Упр.199 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 6 класс (Математика)

1) (-7/18 + 11/12) : (-19/48);
2) (7/16 — (-5/24)) : (-1 15/16);
3) (10/21 — 25/28) : (-11/14 + 24/35);
4) -2 2/3 + 2 1/3 · (-15 3/7 — (-4,8) : 4/15).

1) $$\left(-\frac{7}{18}+\frac{11}{12}\right):\left(-\frac{19}{48}\right)$$

$$-\frac{7}{18}+\frac{11}{12}=-\frac{14}{36}+\frac{33}{36}=\frac{19}{36}$$
$$\frac{19}{36}:\left(-\frac{19}{48}\right)=\frac{19}{36}\cdot\left(-\frac{48}{19}\right)=-\frac{48}{36}=-\frac{4}{3}=-1\frac{1}{3}$$

2) $$\left(\frac{7}{16}-\left(-\frac{5}{24}\right)\right):\left(-1\frac{15}{16}\right)$$

$$\frac{7}{16}+\frac{5}{24}=\frac{21}{48}+\frac{10}{48}=\frac{31}{48}$$
$$-1\frac{15}{16}=-\frac{31}{16}$$
$$\frac{31}{48}:\left(-\frac{31}{16}\right)=\frac{31}{48}\cdot\left(-\frac{16}{31}\right)=-\frac{16}{48}=-\frac{1}{3}$$

3) $$\left(\frac{10}{21}-\frac{25}{28}\right):\left(-\frac{11}{14}+\frac{24}{35}\right)$$

$$\frac{10}{21}-\frac{25}{28}=\frac{40}{84}-\frac{75}{84}=-\frac{35}{84}$$
$$-\frac{11}{14}+\frac{24}{35}=-\frac{55}{70}+\frac{48}{70}=-\frac{7}{70}=-\frac{1}{10}$$
$$-\frac{35}{84}:\left(-\frac{1}{10}\right)=\frac{35}{84}\cdot 10=\frac{350}{84}=\frac{25}{6}=4\frac{1}{6}$$

4) $$-2\frac{2}{3}+2\frac{1}{3}\cdot\left(-15\frac{3}{7}-(-4{,}8):\frac{4}{15}\right)$$

$$-2\frac{2}{3}=-\frac{8}{3}, \qquad 2\frac{1}{3}=\frac{7}{3}, \qquad -15\frac{3}{7}=-\frac{108}{7}, \qquad -4{,}8=-\frac{24}{5}$$
$$(-4{,}8):\frac{4}{15}=-\frac{24}{5}\cdot\frac{15}{4}=-18$$
$$-\frac{108}{7}-(-18)=-\frac{108}{7}+18=-\frac{108}{7}+\frac{126}{7}=\frac{18}{7}$$
$$-\frac{8}{3}+\frac{7}{3}\cdot\frac{18}{7}=-\frac{8}{3}+6=\frac{10}{3}=3\frac{1}{3}$$

Ответ

1) $$-1\frac{1}{3}$$; 2) $$-\frac{1}{3}$$; 3) $$4\frac{1}{6}$$; 4) $$3\frac{1}{3}$$.