Упр.289 ГДЗ Мерзляк Полонский 6 класс (Математика)

1) (x+ 5/12)? 9/20= 11/15;
2) (x? 11/30)? 16/45= 2/9;
3) (x? 7/15)+ 5/8= 17/24;
4) 4/5?(x+ 1/60)= 2/3;
5) 4*3/4?(x?2*5/8)=3*5/6;
6) 9*9/28?(4*5/21?x)=6*2/7.

1) $$\left(x+\frac{5}{12}\right)-\frac{9}{20}=\frac{11}{15}$$

$$x+\frac{5}{12}=\frac{11}{15}+\frac{9}{20}$$

$$x+\frac{5}{12}=\frac{44}{60}+\frac{27}{60}=\frac{71}{60}$$

$$x=\frac{71}{60}-\frac{5}{12}=\frac{71}{60}-\frac{25}{60}=\frac{46}{60}=\frac{23}{30}$$

2) $$\left(x-\frac{11}{30}\right)-\frac{16}{45}=\frac{2}{9}$$

$$x-\frac{11}{30}=\frac{2}{9}+\frac{16}{45}$$

$$x-\frac{11}{30}=\frac{10}{45}+\frac{16}{45}=\frac{26}{45}$$

$$x=\frac{26}{45}+\frac{11}{30}=\frac{52}{90}+\frac{33}{90}=\frac{85}{90}=\frac{17}{18}$$

3) $$\left(x-\frac{7}{15}\right)+\frac{5}{8}=\frac{17}{24}$$

$$x-\frac{7}{15}=\frac{17}{24}-\frac{5}{8}$$

$$x-\frac{7}{15}=\frac{17}{24}-\frac{15}{24}=\frac{2}{24}=\frac{1}{12}$$

$$x=\frac{1}{12}+\frac{7}{15}=\frac{5}{60}+\frac{28}{60}=\frac{33}{60}=\frac{11}{20}$$

4) $$\frac{4}{5}-\left(x+\frac{1}{60}\right)=\frac{2}{3}$$

$$x+\frac{1}{60}=\frac{4}{5}-\frac{2}{3}$$

$$x+\frac{1}{60}=\frac{12}{15}-\frac{10}{15}=\frac{2}{15}$$

$$x=\frac{2}{15}-\frac{1}{60}=\frac{8}{60}-\frac{1}{60}=\frac{7}{60}$$

5) $$4\frac{3}{4}-\left(x-2\frac{5}{8}\right)=3\frac{5}{6}$$

$$x-2\frac{5}{8}=4\frac{3}{4}-3\frac{5}{6}$$

$$x-2\frac{5}{8}=4\frac{9}{12}-3\frac{10}{12}=1\frac{11}{12}$$

$$x=1\frac{11}{12}+2\frac{5}{8}$$

$$x=\frac{11}{12}+\frac{5}{8}+2=\frac{22}{24}+\frac{15}{24}+2=2\frac{37}{24}=3\frac{13}{24}$$

6) $$9\frac{9}{28}-\left(4\frac{5}{21}-x\right)=6\frac{2}{7}$$

$$4\frac{5}{21}-x=9\frac{9}{28}-6\frac{2}{7}$$

$$4\frac{5}{21}-x=9\frac{9}{28}-6\frac{8}{28}=3\frac{1}{28}$$

$$x=4\frac{5}{21}-3\frac{1}{28}$$

$$x=4\frac{20}{84}-3\frac{3}{84}=1\frac{17}{84}$$

Ответ

1) $$x=\frac{23}{30}$$; 2) $$x=\frac{17}{18}$$; 3) $$x=\frac{11}{20}$$; 4) $$x=\frac{7}{60}$$; 5) $$x=3\frac{13}{24}$$; 6) $$x=1\frac{17}{84}$$.