Упр.199 Вариант 2 Дидактические материалы ГДЗ Мерзляк Полонский 6 класс (Математика)

Найдите значение выражения: 1) $$\left(-\frac{5}{12}+\frac{11}{16}\right):\left(-\frac{13}{72}\right)$$; 2) $$\left(\frac{9}{14}-\left(-\frac{5}{21}\right)\right):\left(-2\frac{9}{14}\right)$$; 3) $$\left(\frac{7}{16}-\frac{31}{40}\right):\left(-\frac{17}{24}+\frac{27}{40}\right)$$; 4) $$-3\frac{3}{4}-\left(-8\frac{2}{9}-\left(-4{,}5\right):\frac{9}{14}\right)\cdot2\frac{1}{4}$$.

1) $$\left(-\frac{5}{12}+\frac{11}{16}\right):\left(-\frac{13}{72}\right)$$

$$-\frac{5}{12}+\frac{11}{16}=-\frac{20}{48}+\frac{33}{48}=\frac{13}{48}$$

$$\frac{13}{48}:\left(-\frac{13}{72}\right)=\frac{13}{48}\cdot\left(-\frac{72}{13}\right)=-\frac{72}{48}=-\frac{3}{2}=-1{,}5$$

2) $$\left(\frac{9}{14}-\left(-\frac{5}{21}\right)\right):\left(-2\frac{9}{14}\right)$$

$$\frac{9}{14}+\frac{5}{21}=\frac{27}{42}+\frac{10}{42}=\frac{37}{42}$$

$$-2\frac{9}{14}=-\frac{37}{14}$$

$$\frac{37}{42}:\left(-\frac{37}{14}\right)=\frac{37}{42}\cdot\left(-\frac{14}{37}\right)=-\frac{14}{42}=-\frac{1}{3}$$

3) $$\left(\frac{7}{16}-\frac{31}{40}\right):\left(-\frac{17}{24}+\frac{27}{40}\right)$$

$$\frac{7}{16}-\frac{31}{40}=\frac{35}{80}-\frac{62}{80}=-\frac{27}{80}$$

$$-\frac{17}{24}+\frac{27}{40}=-\frac{85}{120}+\frac{81}{120}=-\frac{4}{120}=-\frac{1}{30}$$

$$-\frac{27}{80}:\left(-\frac{1}{30}\right)=\frac{27}{80}\cdot 30=\frac{27\cdot 3}{8}=\frac{81}{8}=10\frac{1}{8}$$

4) $$-3\frac{3}{4}-\left(-8\frac{2}{9}-(-4{,}5):\frac{9}{14}\right)\cdot 2\frac{1}{4}$$

$$-4{,}5=-\frac{9}{2},\qquad 2\frac{1}{4}=\frac{9}{4},\qquad -3\frac{3}{4}=-\frac{15}{4},\qquad -8\frac{2}{9}=-\frac{74}{9}$$

$$(-4{,}5):\frac{9}{14}=-\frac{9}{2}\cdot\frac{14}{9}=-7$$

$$-\frac{74}{9}-(-7)=-\frac{74}{9}+7=-\frac{74}{9}+\frac{63}{9}=-\frac{11}{9}$$

$$-\frac{15}{4}-\left(-\frac{11}{9}\right)\cdot\frac{9}{4}=-\frac{15}{4}+\frac{11}{4}=-1$$

Ответ: 1) $$-1{,}5$$; 2) $$-\frac{1}{3}$$; 3) $$10\frac{1}{8}$$; 4) $$-1$$.