Упр.789 ГДЗ Зубарева Мордкович 6 класс ФГОС (Математика)

а) (4 7/12-5 3/4) :(7/36-1 1/6);
б) 3/8 :5/12-3 1/2•2/5+1:3 1/3;
в) 1 1/4•(-2 2/3)+4/5•2 11/12-1 1/6 :21/22;
г) 3/4 :(1/14-5/7)+(5/6-7/12)•6 2/3;
д)(2 3/11-1 3/22)•(3 1/7+5 1/2);
е) 15/37•1 7/30-1 29/48•1 1/63.

а) $$\left(4\frac{7}{12}-5\frac{3}{4}\right):\left(\frac{7}{36}-1\frac{1}{6}\right)$$

$$4\frac{7}{12}-5\frac{3}{4}=4\frac{7}{12}-5\frac{9}{12}=-1\frac{2}{12}=-1\frac{1}{6}$$

$$\frac{7}{36}-1\frac{1}{6}=\frac{7}{36}-\frac{42}{36}=-\frac{35}{36}$$

$$-1\frac{1}{6}:\left(-\frac{35}{36}\right)=\frac{7}{6}\cdot\frac{36}{35}=\frac{6}{5}=1{,}2$$

б) $$\frac{3}{8}:\frac{5}{12}-3\frac{1}{2}\cdot\frac{2}{5}+1:3\frac{1}{3}$$

$$\frac{3}{8}:\frac{5}{12}=\frac{3}{8}\cdot\frac{12}{5}=\frac{9}{10}$$

$$3\frac{1}{2}\cdot\frac{2}{5}=\frac{7}{2}\cdot\frac{2}{5}=\frac{7}{5}$$

$$1:3\frac{1}{3}=1:\frac{10}{3}=\frac{3}{10}$$

$$\frac{9}{10}-\frac{7}{5}+\frac{3}{10}=\frac{12}{10}-\frac{7}{5}=\frac{6}{5}-\frac{7}{5}=-\frac{1}{5}=-0{,}2$$

в) $$1\frac{1}{4}\cdot\left(-2\frac{2}{3}\right)+\frac{4}{5}\cdot2\frac{11}{12}-1\frac{1}{6}:\frac{21}{22}$$

$$1\frac{1}{4}\cdot\left(-2\frac{2}{3}\right)=\frac{5}{4}\cdot\left(-\frac{8}{3}\right)=-\frac{10}{3}$$

$$\frac{4}{5}\cdot2\frac{11}{12}=\frac{4}{5}\cdot\frac{35}{12}=\frac{7}{3}$$

$$1\frac{1}{6}:\frac{21}{22}=\frac{7}{6}\cdot\frac{22}{21}=\frac{11}{9}$$

$$-\frac{10}{3}+\frac{7}{3}-\frac{11}{9}=-1-\frac{2}{9}=-1\frac{2}{9}=-2\frac{2}{9}$$

г) $$\frac{3}{4}:\left(\frac{1}{14}-\frac{5}{7}\right)+\left(\frac{5}{6}-\frac{7}{12}\right)\cdot6\frac{2}{3}$$

$$\frac{1}{14}-\frac{5}{7}=\frac{1}{14}-\frac{10}{14}=-\frac{9}{14}$$

$$\frac{3}{4}:\left(-\frac{9}{14}\right)=\frac{3}{4}\cdot\left(-\frac{14}{9}\right)=-\frac{7}{6}$$

$$\frac{5}{6}-\frac{7}{12}=\frac{10}{12}-\frac{7}{12}=\frac{1}{4}$$

$$\frac{1}{4}\cdot6\frac{2}{3}=\frac{1}{4}\cdot\frac{20}{3}=\frac{5}{3}$$

$$-\frac{7}{6}+\frac{5}{3}=-\frac{7}{6}+\frac{10}{6}=\frac{3}{6}=\frac{1}{2}=0{,}5$$

д) $$\left(2\frac{3}{11}-1\frac{3}{22}\right)\cdot\left(3\frac{1}{7}+5\frac{1}{2}\right)$$

$$2\frac{3}{11}-1\frac{3}{22}=\frac{25}{11}-\frac{25}{22}=\frac{25}{22}$$

$$3\frac{1}{7}+5\frac{1}{2}=\frac{22}{7}+\frac{11}{2}=\frac{44}{14}+\frac{77}{14}=\frac{121}{14}$$

$$\frac{25}{22}\cdot\frac{121}{14}=\frac{25}{2}\cdot\frac{11}{14}=\frac{275}{28}=9\frac{23}{28}$$

е) $$\frac{15}{37}\cdot1\frac{7}{30}-1\frac{29}{48}\cdot1\frac{1}{63}$$

$$\frac{15}{37}\cdot1\frac{7}{30}=\frac{15}{37}\cdot\frac{37}{30}=\frac{1}{2}$$

$$1\frac{29}{48}\cdot1\frac{1}{63}=\frac{77}{48}\cdot\frac{64}{63}=\frac{11}{9}\cdot\frac{4}{3}=\frac{44}{27}=1\frac{17}{27}$$

$$\frac{1}{2}-\frac{44}{27}=\frac{27}{54}-\frac{88}{54}=-\frac{61}{54}=-1\frac{7}{54}$$

Ответ

а) $$1{,}2$$; б) $$-\frac{1}{5}$$; в) $$-2\frac{2}{9}$$; г) $$\frac{1}{2}$$; д) $$9\frac{23}{28}$$; е) $$-1\frac{7}{54}$$.