Упр.503 Рабочая тетрадь №3 ГДЗ Мерзляк Полонский 6 класс (Математика)

Задача

1) 4,8 :(-8) + (-3,6) : (-0,9);
2) -2,5 · 6 — 5,4 : (-0,6);
3) -16 : 1 11/13 + 1 1/4 : (-15/38);
4) (-8 -1 3/13 : (-1 17/39)) : (-5 5/14).

Подробный ответ

1) $$4,8 : (-8) + (-3,6) : (-0,9)$$

$$4,8 : (-8) = -0,6$$

$$(-3,6) : (-0,9) = 4$$

$$-0,6 + 4 = 3,4$$

2) $$-2,5 \cdot 6 — 5,4 : (-0,6)$$

$$-2,5 \cdot 6 = -15$$

$$5,4 : (-0,6) = -9$$

$$-15 — (-9) = -15 + 9 = -6$$

3) $$-16 : 1\frac{11}{13} + 1\frac{1}{4} : \left(-\frac{15}{38}\right)$$

$$1\frac{11}{13} = \frac{24}{13}, \qquad 1\frac{1}{4} = \frac{5}{4}$$

$$-16 : \frac{24}{13} = -16 \cdot \frac{13}{24} = -\frac{26}{3} = -8\frac{2}{3}$$

$$\frac{5}{4} : \left(-\frac{15}{38}\right) = \frac{5}{4} \cdot \left(-\frac{38}{15}\right) = -\frac{19}{6} = -3\frac{1}{6}$$

$$-8\frac{2}{3} + \left(-3\frac{1}{6}\right) = -8\frac{4}{6} — 3\frac{1}{6} = -11\frac{5}{6}$$

4) $$\left(-8 — 1\frac{3}{13} : \left(-1\frac{17}{39}\right)\right) : \left(-5\frac{5}{14}\right)$$

$$1\frac{3}{13} = \frac{16}{13}, \qquad -1\frac{17}{39} = -\frac{56}{39}, \qquad -5\frac{5}{14} = -\frac{75}{14}$$

$$1\frac{3}{13} : \left(-1\frac{17}{39}\right) = \frac{16}{13} : \left(-\frac{56}{39}\right) = \frac{16}{13} \cdot \left(-\frac{39}{56}\right) = -\frac{6}{7}$$

$$-8 — \left(-\frac{6}{7}\right) = -8 + \frac{6}{7} = -7\frac{1}{7}$$

$$-7\frac{1}{7} : \left(-5\frac{5}{14}\right) = -\frac{50}{7} : \left(-\frac{75}{14}\right) = \frac{50}{7} \cdot \frac{14}{75} = \frac{4}{3} = 1\frac{1}{3}$$