Упр.184 Вариант 4 Дидактические материалы ГДЗ Мерзляк Полонский 6 класс (Математика)

Выполните действия:

1) $$4{,}8\cdot(-3{,}2)-11{,}4\cdot(-0{,}7);$$
2) $$(-6{,}23+6{,}17)\cdot(4{,}2-6);$$
3) $$\frac{4}{7}\cdot\left(-2\frac{5}{8}\right)-\left(-4\frac{3}{7}\right)\cdot\frac{11}{62};$$
4) $$\left(3\frac{5}{6}-4\frac{1}{2}\right)\cdot\left(3\frac{4}{5}-0{,}55\right).$$

1) $$4{,}8\cdot(-3{,}2)-11{,}4\cdot(-0{,}7)=-15{,}36+7{,}98=-7{,}38$$

2) $$(-6{,}23+6{,}17)\cdot(4{,}2-6)=-0{,}06\cdot(-1{,}8)=0{,}108$$

3) $$\frac{4}{7}\cdot\left(-2\frac{5}{8}\right)-\left(-4\frac{3}{7}\right)\cdot\frac{11}{62}$$

$$=-\frac{4}{7}\cdot\frac{21}{8}+\frac{31}{7}\cdot\frac{11}{62}=-\frac{4\cdot21}{7\cdot8}+\frac{31\cdot11}{7\cdot62}$$

$$=-\frac{1\cdot3}{1\cdot2}+\frac{1\cdot11}{7\cdot2}=-\frac{3}{2}+\frac{11}{14}=-\frac{21}{14}+\frac{11}{14}=-\frac{10}{14}=-\frac{5}{7}$$

4) $$\left(3\frac{5}{6}-4\frac{1}{2}\right)\cdot\left(3\frac{4}{5}-0{,}55\right)$$

$$=\left(3\frac{5}{6}-4\frac{3}{6}\right)\cdot\left(3\frac{4}{5}-\frac{55}{100}\right)$$

$$=\left(3\frac{5}{6}-3\frac{4}{6}\right)\cdot\left(3\frac{4}{5}-\frac{11}{20}\right)$$

$$=\frac{1}{6}\cdot\left(3\frac{16}{20}-\frac{11}{20}\right)=\frac{1}{6}\cdot\left(3\frac{5}{20}\right)=\frac{1}{6}\cdot3\frac{1}{4}$$

$$=\frac{1}{6}\cdot\frac{13}{4}=\frac{13}{24}$$

Ответ: 1) $$-7{,}38$$; 2) $$0{,}108$$; 3) $$-\frac{5}{7}$$; 4) $$\frac{13}{24}$$.