Упр.199 Вариант 4 Дидактические материалы ГДЗ Мерзляк Полонский 6 класс (Математика)

1. Найдите значение выражения:
   1) $$\left(-\frac{5}{9}+\frac{14}{15}\right):\left(-\frac{17}{30}\right)$$;
   2) $$\left(\frac{5}{18}-\left(-\frac{11}{27}\right)\right):\left(-2\frac{5}{16}\right)$$;
   3) $$\left(\frac{11}{18}-\frac{17}{24}\right):\left(-\frac{5}{18}+\frac{4}{15}\right)$$;
   4) $$-4\frac{5}{6}+3\frac{3}{23}\cdot\left(-11\frac{4}{9}-\left(-3{,}6\right):\frac{9}{35}\right)$$.

1)

$$\left(-\frac{5}{9}+\frac{14}{15}\right):\left(-\frac{17}{30}\right) = \left(-\frac{25}{45}+\frac{42}{45}\right)\cdot\left(-\frac{30}{17}\right) = \frac{17}{45}\cdot\left(-\frac{30}{17}\right) = -\frac{30}{45} = -\frac{2}{3}$$

2)

$$\left(\frac{5}{18}-\left(-\frac{11}{27}\right)\right):\left(-2\frac{5}{16}\right) = \left(\frac{15}{54}+\frac{22}{54}\right):\left(-\frac{37}{16}\right) = \frac{37}{54}\cdot\left(-\frac{16}{37}\right) = -\frac{16}{54} = -\frac{8}{27}$$

3)

$$\left(\frac{11}{18}-\frac{17}{24}\right):\left(-\frac{5}{18}+\frac{4}{15}\right) = \left(\frac{44}{72}-\frac{51}{72}\right):\left(-\frac{25}{90}+\frac{24}{90}\right) = -\frac{7}{72}:\left(-\frac{1}{90}\right) = -\frac{7}{72}\cdot(-90) = \frac{35}{4} = 8\frac{3}{4}$$

4)

$$-4\frac{5}{6}+3\frac{3}{23}\cdot\left(-11\frac{4}{9}-(-3{,}6):\frac{9}{35}\right)$$

$$-3{,}6=-\frac{36}{10}=-\frac{18}{5},\qquad \left(-3{,}6\right):\frac{9}{35}=-\frac{18}{5}\cdot\frac{35}{9}=-14$$

$$-11\frac{4}{9}-(-14)=-11\frac{4}{9}+14=2\frac{5}{9}$$

$$3\frac{3}{23}\cdot 2\frac{5}{9} = \frac{72}{23}\cdot\frac{23}{9} = 8$$

$$-4\frac{5}{6}+8=3\frac{1}{6}$$

Ответ: 1) $$-\frac{2}{3}$$; 2) $$-\frac{8}{27}$$; 3) $$8\frac{3}{4}$$; 4) $$3\frac{1}{6}$$.