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

1) (-5/12 + 11/16) : (-13/72);
2) (9/14 — (-5/21)) : (-2 9/14);
3) (7/16 — 31/40) : (-17/24 + 27/40);
4) -3 3/4 — (-8 2/9 — (-4,5) : 9/14) · 2 1/4.

1)

$$ \left(-\frac{5}{12}+\frac{11}{16}\right):\left(-\frac{13}{72}\right) = \left(-\frac{20}{48}+\frac{33}{48}\right):\left(-\frac{13}{72}\right) = \frac{13}{48}:\left(-\frac{13}{72}\right) $$
$$ =\frac{13}{48}\cdot\left(-\frac{72}{13}\right) =-\frac{72}{48} =-\frac{3}{2} =-1{,}5 $$

2)

$$ \left(\frac{9}{14}-\left(-\frac{5}{21}\right)\right):\left(-2\frac{9}{14}\right) = \left(\frac{27}{42}+\frac{10}{42}\right):\left(-\frac{37}{14}\right) = \frac{37}{42}:\left(-\frac{37}{14}\right) $$
$$ =\frac{37}{42}\cdot\left(-\frac{14}{37}\right) =-\frac{14}{42} =-\frac{1}{3} $$

3)

$$ \left(\frac{7}{16}-\frac{31}{40}\right):\left(-\frac{17}{24}+\frac{27}{40}\right) = \left(\frac{35}{80}-\frac{62}{80}\right):\left(-\frac{85}{120}+\frac{81}{120}\right) $$
$$ = -\frac{27}{80}:\left(-\frac{4}{120}\right) = -\frac{27}{80}:\left(-\frac{1}{30}\right) = \frac{27}{80}\cdot 30 = \frac{81}{8} = 10\frac{1}{8} $$

4)

$$ -3\frac{3}{4}-\left(-8\frac{2}{9}-(-4{,}5):\frac{9}{14}\right)\cdot 2\frac{1}{4} $$
$$ =-3\frac{3}{4}-\left(-8\frac{2}{9}+\frac{45}{10}\cdot\frac{14}{9}\right)\cdot\frac{9}{4} $$
$$ =-3\frac{3}{4}-\left(-8\frac{2}{9}+7\right)\cdot\frac{9}{4} =-3\frac{3}{4}-\left(-1\frac{2}{9}\right)\cdot\frac{9}{4} $$
$$ =-3\frac{3}{4}+\frac{11}{9}\cdot\frac{9}{4} =-3\frac{3}{4}+\frac{11}{4} =-3\frac{3}{4}+2\frac{3}{4} =-1 $$

Ответ

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