9. Задачи на все действия с дробными числами 1. Вычислите. a) 4$$\frac{1}{6}$$-(1$$\frac{1}{2}$$-$$\frac{3}{5}$$)+($$\frac{3}{4}$$+$$\frac{5}{6}$$)\cdot6; б) (6-2$$\frac{4}{5}$$)\cdot3$$\frac{1}{8}$$-1$$\frac{3}{5}$$:\frac{1}{4}$$; в) 24-(3$$\frac{3}{5}$$-1$$\frac{7}{9}$$):($$\frac{1}{2}$$-$$\frac{1}{3}$$); г) 4\cdot(2$$\frac{1}{2}$$+1$$\frac{3}{4}$$)-(6$$\frac{2}{3}$$+4$$\frac{4}{5}$$):2.

1. Вычислите.

a) 4$$\frac{1}{6}$$-(1$$\frac{1}{2}$$-$$\frac{3}{5}$$)+($$\frac{3}{4}$$+$$\frac{5}{6}$$)\cdot6=$$\frac{25}{6}$$-($$\frac{3}{2}$$-$$\frac{3}{5}$$)+($$\frac{9}{12}$$+$$\frac{10}{12}$$)\cdot6=$$\frac{25}{6}$$-($$\frac{15}{10}$$-$$\frac{6}{10}$$)+$$\frac{19}{12}$$\cdot6=\frac{25}{6}$$-$$\frac{9}{10}$$+$$\frac{19}{2}=\frac{125}{30}$$-$$\frac{27}{30}$$+$$\frac{285}{30}=\frac{125-27+285}{30}=\frac{383}{30}=12\frac{23}{30}$$

Ответ: 12$$\frac{23}{30}$$

б) (6-2$$\frac{4}{5}$$)\cdot3$$\frac{1}{8}$$-1$$\frac{3}{5}$$:\frac{1}{4}$$=(6-\frac{14}{5})\cdot\frac{25}{8}-\frac{8}{5}:\frac{1}{4}=\frac{30-14}{5}\cdot\frac{25}{8}-\frac{8}{5}\cdot4=\frac{16}{5}\cdot\frac{25}{8}-\frac{32}{5}=\frac{2}{1}\cdot\frac{5}{1}-\frac{32}{5}=10-\frac{32}{5}=\frac{50-32}{5}=\frac{18}{5}=3\frac{3}{5}$$

Ответ: 3$$\frac{3}{5}$$

в) 24-(3$$\frac{3}{5}$$-1$$\frac{7}{9}$$):($$\frac{1}{2}$$-$$\frac{1}{3}$$)=24-(\frac{18}{5}-\frac{16}{9}):(\frac{3}{6}-\frac{2}{6})=24-\frac{162-80}{45}:\frac{1}{6}=24-\frac{82}{45}\cdot6=24-\frac{82}{15}\cdot2=24-\frac{164}{15}=\frac{360-164}{15}=\frac{196}{15}=13\frac{1}{15}$$

Ответ: 13$$\frac{1}{15}$$

г) 4\cdot(2$$\frac{1}{2}$$+1$$\frac{3}{4}$$)-(6$$\frac{2}{3}$$+4$$\frac{4}{5}$$):2=4\cdot(\frac{5}{2}+\frac{7}{4})-(\frac{20}{3}+\frac{24}{5}):2=4\cdot(\frac{10}{4}+\frac{7}{4})-(\frac{100}{15}+\frac{72}{15}):2=4\cdot\frac{17}{4}-\frac{172}{15}:2=17-\frac{172}{15}\cdot\frac{1}{2}=17-\frac{86}{15}=\frac{255-86}{15}=\frac{169}{15}=11\frac{4}{15}$$

Ответ: 11$$\frac{4}{15}$$