Упр.863 ГДЗ Муравин 6 класс (Математика)

Задача

1) (1 2/9•3 4/7•4 1/2)/(5 1/2•6 3/7•2 7/9)•(12,1•2/11+4,2:2 1/3)/(1 5/13•0,16-5/13•0,16);
2) ((1,75+2 1/3)•1 5/7)/(3/250 :(1,23-3/5•1,05)+0,12);
3) (5 4/5+0,2(3,8•1 2/7-2,8•1 2/7)•8 5/9)/((5/9-11/36)•6,4);
4) ((2 5/6-7 1/9)•(-0,54) :(-0,7))/((4/23•(-5/19)-3/23•(-3/19))•(-5,75) ).

Подробный ответ

$$ \frac{\left(1\frac{2}{9}\cdot 3\frac{4}{7}\cdot 4\frac{1}{2}\right)}{\left(5\frac{1}{2}\cdot 6\frac{3}{7}\cdot 2\frac{7}{9}\right)} \cdot \frac{12{,}1\cdot \frac{2}{11}+4{,}2:2\frac{1}{3}}{1\frac{5}{13}\cdot 0{,}16-\frac{5}{13}\cdot 0{,}16} $$
$$ = \frac{\frac{11}{9}\cdot \frac{25}{7}\cdot \frac{9}{2}}{\frac{11}{2}\cdot \frac{45}{7}\cdot \frac{25}{9}} \cdot \frac{\frac{121}{10}\cdot \frac{2}{11}+\frac{42}{10}:\frac{7}{3}}{0{,}16\cdot \left(1\frac{5}{13}-\frac{5}{13}\right)} $$
$$ = \frac{11\cdot 25}{7\cdot 2}\cdot \frac{2\cdot 7}{11\cdot 5\cdot 25} \cdot \frac{\frac{11}{5}+\frac{21}{5}\cdot \frac{3}{7}}{0{,}16\cdot 1} $$
$$ = \frac{1}{5}\cdot \frac{\frac{11}{5}+\frac{3}{5}}{0{,}16} = \frac{1}{5}\cdot \frac{\frac{14}{5}}{0{,}16} = \frac{14}{25\cdot 0{,}16} = \frac{14}{4} =5. $$

$$ \frac{(1{,}75+2\frac{1}{3})\cdot 1\frac{5}{7}}{\frac{3}{250}:(1{,}23-\frac{3}{5}\cdot 1{,}05)+0{,}12} $$
$$ = \frac{\left(1\frac{3}{4}+2\frac{1}{3}\right)\cdot \frac{12}{7}}{\frac{3}{250}:(1{,}23-3\cdot 0{,}21)+0{,}12} = \frac{\left(1\frac{9}{12}+2\frac{4}{12}\right)\cdot \frac{12}{7}}{\frac{3}{250}:(1{,}23-0{,}63)+0{,}12} $$
$$ = \frac{3\frac{13}{12}\cdot \frac{12}{7}}{0{,}012:0{,}6+0{,}12} = \frac{\frac{49}{12}\cdot \frac{12}{7}}{0{,}02+0{,}12} = \frac{7}{0{,}14} =50. $$

$$ \frac{5\frac{4}{5}+0{,}2(3{,}8\cdot 1\frac{2}{7}-2{,}8\cdot 1\frac{2}{7})\cdot 8\frac{5}{9}}{\left(\frac{5}{9}-\frac{11}{36}\right)\cdot 6{,}4} $$
$$ = \frac{5{,}8+0{,}2\cdot 1\frac{2}{7}\cdot (3{,}8-2{,}8)\cdot \frac{77}{9}}{\left(\frac{20}{36}-\frac{11}{36}\right)\cdot 6{,}4} = \frac{5{,}8+0{,}2\cdot \frac{9}{7}\cdot 1\cdot \frac{77}{9}}{\frac{1}{4}\cdot 6{,}4} $$
$$ = \frac{5{,}8+0{,}2\cdot 11}{1{,}6} = \frac{5{,}8+2{,}2}{1{,}6} = \frac{8}{1{,}6} = \frac{80}{16} =5. $$

$$ \frac{(2\frac{5}{6}-7\frac{1}{9})\cdot (-0{,}54):(-0{,}7)}{\left(\frac{4}{23}\cdot \left(-\frac{5}{19}\right)-\frac{3}{23}\cdot \left(-\frac{3}{19}\right)\right)\cdot (-5{,}75)} $$
$$ = \frac{\left(2\frac{30}{36}-7\frac{4}{36}\right)\cdot \left(-\frac{54}{100}\right):(-0{,}7)}{\left(-\frac{20}{437}+\frac{9}{437}\right)\cdot \left(-5\frac{3}{4}\right)} $$
$$ = \frac{\left(-4\frac{10}{36}\right)\cdot \left(-\frac{27}{50}\right):\left(-\frac{7}{10}\right)}{\left(-\frac{11}{437}\right)\cdot \left(-\frac{23}{4}\right)} = \frac{-4\frac{5}{18}\cdot \left(-\frac{27}{50}\right)\cdot \left(-\frac{10}{7}\right)}{\frac{11}{76}} $$
$$ = \frac{-\frac{77}{18}\cdot \frac{27}{50}\cdot \frac{10}{7}}{\frac{11}{76}} = \frac{-\frac{11\cdot 3\cdot 1}{2\cdot 5\cdot 1}}{\frac{11}{76}} = -\frac{3}{10}\cdot 76 = -\frac{114}{5} =-22{,}8. $$