Упр.2.176 ГДЗ Виленкин Жохов 6 класс Часть 1, Просвещение (Математика)

Используем свойство вычитания суммы из числа:

$$a-(b+c)=(a-b)-c.$$

а)

$$\frac{5}{7}-\left(\frac{3}{7}+\frac{3}{14}\right) =\left(\frac{5}{7}-\frac{3}{7}\right)-\frac{3}{14} =\frac{2}{7}-\frac{3}{14} =\frac{4}{14}-\frac{3}{14} =\frac{1}{14}$$

б)

$$\frac{23}{36}-\left(\frac{1}{30}+\frac{5}{36}\right) =\left(\frac{23}{36}-\frac{5}{36}\right)-\frac{1}{30} =\frac{18}{36}-\frac{1}{30} =\frac{1}{2}-\frac{1}{30} =\frac{15}{30}-\frac{1}{30} =\frac{14}{30} =\frac{7}{15}$$

а)

$$t-\frac{11}{18}=\frac{11}{12}-\frac{5}{9}$$

$$\frac{11}{12}-\frac{5}{9} =\frac{33}{36}-\frac{20}{36} =\frac{13}{36}$$

Тогда

$$t=\frac{13}{36}+\frac{11}{18} =\frac{13}{36}+\frac{22}{36} =\frac{35}{36}$$

б)

$$\frac{4}{5}-\left(\frac{9}{10}-z\right)=\frac{1}{5}$$

$$\frac{9}{10}-z=\frac{4}{5}-\frac{1}{5}=\frac{3}{5}$$

Тогда

$$z=\frac{9}{10}-\frac{3}{5} =\frac{9}{10}-\frac{6}{10} =\frac{3}{10}$$

в)

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

$$z+\frac{5}{12}=\frac{11}{15}+\frac{9}{20} =\frac{44}{60}+\frac{27}{60} =\frac{71}{60}$$

Тогда

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

г)

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

$$x+\frac{1}{60}=\frac{4}{5}-\frac{2}{3} =\frac{12}{15}-\frac{10}{15} =\frac{2}{15}$$

Тогда

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

Ответ

$$\frac{1}{14};\ \frac{7}{15};\ t=\frac{35}{36};\ z=\frac{3}{10};\ z=\frac{23}{30};\ x=\frac{7}{60}.$$