Упр.523 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1. $$\left(3\frac{4}{25}+20{,}24\right)\cdot 2{,}15+\left(5{,}1625-2\frac{3}{16}\right)\cdot \frac{2}{5}$$

   $$3\frac{4}{25}=\frac{79}{25},\quad 20{,}24=\frac{506}{25},\quad 2{,}15=\frac{43}{20}$$

   $$5{,}1625=\frac{413}{80},\quad 2\frac{3}{16}=\frac{35}{16}$$

   $$\left(\frac{79}{25}+\frac{506}{25}\right)\cdot \frac{43}{20} +\left(\frac{413}{80}-\frac{35}{16}\right)\cdot \frac{2}{5}$$

   $$\frac{585}{25}\cdot \frac{43}{20}+\frac{413-175}{80}\cdot \frac{2}{5} =\frac{117}{5}\cdot \frac{43}{20}+\frac{238}{80}\cdot \frac{2}{5}$$

   $$\frac{5031}{100}+\frac{119}{40}\cdot \frac{2}{5} =\frac{5031}{100}+\frac{119}{100} =\frac{5150}{100}=51{,}5$$

2. $$0{,}364:\frac{7}{25}+\frac{5}{16}:0{,}125+2{,}5\cdot 0{,}8$$

   $$0{,}364=\frac{364}{1000},\quad 0{,}125=\frac{125}{1000},\quad 2{,}5=\frac{25}{10},\quad 0{,}8=\frac{8}{10}$$

   $$\frac{364}{1000}:\frac{7}{25}+\frac{5}{16}:\frac{125}{1000}+\frac{25}{10}\cdot \frac{8}{10}$$

   $$\frac{364}{1000}\cdot \frac{25}{7}+\frac{5}{16}\cdot \frac{1000}{125}+\frac{25}{10}\cdot \frac{8}{10} =\frac{91}{250}+\frac{5}{2}\cdot \frac{8}{5}+\frac{5}{2}\cdot \frac{4}{5}$$

   $$\frac{91}{250}+\frac{5}{2}\cdot \frac{8}{5}+\frac{5}{2}\cdot \frac{4}{5} =0{,}364+2{,}5+2=5{,}8$$

3. $$\frac{\left(3{,}25-\frac{3}{4}\right)\cdot 6{,}25}{(2-0{,}75):\frac{4}{5}} +\frac{(5{,}25-3\frac{3}{4}):5}{(-2-0{,}8)\cdot 1\frac{3}{4}}$$

   $$3{,}25=\frac{13}{4},\quad 6{,}25=\frac{25}{4},\quad 0{,}75=\frac{3}{4},\quad 5{,}25=\frac{21}{4}$$

   $$3\frac{3}{4}=\frac{15}{4},\quad 0{,}8=\frac{4}{5},\quad 1\frac{3}{4}=\frac{7}{4}$$

   $$\frac{\left(\frac{13}{4}-\frac{3}{4}\right)\cdot \frac{25}{4}}{\left(2-\frac{3}{4}\right):\frac{4}{5}} +\frac{\left(\frac{21}{4}-\frac{15}{4}\right):5}{\left(-2-\frac{4}{5}\right)\cdot \frac{7}{4}}$$

   $$\frac{\frac{10}{4}\cdot \frac{25}{4}}{\frac{5}{4}:\frac{4}{5}} +\frac{\frac{6}{4}:5}{-\frac{14}{5}\cdot \frac{7}{4}} = \frac{\frac{10}{4}\cdot \frac{25}{4}}{\frac{25}{16}} +\frac{\frac{6}{4}\cdot \frac{1}{5}}{-\frac{49}{10}}$$

   $$\frac{10}{4}\cdot \frac{25}{4}\cdot \frac{16}{25} -\frac{6}{4}\cdot \frac{1}{5}\cdot \frac{10}{49} =10-\frac{3}{49} =\frac{490-3}{49} =\frac{487}{49} =9\frac{46}{49}$$

4. $$\frac{\left(2\frac{3}{20}+1\frac{5}{16}\right):27{,}7}{\left(1{,}75\cdot \frac{2}{3}-1{,}75\cdot 1\frac{1}{8}\right):\frac{7}{12}}$$

   $$2\frac{3}{20}=\frac{43}{20},\quad 1\frac{5}{16}=\frac{21}{16},\quad 27{,}7=\frac{277}{10}$$

   $$1{,}75=\frac{7}{4},\quad 1\frac{1}{8}=\frac{9}{8}$$

   $$\frac{\left(\frac{43}{20}+\frac{21}{16}\right):\frac{277}{10}}{\left(\frac{7}{4}\cdot \frac{2}{3}-\frac{7}{4}\cdot \frac{9}{8}\right):\frac{7}{12}}$$

   $$\frac{\frac{172+105}{80}:\frac{277}{10}}{\left(\frac{7}{4}\right)\left(\frac{2}{3}-\frac{9}{8}\right):\frac{7}{12}} = \frac{\frac{277}{80}\cdot \frac{10}{277}}{\frac{7}{4}\cdot \left(-\frac{11}{24}\right)\cdot \frac{12}{7}}$$

   $$\frac{\frac{1}{8}}{-\frac{11}{8}}=-\frac{1}{11}$$

Ответ

1) $$51{,}5$$; 2) $$5{,}8$$; 3) $$9\frac{46}{49}$$; 4) $$-\frac{1}{11}$$.