Упр.466 Рабочая тетрадь №3 ГДЗ Мерзляк Полонский 6 класс (Математика)

1. Выполните действия:
   
   1) $$-3{,}6\cdot0{,}3+2{,}8\cdot(-0{,}5);$$
   
   2) $$5{,}4\cdot(-0{,}7)-(-2{,}5)\cdot(-2{,}8);$$
   
   3) $$-6{,}6\cdot0{,}8-3{,}2\cdot(-1{,}6);$$
   
   4) $$-1\frac{3}{5}\cdot3\frac{1}{3}-\left(1-\frac{3}{8}\right)\cdot\left(\frac{1}{3}-1\right);$$
   
   5) $$\left(-6-2\frac{2}{7}\cdot\left(-1\frac{5}{44}\right)\right)\cdot\left(-2\frac{17}{19}\right).$$

1) $$-3{,}6 \cdot 0{,}3 + 2{,}8 \cdot (-0{,}5) = -1{,}08 + (-1{,}4) = -2{,}48.$$

2) $$5{,}4 \cdot (-0{,}7) — (-2{,}5) \cdot (-2{,}8) = -3{,}78 — 7 = -10{,}78.$$

3) $$-6{,}6 \cdot 0{,}8 — 3{,}2 \cdot (-1{,}6) = -5{,}28 — (-5{,}12) = -5{,}28 + 5{,}12 = -0{,}16.$$

4) $$-1 \frac{3}{5} \cdot 3 \frac{1}{3} — \left(1 — \frac{3}{8}\right)\cdot\left(\frac{1}{3} — 1\right).$$

$$-1 \frac{3}{5} = -\frac{8}{5}, \qquad 3 \frac{1}{3} = \frac{10}{3}, \qquad 1 — \frac{3}{8} = \frac{5}{8}, \qquad \frac{1}{3} — 1 = -\frac{2}{3}.$$

$$-\frac{8}{5}\cdot\frac{10}{3} = -\frac{16}{3} = -5 \frac{1}{3},$$

$$\frac{5}{8}\cdot\left(-\frac{2}{3}\right) = -\frac{10}{24} = -\frac{5}{12}.$$

Тогда

$$-5 \frac{1}{3} — \left(-\frac{5}{12}\right) = -5 \frac{1}{3} + \frac{5}{12} = -4 \frac{11}{12}.$$

5) $$\left(-6 — 2 \frac{2}{7}\cdot\left(-1 \frac{5}{44}\right)\right)\cdot\left(-2 \frac{17}{19}\right).$$

$$2 \frac{2}{7} = \frac{16}{7}, \qquad -1 \frac{5}{44} = -\frac{49}{44}, \qquad -2 \frac{17}{19} = -\frac{55}{19}.$$

$$\frac{16}{7}\cdot\left(-\frac{49}{44}\right) = -\frac{16\cdot49}{7\cdot44} = -\frac{4\cdot7}{11} = -\frac{28}{11} = -2 \frac{6}{11}.$$

$$-6 — \left(-2 \frac{6}{11}\right) = -6 + 2 \frac{6}{11} = -3 \frac{5}{11}.$$

$$-3 \frac{5}{11}\cdot\left(-2 \frac{17}{19}\right) = \frac{38}{11}\cdot\frac{55}{19} = \frac{2\cdot5}{1\cdot1} = 10.$$

Ответ: 1) $$-2{,}48$$; 2) $$-10{,}78$$; 3) $$-0{,}16$$; 4) $$-4 \frac{11}{12}$$; 5) $$10$$.