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

1. Выполните действия.
   1) $$4{,}8:(-8)+(-3{,}6):(-0{,}9)$$;
   2) $$-2{,}5\cdot 6-5{,}4:(-0{,}6)$$;
   3) $$-16:1\frac{11}{13}+1\frac{1}{4}:\left(-\frac{15}{38}\right)$$;
   4) $$\left(-8-1\frac{3}{13}:\left(-1\frac{17}{39}\right)\right):\left(-5\frac{5}{14}\right)$$.

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

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

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

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

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

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

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

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

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

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

Ответ: 1) $$3{,}4$$; 2) $$-6$$; 3) $$-11\frac{5}{6}$$; 4) $$1\frac{1}{3}$$.