Упр.199 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 6 класс (Математика)

1) (-4/15 + 7/12) : (-38/45);
2) (11/16 — (-17/24)) : (-5 7/12);
3) (-11/18 + 29/45) : (35/54 — 19/27);
4) -4 1/7 + 2 1/4 · (-11 2/9 — (-5,4) : 9/35).

1) $$\left(-\frac{4}{15}+\frac{7}{12}\right):\left(-\frac{38}{45}\right)$$

$$ -\frac{4}{15}+\frac{7}{12}=-\frac{16}{60}+\frac{35}{60}=\frac{19}{60} $$
$$ \frac{19}{60}:\left(-\frac{38}{45}\right)=\frac{19}{60}\cdot\left(-\frac{45}{38}\right) $$
$$ =-\frac{19\cdot 45}{60\cdot 38}=-\frac{1\cdot 3}{4\cdot 2}=-\frac{3}{8} $$

2) $$\left(\frac{11}{16}-\left(-\frac{17}{24}\right)\right):\left(-5\frac{7}{12}\right)$$

$$ \frac{11}{16}-\left(-\frac{17}{24}\right)=\frac{33}{48}+\frac{34}{48}=\frac{67}{48} $$
$$ -5\frac{7}{12}=-\frac{67}{12} $$
$$ \frac{67}{48}:\left(-\frac{67}{12}\right)=\frac{67}{48}\cdot\left(-\frac{12}{67}\right)=-\frac{1}{4} $$

3) $$\left(-\frac{11}{18}+\frac{29}{45}\right):\left(\frac{35}{54}-\frac{19}{27}\right)$$

$$ -\frac{11}{18}+\frac{29}{45}=-\frac{55}{90}+\frac{58}{90}=\frac{3}{90} $$
$$ \frac{35}{54}-\frac{19}{27}=\frac{35}{54}-\frac{38}{54}=-\frac{3}{54} $$
$$ \frac{3}{90}:\left(-\frac{3}{54}\right)=\frac{3}{90}\cdot\left(-\frac{54}{3}\right)=-\frac{54}{90}=-\frac{3}{5} $$

4) $$-4\frac{1}{7}+2\frac{1}{4}\cdot\left(-11\frac{2}{9}-(-5{,}4):\frac{9}{35}\right)$$

$$ -5{,}4=-\frac{54}{10}=-\frac{27}{5} $$
$$ (-5{,}4):\frac{9}{35}=-\frac{27}{5}\cdot\frac{35}{9}=-21 $$
$$ -11\frac{2}{9}-(-21)=-11\frac{2}{9}+21=9\frac{7}{9} $$
$$ 2\frac{1}{4}\cdot 9\frac{7}{9}=\frac{9}{4}\cdot\frac{88}{9}=22 $$
$$ -4\frac{1}{7}+22=-\frac{29}{7}+\frac{154}{7}=\frac{125}{7}=17\frac{6}{7} $$

Ответ

1) $$-\frac{3}{8}$$; 2) $$-\frac{1}{4}$$; 3) $$-\frac{3}{5}$$; 4) $$17\frac{6}{7}$$.