Упр.302 Часть 3 ГДЗ Дорофеев Петерсон 6 класс (Математика)

Задача

а) 3/14-5/7;
б)-1 5/6-7/15;
в)-2 1/7•(-1 3/25);
г) 5 5/6 :(-2 1/3);
д)-5,4•(-1 2/9) :3,75•(-4 1/6);
е)-3 3/5 :(-1 5/12)•(-6,8)•9 3/8 :(-1 2/7).

Подробный ответ

а) $$\frac{3}{14}-\frac{5}{7}=\frac{3}{14}-\frac{10}{14}=-\frac{7}{14}=-\frac{1}{2}=-0{,}5.$$

б) $$-1\frac{5}{6}-\frac{7}{15}=-\frac{11}{6}-\frac{7}{15}=-\frac{55}{30}-\frac{14}{30}=-\frac{69}{30}=-\frac{23}{10}=-2\frac{3}{10}=-2{,}3.$$

в) $$-2\frac{1}{7}\cdot\left(-1\frac{3}{25}\right)=-\frac{15}{7}\cdot\left(-\frac{28}{25}\right)=\frac{15\cdot 28}{7\cdot 25}=\frac{3\cdot 4}{1\cdot 5}=\frac{12}{5}=2{,}4.$$

г) $$5\frac{5}{6}:\left(-2\frac{1}{3}\right)=\frac{35}{6}:\left(-\frac{7}{3}\right)=\frac{35}{6}\cdot\left(-\frac{3}{7}\right)=-\frac{35}{14}=-\frac{5}{2}=-2{,}5.$$

д) $$-5{,}4\cdot\left(-1\frac{2}{9}\right):3{,}75\cdot\left(-4\frac{1}{6}\right)$$

$$=-\frac{54}{10}\cdot\frac{11}{9}:\frac{375}{100}\cdot\left(-\frac{25}{6}\right)$$

$$=-\frac{27}{5}\cdot\frac{11}{9}:\frac{15}{4}\cdot\left(-\frac{25}{6}\right)$$

$$=-\frac{27\cdot 11\cdot 4\cdot 25}{5\cdot 9\cdot 15\cdot 6}=-\frac{11\cdot 2}{3}=-\frac{22}{3}=-7\frac{1}{3}.$$

е) $$-3\frac{3}{5}:\left(-1\frac{5}{12}\right)\cdot(-6{,}8)\cdot 9\frac{3}{8}:\left(-1\frac{2}{7}\right)$$

$$=-\frac{18}{5}:\left(-\frac{17}{12}\right)\cdot\left(-\frac{68}{10}\right)\cdot\frac{75}{8}:\left(-\frac{9}{7}\right)$$

$$=\frac{18}{5}\cdot\frac{12}{17}\cdot\frac{34}{5}\cdot\frac{75}{8}\cdot\frac{7}{9}$$

$$=\frac{2\cdot 12\cdot 2\cdot 3\cdot 7}{1\cdot 1\cdot 1\cdot 8\cdot 1}=126.$$