\tfrac{60}{7}\cdot\tfrac{21}{5}=36 $$
$$ -0{,}3+36=35{,}7 $$
$$ -1\tfrac{4}{7}=-\tfrac{11}{7} $$
$$ 35{,}7:\left(-\tfrac{11}{7}\right)=\tfrac{357}{10}\cdot\left(-\tfrac{7}{11}\right)=-\tfrac{2499}{110}=-22\tfrac{79}{110} $$

г)

$$ \left(-\tfrac{1}{4}\right)^3:\left(-1{,}3+3{,}8-3\tfrac{1}{8}\right) $$
$$ \left(-\tfrac{1}{4}\right)^3=-\tfrac{1}{64} $$
$$ -1{,}3+3{,}8-3\tfrac{1}{8}=2{,}5-3{,}125=-0{,}625=-\tfrac{5}{8} $$
$$ -\tfrac{1}{64}:\left(-\tfrac{5}{8}\right)=-\tfrac{1}{64}\cdot\left(-\tfrac{8}{5}\right)=\tfrac{1}{40} $$