Упр.1037 ГДЗ Мерзляк Полонский 6 класс (Математика)

Задача

1) -3,2- 0,4 + 2,6- (-0,5);
2) 5,2 * (-0,8) — (-1,5) * (-3,4);
3) (7,6-20) * (-3,14 + 5,24);
4) (-1*3/25) * 2*1/7 + (-2*1/9) * (-27/190);
5) (8+ 2*1/7 * (*3*1/9)) * (-27/44);
6) (-5*1/16 + 1*1/8) * (-5/6-3/14).

Подробный ответ

1) $$-3,2 \cdot 0,4 + 2,6 \cdot (-0,5) = -1,28 — 1,3 = -2,58.$$

2) $$5,2 \cdot (-0,8) — (-1,5) \cdot (-3,4) = -4,16 — 5,1 = -9,26.$$

3) $$\left(7,6 — 20\right)\cdot\left(-3,14 + 5,24\right) = -12,4 \cdot 2,1 = -26,04.$$

4) $$\left(-1\frac{3}{25}\right)\cdot 2\frac{1}{7} + \left(-2\frac{1}{9}\right)\cdot\left(-\frac{27}{190}\right)$$

$$= -\frac{28}{25}\cdot\frac{15}{7} + \frac{19}{9}\cdot\frac{27}{190}$$

$$= -\frac{4}{5}\cdot\frac{3}{1} + \frac{3}{10} = -\frac{12}{5} + \frac{3}{10} = -2\frac{2}{5} + \frac{3}{10} = -2\frac{4}{10} + \frac{3}{10} = -2\frac{1}{10} = -2,1.$$

5) $$\left(8 + 2\frac{1}{7}\cdot\left(-3\frac{1}{9}\right)\right)\cdot\left(-\frac{27}{44}\right)$$

$$= \left(8 + \frac{15}{7}\cdot\left(-\frac{28}{9}\right)\right)\cdot\left(-\frac{27}{44}\right)$$

$$= \left(8 — \frac{5}{1}\cdot\frac{4}{3}\right)\cdot\left(-\frac{27}{44}\right) = \left(8 — \frac{20}{3}\right)\cdot\left(-\frac{27}{44}\right)$$

$$= \left(8 — 6\frac{2}{3}\right)\cdot\left(-\frac{27}{44}\right) = 1\frac{1}{3}\cdot\left(-\frac{27}{44}\right)$$

$$= \frac{4}{3}\cdot\left(-\frac{27}{44}\right) = -\frac{9}{11}.$$

6) $$\left(-5\frac{1}{16} + 1\frac{1}{8}\right)\cdot\left(-\frac{5}{6} — \frac{3}{14}\right)$$

$$= \left(-4\frac{17}{16} + 1\frac{2}{16}\right)\cdot\left(-\frac{35}{42} — \frac{9}{42}\right)$$

$$= -3\frac{15}{16}\cdot\left(-\frac{44}{42}\right) = \frac{63}{16}\cdot\frac{22}{21} = \frac{3}{8}\cdot 11 = \frac{33}{8} = 4\frac{1}{8}.$$