Упр.290 ГДЗ Мерзляк Полонский 6 класс (Математика)

1) (x+ 4/21)? 4/15= 16/35 ;
2) (x? 8/19)? 4/57= 2/3 ;
3) (x? 8/9)+ 3/8= 19/36 ;
4) 3*1/6?(x+1*1/12)= 1/4 ;
5) 6*5/27?(x?1*2/9)=3*20/81 ;
6) 3*5/36?(1*4/9?x)=1*17/18.

1) $$\left(x+\frac{4}{21}\right)-\frac{4}{15}=\frac{16}{35}$$

$$x+\frac{4}{21}=\frac{16}{35}+\frac{4}{15}$$

$$x=\frac{16}{35}+\frac{4}{15}-\frac{4}{21}$$

$$x=\frac{48}{105}+\frac{28}{105}-\frac{20}{105}=\frac{56}{105}=\frac{8}{15}$$

2) $$\left(x-\frac{8}{19}\right)-\frac{4}{57}=\frac{2}{3}$$

$$x-\frac{8}{19}=\frac{2}{3}+\frac{4}{57}$$

$$x=\frac{2}{3}+\frac{4}{57}+\frac{8}{19}$$

$$x=\frac{38}{57}+\frac{4}{57}+\frac{24}{57}=\frac{66}{57}=\frac{22}{19}=1\frac{3}{19}$$

3) $$\left(x-\frac{8}{9}\right)+\frac{3}{8}=\frac{19}{36}$$

$$x-\frac{8}{9}=\frac{19}{36}-\frac{3}{8}$$

$$x=\frac{19}{36}-\frac{3}{8}+\frac{8}{9}$$

$$x=\frac{38}{72}-\frac{27}{72}+\frac{64}{72}=\frac{75}{72}=\frac{25}{24}=1\frac{1}{24}$$

4) $$3\frac{1}{6}-\left(x+1\frac{1}{12}\right)=\frac{1}{4}$$

$$x+1\frac{1}{12}=3\frac{1}{6}-\frac{1}{4}$$

$$x=3\frac{1}{6}-\frac{1}{4}-1\frac{1}{12}$$

$$x=3\frac{2}{12}-\frac{3}{12}-1\frac{1}{12}=2\frac{14}{12}-\frac{3}{12}-1\frac{1}{12}=1\frac{5}{6}$$

5) $$6\frac{5}{27}-\left(x-1\frac{2}{9}\right)=3\frac{20}{81}$$

$$x-1\frac{2}{9}=6\frac{5}{27}-3\frac{20}{81}$$

$$x=6\frac{5}{27}-3\frac{20}{81}+1\frac{2}{9}$$

$$x=6\frac{15}{81}-3\frac{20}{81}+1\frac{18}{81}=3\frac{94}{81}=4\frac{13}{81}$$

6) $$3\frac{5}{36}-\left(1\frac{4}{9}-x\right)=1\frac{17}{18}$$

$$1\frac{4}{9}-x=3\frac{5}{36}-1\frac{17}{18}$$

$$1\frac{4}{9}-x=2\frac{41}{36}-1\frac{34}{36}=1\frac{7}{36}$$

$$x=1\frac{4}{9}-1\frac{7}{36}$$

$$x=1\frac{16}{36}-1\frac{7}{36}=\frac{9}{36}=\frac{1}{4}$$

Ответ

1) $$x=\frac{8}{15}$$; 2) $$x=1\frac{3}{19}$$; 3) $$x=1\frac{1}{24}$$; 4) $$x=1\frac{5}{6}$$; 5) $$x=4\frac{13}{81}$$; 6) $$x=\frac{1}{4}$$.