Упр.410 Часть 2 ГДЗ Дорофеев Петерсон 6 класс (Математика)

1) (2/3 a-0,7) :1,5+0,5=29/30;
2) 4,2-0,2:(1/6+3b)=3 3/5;
3) 2c+0,2c-0,8c+3,4c=6,4;
4) 2/3 d-1/2 d+d+2 1/6=4,5;
5) (5 1/3)/0,2x=8/0,75;
6) 0,2:3/16=2 2/3 :(0,4y-1,5);
7) 6m-2,6=2,8m+1/15;
8) 4(n+5/12)=1 1/6 (6n-1 1/7).

1) $$\left(\frac{2}{3}a-0,7\right):1,5+0,5=\frac{29}{30}$$

$$\left(\frac{2}{3}a-0,7\right):1,5=\frac{29}{30}-0,5=\frac{29}{30}-\frac{15}{30}=\frac{14}{30}=\frac{7}{15}$$

$$\frac{2}{3}a-0,7=\frac{7}{15}\cdot 1,5=\frac{7}{15}\cdot\frac{3}{2}=\frac{7}{10}$$

$$\frac{2}{3}a=\frac{7}{10}+0,7=\frac{7}{10}+\frac{7}{10}=\frac{14}{10}=\frac{7}{5}$$

$$a=\frac{7}{5}:\frac{2}{3}=\frac{7}{5}\cdot\frac{3}{2}=\frac{21}{10}=2,1$$

2) $$4,2-0,2:\left(\frac{1}{6}+3b\right)=3\frac{3}{5}$$

$$0,2:\left(\frac{1}{6}+3b\right)=4,2-3\frac{3}{5}=4,2-3,6=0,6$$

$$\frac{1}{6}+3b=0,2:0,6=\frac{2}{10}:\frac{6}{10}=\frac{1}{3}$$

$$3b=\frac{1}{3}-\frac{1}{6}=\frac{1}{6}$$

$$b=\frac{1}{6}:3=\frac{1}{18}$$

3) $$2c+0,2c-0,8c+3,4c=6,4$$

$$4,8c=6,4$$

$$c=\frac{6,4}{4,8}=\frac{64}{48}=\frac{4}{3}=1\frac{1}{3}$$

4) $$\frac{2}{3}d-\frac{1}{2}d+d+2\frac{1}{6}=4,5$$

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

$$\left(\frac{4}{6}-\frac{3}{6}+\frac{6}{6}\right)d=\frac{9}{2}-\frac{13}{6}$$

$$\frac{7}{6}d=\frac{27}{6}-\frac{13}{6}=\frac{14}{6}=\frac{7}{3}$$

$$d=\frac{7}{3}:\frac{7}{6}=\frac{7}{3}\cdot\frac{6}{7}=2$$

5) $$\frac{5\frac{1}{3}}{0,2x}=\frac{8}{0,75}$$

$$0,2x\cdot 8=5\frac{1}{3}\cdot 0,75$$

$$1,6x=\frac{16}{3}\cdot\frac{3}{4}=4$$

$$x=\frac{4}{1,6}=2,5$$

6) $$0,2:\frac{3}{16}=2\frac{2}{3}:(0,4y-1,5)$$

$$0,2\cdot(0,4y-1,5)=\frac{3}{16}\cdot 2\frac{2}{3}$$

$$0,4y-1,5=\frac{3}{16}:\,0,2\cdot 2\frac{2}{3}$$

$$0,4y-1,5=\frac{1}{2}:\frac{1}{5}=\frac{1}{2}\cdot 5=2,5$$

$$0,4y=2,5+1,5=4$$

$$y=\frac{4}{0,4}=10$$

7) $$6m-2,6=2,8m+\frac{1}{15}$$

$$6m-2,8m=\frac{1}{15}+2,6$$

$$3,2m=\frac{1}{15}+2\frac{3}{5}=\frac{1}{15}+\frac{39}{15}=\frac{40}{15}=\frac{8}{3}$$

$$m=\frac{8}{3}:\frac{16}{5}=\frac{8}{3}\cdot\frac{5}{16}=\frac{5}{6}$$

8) $$4\left(n+\frac{5}{12}\right)=1\frac{1}{6}\left(6n-1\frac{1}{7}\right)$$

$$4n+\frac{5}{3}=\frac{7}{6}\left(6n-\frac{8}{7}\right)$$

$$4n+\frac{5}{3}=7n-\frac{4}{3}$$

$$7n-4n=\frac{5}{3}+\frac{4}{3}$$

$$3n=3$$

$$n=1$$

Ответ

1) $$a=2,1$$; 2) $$b=\frac{1}{18}$$; 3) $$c=1\frac{1}{3}$$; 4) $$d=2$$; 5) $$x=2,5$$; 6) $$y=10$$; 7) $$m=\frac{5}{6}$$; 8) $$n=1$$.