Упр.464 ГДЗ Мерзляк Полонский 6 класс (Математика)

Задача

1) 2*2/11x? 5/16=1*3/4;
2) 4*2/9x+3*5/14=6*11/21;
3) 11/18? 14/27x= 5/12;
4) 1/3x+ 1/4x+ 1/5x=1*19/75;
5) 4*1/2:x+1 3/4=3 19/28 ;
6) 3*2/3:(x?2*4/15)=3*5/13.

Подробный ответ

1) $$2\frac{2}{11}x-\frac{5}{16}=1\frac{3}{4}$$

$$2\frac{2}{11}x=1\frac{3}{4}+\frac{5}{16}$$
$$\frac{24}{11}x=\frac{12}{16}+\frac{5}{16}=\frac{17}{16}$$
$$x=\frac{17}{16}:\frac{24}{11}=\frac{17}{16}\cdot\frac{11}{24}=\frac{121}{128}$$

2) $$4\frac{2}{9}x+3\frac{5}{14}=6\frac{11}{21}$$

$$4\frac{2}{9}x=6\frac{11}{21}-3\frac{5}{14}$$
$$\frac{38}{9}x=6\frac{22}{42}-3\frac{15}{42}=3\frac{7}{42}=3\frac{1}{6}=\frac{19}{6}$$
$$x=\frac{19}{6}:\frac{38}{9}=\frac{19}{6}\cdot\frac{9}{38}=\frac{3}{4}$$

3) $$\frac{11}{18}-\frac{14}{27}x=\frac{5}{12}$$

$$\frac{14}{27}x=\frac{11}{18}-\frac{5}{12}$$
$$\frac{14}{27}x=\frac{22}{36}-\frac{15}{36}=\frac{7}{36}$$
$$x=\frac{7}{36}:\frac{14}{27}=\frac{7}{36}\cdot\frac{27}{14}=\frac{3}{8}$$

4) $$\frac{1}{3}x+\frac{1}{4}x+\frac{1}{5}x=1\frac{19}{75}$$

$$\left(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}\right)x=1\frac{19}{75}$$
$$\frac{20}{60}x+\frac{15}{60}x+\frac{12}{60}x=\frac{94}{75}$$
$$\frac{47}{60}x=\frac{94}{75}$$
$$x=\frac{94}{75}:\frac{47}{60}=\frac{94}{75}\cdot\frac{60}{47}=\frac{8}{5}=1\frac{3}{5}$$

5) $$4\frac{1}{2}:x+1\frac{3}{4}=3\frac{19}{28}$$

$$4\frac{1}{2}:x=3\frac{19}{28}-1\frac{3}{4}$$
$$\frac{9}{2}:x=3\frac{19}{28}-1\frac{21}{28}=2\frac{26}{28}=2\frac{13}{14}=\frac{41}{14}$$
$$\frac{9}{2}:x=\frac{41}{14}$$
$$x=\frac{9}{2}:\frac{41}{14}=\frac{9}{2}\cdot\frac{14}{41}=\frac{63}{41}$$

6) $$3\frac{2}{3}:(x-2\frac{4}{15})=3\frac{5}{13}$$

$$x-2\frac{4}{15}=3\frac{2}{3}:3\frac{5}{13}$$
$$x-2\frac{4}{15}=\frac{11}{3}:\frac{44}{13}=\frac{11}{3}\cdot\frac{13}{44}=\frac{13}{12}$$
$$x=\frac{13}{12}+2\frac{4}{15}$$
$$x=\frac{65}{60}+\frac{144}{60}=\frac{209}{60}=3\frac{29}{60}$$