Упр.617 ГДЗ Никольский Потапов 8 класс (Алгебра)

Рассмотрим вариант решения задания из учебника Никольский, Потапов 8 класс, Просвещение: 617

1. а)

   $$\frac{1}{3}:\frac{\left(\frac{3}{5}+0{,}425-\frac{1}{200}\right):0{,}01}{30{,}75+\frac{1}{12}+3\frac{1}{6}}:\frac{2}{3}$$
   $$=\frac{1}{3}:\frac{\left(\frac{120}{200}+\frac{17}{40}-\frac{1}{200}\right):\frac{1}{100}}{30\frac{3}{4}+\frac{1}{12}+3\frac{1}{6}}:\frac{2}{3}$$
   $$=\frac{1}{3}:\frac{\left(\frac{119}{200}+\frac{85}{200}\right):\frac{1}{100}}{30\frac{9}{12}+\frac{1}{12}+3\frac{2}{12}}:\frac{2}{3}$$
   $$=\frac{1}{3}:\frac{\frac{204}{200}:\frac{1}{100}}{33\frac{12}{12}}:\frac{2}{3}$$
   $$=\frac{1}{3}:\frac{\frac{102}{34}\cdot 2}{33}:\frac{2}{3}=\frac{1}{3}:3:\frac{2}{3}=\frac{1}{6}.$$

2. б)

   $$\frac{\frac{3}{4}\cdot\left(4{,}4-3{,}75+8\frac{7}{15}+8\frac{7}{60}\right)}{\left(3\frac{1}{2}-2{,}75\right):0{,}2}$$
   $$=\frac{\frac{3}{4}\cdot\left(4\frac{4}{10}-3\frac{75}{100}+8\frac{7}{15}+8\frac{7}{60}\right)}{\left(3\frac{1}{2}-2\frac{75}{100}\right):0{,}2}$$
   $$=\frac{\frac{3}{4}\cdot\left(4\frac{24}{60}-3\frac{45}{60}+8\frac{28}{60}+8\frac{7}{60}\right)}{\left(3\frac{2}{4}-2\frac{3}{4}\right):0{,}2}$$
   $$=\frac{\frac{3}{4}\cdot 16\frac{74}{60}}{\frac{3}{4}: \frac{1}{5}}=\frac{\frac{3}{4}\cdot \frac{517}{30}}{\frac{3}{4}\cdot 5}=\frac{517}{30}\cdot\frac{1}{5}=\frac{517}{150}=3\frac{67}{150}.$$

3. в)

   $$\frac{\left(\frac{7}{2000}+0{,}0065\right):0{,}001}{\left(\frac{3}{3125}+0{,}00004\right)\cdot\frac{1}{0{,}0001}}$$
   $$=\frac{\left(\frac{7}{2000}+\frac{65}{10000}\right):\frac{1}{1000}}{\left(\frac{3}{3125}+\frac{4}{100000}\right)\cdot 10000}$$
   $$=\frac{\left(\frac{7}{2000}+\frac{13}{2000}\right)\cdot 1000}{\left(\frac{24}{25000}+\frac{1}{25000}\right)\cdot 10000}$$
   $$=\frac{\frac{20}{2000}\cdot 1000}{\frac{25}{25000}\cdot 10000}=\frac{\frac{10}{25}\cdot 1000}{\frac{25}{25000}\cdot 10000}=\frac{10}{10}=1.$$

4. г)

   $$\frac{3\frac{1}{3}-\left(6\frac{1}{7}-5\frac{3}{4}\right):\frac{5}{7}}{8+0{,}375:0{,}5625}+\frac{0{,}625:\frac{5}{6}}{}$$
   $$=\frac{3\frac{1}{3}-\left(6\frac{4}{28}-5\frac{21}{28}\right)\cdot\frac{7}{5}}{8+\frac{375}{1000}:\frac{5625}{10000}}+\frac{\frac{625}{1000}:\frac{5}{6}}{}$$
   $$=\frac{3\frac{1}{3}-\frac{11}{28}\cdot\frac{7}{5}}{8+\frac{3}{8}:\frac{9}{16}}+\frac{\frac{5}{8}\cdot\frac{6}{5}}{}$$
   $$=\frac{3\frac{1}{3}-\frac{11}{20}}{8+\frac{2}{3}}+\frac{3}{4} =\frac{\frac{10}{3}-\frac{11}{20}}{\frac{26}{3}}+\frac{3}{4}$$
   $$=\frac{\frac{200}{60}-\frac{33}{60}}{\frac{26}{3}}+\frac{3}{4} =\frac{\frac{167}{60}}{\frac{26}{3}}+\frac{3}{4}$$
   $$=\frac{167}{60}\cdot\frac{3}{26}+\frac{3}{4} =\frac{167}{520}+\frac{390}{520} =\frac{557}{520}=1\frac{37}{520}.$$

Ответ

а) $$\frac{1}{6}$$; б) $$3\frac{67}{150}$$; в) $$1$$; г) $$1\frac{37}{520}$$.