Упр.616 ГДЗ Никольский Потапов 8 класс (Алгебра)

Рассмотрим вариант решения задания из учебника Никольский, Потапов 8 класс, Просвещение: 616

1. а)
   $$\frac{\left(\frac16+0{,}1+\frac1{15}\right):\left(\frac16+0{,}1-\frac1{15}\right)}{\left(0{,}5-\frac13+0{,}25-\frac15\right):\left(0{,}25-\frac16\right)}$$
   $$=\frac{\left(\frac{5}{30}+\frac{3}{30}+\frac{2}{30}\right):\left(\frac{5}{30}+\frac{3}{30}-\frac{2}{30}\right)}{\left(\frac12-\frac13+\frac14-\frac15\right):\left(\frac14-\frac16\right)}$$
   $$=\frac{\frac{10}{30}:\frac{6}{30}}{\frac{13}{60}:\frac{1}{12}}=\frac{\frac13:\frac15}{\frac{13}{60}:\frac{1}{12}}$$
   $$=\frac{\frac53}{\frac{13}{60}\cdot 12}=\frac{\frac53}{\frac{13}{5}}=\frac53\cdot\frac5{13}=\frac{25}{39}.$$

2. б)
   $$\frac{0{,}4+8:(5{,}3-0{,}8\cdot\frac38)-5:2\frac12}{1\frac78\cdot 8-(8{,}9-2{,}6:\frac23)}$$
   $$=\frac{0{,}4+8:(5{,}3-0{,}3)-2}{15-(8{,}9-3{,}9)}$$
   $$=\frac{0{,}4+8:5-2}{15-5}=\frac{0{,}4+1{,}6-2}{10}=\frac{0}{10}=0.$$

3. в)
   $$\frac{\left(0{,}5:1{,}25+\frac75:\,1\frac47-\frac3{11}\right)\cdot 3}{\left(1{,}5+\frac14\right):18\frac13}$$
   $$=\frac{\left(\frac12:\frac54+\frac75:\frac{11}{7}-\frac3{11}\right)\cdot 3}{\left(1\frac12+\frac14\right):\frac{55}{3}}$$
   $$=\frac{\left(\frac12\cdot\frac45+\frac75\cdot\frac7{11}-\frac3{11}\right)\cdot 3}{\left(1\frac34\right)\cdot\frac3{55}}$$
   $$=\frac{\left(\frac25+\frac{49}{55}-\frac3{11}\right)\cdot 3}{\frac74\cdot\frac3{55}}$$
   $$=\frac{\left(\frac{22}{55}+\frac{49}{55}-\frac{15}{55}\right)\cdot 3}{\frac{21}{220}}=\frac{\frac{56}{55}\cdot 3}{\frac{21}{220}}$$
   $$=\frac{168}{55}\cdot\frac{220}{21}=32.$$

4. г)
   $$\frac{(0{,}6+0{,}425-0{,}005):0{,}01}{10{,}5+5\frac14+3\frac16+15\frac1{12}}\cdot 60$$
   $$=\frac{(1{,}025-0{,}005):0{,}01}{10\frac12+5\frac14+3\frac16+15\frac1{12}}\cdot 60$$
   $$=\frac{1{,}02:0{,}01}{15\frac9{12}+18\frac3{12}}\cdot 60 =\frac{102}{33\frac{12}{12}} \cdot 60$$
   $$=\frac{102\cdot 60}{34}=3\cdot 60=180.$$

Ответ

а) $$\frac{25}{39}$$;
б) $$0$$;
в) $$32$$;
г) $$180$$.