Упр.843 ГДЗ Муравин 6 класс (Математика)

Задача

1) (3 1/6-2 7/16) :1 2/5;
2) ((1 1/2)^2-3/4) :7/8;
3) (1 2/3+2 4/9) :(4 26/27-2 2/9);
4) (3 1/2 :4 2/3+4 2/3 :3 1/2)•4 4/5;
5) (1 4/9+2 5/6-2 3/4)•(5/11+10/20);
6) 2 3/4 :(1 1/2-2/5)+(3/4+5/6) :3 1/6.

Подробный ответ

1) $$\left(3\frac{1}{6}-2\frac{7}{16}\right):1\frac{2}{5}$$

$$3\frac{1}{6}= \frac{19}{6}=\frac{152}{48}, \quad 2\frac{7}{16}= \frac{39}{16}=\frac{117}{48}$$
$$\frac{152}{48}-\frac{117}{48}=\frac{35}{48}$$
$$1\frac{2}{5}=\frac{7}{5}$$
$$\frac{35}{48}:\frac{7}{5}=\frac{35}{48}\cdot\frac{5}{7}=\frac{25}{48}$$

2) $$\left(\left(1\frac{1}{2}\right)^2-\frac{3}{4}\right):\frac{7}{8}$$

$$1\frac{1}{2}=\frac{3}{2}$$
$$\left(\frac{3}{2}\right)^2-\frac{3}{4}=\frac{9}{4}-\frac{3}{4}=\frac{6}{4}=\frac{3}{2}$$
$$\frac{3}{2}:\frac{7}{8}=\frac{3}{2}\cdot\frac{8}{7}=\frac{12}{7}=1\frac{5}{7}$$

3) $$\left(1\frac{2}{3}+2\frac{4}{9}\right):\left(4\frac{26}{27}-2\frac{2}{9}\right)$$

$$1\frac{2}{3}=\frac{5}{3}=\frac{15}{9}, \quad 2\frac{4}{9}=\frac{22}{9}$$
$$\frac{15}{9}+\frac{22}{9}=\frac{37}{9}$$
$$4\frac{26}{27}=\frac{134}{27}, \quad 2\frac{2}{9}=\frac{20}{9}=\frac{60}{27}$$
$$\frac{134}{27}-\frac{60}{27}=\frac{74}{27}$$
$$\frac{37}{9}:\frac{74}{27}=\frac{37}{9}\cdot\frac{27}{74}=\frac{3}{2}=1\frac{1}{2}$$

4) $$\left(3\frac{1}{2}:4\frac{2}{3}+4\frac{2}{3}:3\frac{1}{2}\right)\cdot 4\frac{4}{5}$$

$$3\frac{1}{2}=\frac{7}{2}, \quad 4\frac{2}{3}=\frac{14}{3}, \quad 4\frac{4}{5}=\frac{24}{5}$$
$$\frac{7}{2}:\frac{14}{3}=\frac{7}{2}\cdot\frac{3}{14}=\frac{3}{4}$$
$$\frac{14}{3}:\frac{7}{2}=\frac{14}{3}\cdot\frac{2}{7}=\frac{4}{3}$$
$$\left(\frac{3}{4}+\frac{4}{3}\right)\cdot\frac{24}{5}=\frac{25}{12}\cdot\frac{24}{5}=10$$

5) $$\left(1\frac{4}{9}+2\frac{5}{6}-2\frac{3}{4}\right)\cdot\left(\frac{5}{11}+\frac{10}{20}\right)$$

$$1\frac{4}{9}=\frac{13}{9}=\frac{52}{36}, \quad 2\frac{5}{6}=\frac{17}{6}=\frac{102}{36}, \quad 2\frac{3}{4}=\frac{11}{4}=\frac{99}{36}$$
$$\frac{52}{36}+\frac{102}{36}-\frac{99}{36}=\frac{55}{36}$$
$$\frac{5}{11}+\frac{10}{20}=\frac{5}{11}+\frac{1}{2}=\frac{10}{22}+\frac{11}{22}=\frac{21}{22}$$
$$\frac{55}{36}\cdot\frac{21}{22}=\frac{5}{12}\cdot\frac{7}{2}=\frac{35}{24}=1\frac{11}{24}$$

6) $$2\frac{3}{4}:\left(1\frac{1}{2}-\frac{2}{5}\right)+\left(\frac{3}{4}+\frac{5}{6}\right):3\frac{1}{6}$$

$$2\frac{3}{4}=\frac{11}{4}, \quad 1\frac{1}{2}=\frac{3}{2}, \quad 3\frac{1}{6}=\frac{19}{6}$$
$$\frac{3}{2}-\frac{2}{5}=\frac{15}{10}-\frac{4}{10}=\frac{11}{10}$$
$$\frac{11}{4}:\frac{11}{10}=\frac{11}{4}\cdot\frac{10}{11}=\frac{5}{2}$$
$$\frac{3}{4}+\frac{5}{6}=\frac{9}{12}+\frac{10}{12}=\frac{19}{12}$$
$$\frac{19}{12}:\frac{19}{6}=\frac{19}{12}\cdot\frac{6}{19}=\frac{1}{2}$$
$$\frac{5}{2}+\frac{1}{2}=3$$