Задание 2 Параграф 1 ГДЗ Рабочая тетрадь 1 Мерзляк Полонский 7 класс (Алгебра)

1. Вычислите значение числового выражения:
   
   1) $$\left(1\frac{1}{3}+2\frac{2}{9}\right)\cdot\frac{3}{16}-1\frac{2}{3}\cdot 3$$;
   
   2) $$1\frac{5}{7}:(-6)+\left(1\frac{16}{21}-3\frac{4}{9}\right):\left(-1\frac{11}{42}\right)$$;
   
   3) $$\left(-1\frac{1}{8}+\frac{27}{32}\right):(3{,}05-2{,}84)-\frac{0{,}3}{1{,}4}$$.

1) $$\left(1\frac{1}{3}+2\frac{2}{9}\right)\cdot \frac{3}{16}-1\frac{2}{3}\cdot 3$$

$$1\frac{1}{3}+2\frac{2}{9}=1\frac{3}{9}+2\frac{2}{9}=3\frac{5}{9}$$

$$3\frac{5}{9}\cdot \frac{3}{16}=\frac{32}{9}\cdot \frac{3}{16}=\frac{2}{3}$$

$$1\frac{2}{3}\cdot 3=\frac{5}{3}\cdot 3=5$$

$$\frac{2}{3}-5=-4\frac{1}{3}$$

2) $$1\frac{5}{7}:(-6)+\left(1\frac{16}{21}-3\frac{4}{9}\right):\left(-1\frac{11}{42}\right)$$

$$1\frac{5}{7}:(-6)=\frac{12}{7}:(-6)=\frac{12}{7}\cdot \left(-\frac{1}{6}\right)=-\frac{2}{7}$$

$$1\frac{16}{21}-3\frac{4}{9}=\frac{37}{21}-\frac{31}{9}=\frac{111}{63}-\frac{217}{63}=-\frac{106}{63}=-1\frac{43}{63}$$

$$-1\frac{43}{63}:\left(-1\frac{11}{42}\right)=-\frac{106}{63}:\left(-\frac{53}{42}\right)=\frac{106}{63}\cdot \frac{42}{53}=\frac{4}{3}$$

$$-\frac{2}{7}+\frac{4}{3}=\frac{-6+28}{21}=\frac{22}{21}=1\frac{1}{21}$$

3) $$\left(-1\frac{1}{8}+\frac{27}{32}\right):(3{,}05-2{,}84)-\frac{0{,}3}{1{,}4}$$

$$-1\frac{1}{8}+\frac{27}{32}=-\frac{9}{8}+\frac{27}{32}=-\frac{36}{32}+\frac{27}{32}=-\frac{9}{32}$$

$$3{,}05-2{,}84=0{,}21$$

$$-\frac{9}{32}:0{,}21=-\frac{9}{32}:\frac{21}{100}=-\frac{9}{32}\cdot \frac{100}{21}=-\frac{75}{56}$$

$$\frac{0{,}3}{1{,}4}=\frac{3}{10}:\frac{14}{10}=\frac{3}{14}$$

$$-\frac{75}{56}-\frac{3}{14}=-\frac{75}{56}-\frac{12}{56}=-\frac{87}{56}=-1\frac{31}{56}$$

Ответ

1) $$-4\frac{1}{3}$$; 2) $$1\frac{1}{21}$$; 3) $$-1\frac{31}{56}$$.