Упр.43 Повторение ГДЗ Мерзляк 11 класс Базовый уровень (Алгебра)

Задача

Вычислите значение выражения:

$$\left(\frac{13}{18}-\frac{5}{9}\right)\cdot\frac{3}{20}$$
$$\frac{13}{18}-\frac{5}{9}\cdot\frac{3}{20}$$
$$1\frac{3}{25}\cdot2\frac{1}{7}-1\frac{8}{9}\cdot\frac{27}{170}$$
$$\left(9-2\frac{1}{7}\cdot3\frac{1}{9}\right)\cdot\frac{27}{35}$$
$$\left(5\frac{1}{16}-1\frac{1}{8}\right)\left(\frac{5}{6}-\frac{1}{14}\right)$$
$$2\frac{4}{9}:\left(\frac{5}{12}-\frac{1}{9}\right)$$
$$(-5{,}16+5{,}02)\cdot(2{,}5-4)$$
$$\frac{5}{32}:\frac{5}{12}-3\frac{1}{4}:1\frac{2}{11}$$
$$\left(7-1\frac{5}{9}:\frac{7}{24}\right):\left(-\frac{25}{36}\right)$$
$$\left(28{,}9:\left(-\frac{17}{20}\right)-2{,}08:\left(-\frac{1}{25}\right)\right):\left(-1\frac{2}{7}\right)$$

Подробный ответ

$$\left(\frac{13}{18}-\frac{5}{9}\right)\cdot\frac{3}{20}=\left(\frac{13}{18}-\frac{10}{18}\right)\cdot\frac{3}{20}=\frac{3}{18}\cdot\frac{3}{20}=\frac{1}{6}\cdot\frac{3}{20}=\frac{1}{40}.$$
$$\frac{13}{18}-\frac{5}{9}\cdot\frac{3}{20}=\frac{13}{18}-\frac{1}{12}=\frac{26}{36}-\frac{3}{36}=\frac{23}{36}.$$
$$1\frac{3}{25}\cdot2\frac{1}{7}-1\frac{8}{9}\cdot\frac{27}{170}=\frac{28}{25}\cdot\frac{15}{7}-\frac{17}{9}\cdot\frac{27}{170}=\frac{4\cdot3}{5}-\frac{3\cdot12}{5\cdot10}=2{,}4-0{,}3=2{,}1.$$
$$\left(9-2\frac{1}{7}\cdot3\frac{1}{9}\right)\cdot\frac{27}{35}=\left(9-\frac{15}{7}\cdot\frac{28}{9}\right)\cdot\frac{27}{35}=\left(9-\frac{20}{3}\right)\cdot\frac{27}{35}=\frac{7}{3}\cdot\frac{27}{35}=1{,}8.$$
$$\left(5\frac{1}{16}-1\frac{1}{8}\right)\left(\frac{5}{6}-\frac{1}{14}\right)=\left(\frac{81}{16}-\frac{9}{8}\right)\left(\frac{35}{42}-\frac{3}{42}\right)=\frac{63}{16}\cdot\frac{32}{42}=3.$$
$$2\frac{4}{9}:\left(\frac{5}{12}-\frac{1}{9}\right)=\frac{22}{9}:\left(\frac{15-4}{36}\right)=\frac{22}{9}:\frac{11}{36}=2\cdot4=8.$$
$$(-5{,}16+5{,}02)\cdot(2{,}5-4)=-0{,}14\cdot(-1{,}5)=0{,}21.$$
$$\frac{5}{32}:\frac{5}{12}-3\frac{1}{4}:1\frac{2}{11}=\frac{5}{32}\cdot\frac{12}{5}-\frac{13}{4}:\frac{13}{11}=\frac{3}{8}-\frac{11}{4}=\frac{3-22}{8}=-\frac{19}{8}=-2\frac{3}{8}.$$
$$\left(7-1\frac{5}{9}:\frac{7}{24}\right):\left(-\frac{25}{36}\right)=\left(7-\frac{14}{9}\cdot\frac{24}{7}\right):\left(-\frac{25}{36}\right)=\left(7-\frac{48}{9}\right):\left(-\frac{25}{36}\right)=\frac{5}{3}\cdot\left(-\frac{36}{25}\right)=-2{,}4.$$
$$\left(28{,}9:\left(-\frac{17}{20}\right)-2{,}08:\left(-\frac{1}{25}\right)\right):\left(-1\frac{2}{7}\right)=\left(\frac{28{,}9}{-0{,}85}-\frac{2{,}08}{-0{,}04}\right):\left(-\frac{9}{7}\right)=(-34+52)\cdot\left(-\frac{7}{9}\right)=18\cdot\left(-\frac{7}{9}\right)=-14.$$

Ответ

1) $$\frac{1}{40}$$; 2) $$\frac{23}{36}$$; 3) $$2{,}1$$; 4) $$1{,}8$$; 5) $$3$$; 6) $$8$$; 7) $$0{,}21$$; 8) $$-\frac{19}{8}$$; 9) $$-2{,}4$$; 10) $$-14$$.

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