330. Выполните действия:
a) $$rac{19}{20} - \left(\frac{1}{4} + \frac{2}{5}\right) = \frac{19}{20} - \left(\frac{5}{20} + \frac{8}{20}\right) = \frac{19}{20} - \frac{13}{20} = \frac{6}{20} = \frac{3}{10}$$
б) $$rac{1}{30} + \left(\frac{3}{5} - \frac{1}{6}\right) = \frac{1}{30} + \left(\frac{18}{30} - \frac{5}{30}\right) = \frac{1}{30} + \frac{13}{30} = \frac{14}{30} = \frac{7}{15}$$
331. Выполните действие:
a) $$\frac{7}{20} + \frac{11}{30} = \frac{21}{60} + \frac{22}{60} = \frac{43}{60}$$
б) $$\frac{19}{60} - \frac{8}{45} = \frac{57}{180} - \frac{32}{180} = \frac{25}{180} = \frac{5}{36}$$
в) $$\frac{5}{48} + \frac{17}{36} = \frac{15}{144} + \frac{68}{144} = \frac{83}{144}$$
г) $$\frac{11}{30} - \frac{16}{45} = \frac{33}{90} - \frac{32}{90} = \frac{1}{90}$$
332. Найдите значение выражения:
a) $$\frac{5}{8} + \frac{1}{4} + \frac{7}{12} = \frac{15}{24} + \frac{6}{24} + \frac{14}{24} = \frac{35}{24}$$
б) $$\frac{5}{6} - \frac{3}{8} + \frac{1}{12} = \frac{20}{24} - \frac{9}{24} + \frac{2}{24} = \frac{13}{24}$$
в) $$\frac{3}{7} + \frac{11}{14} - \frac{2}{21} = \frac{18}{42} + \frac{33}{42} - \frac{4}{42} = \frac{47}{42}$$
г) $$\frac{1}{5} + \frac{1}{7} - \frac{1}{9} = \frac{63}{315} + \frac{45}{315} - \frac{35}{315} = \frac{73}{315}$$
д) $$\frac{13}{18} - \frac{1}{24} - \left(\frac{29}{72} + \frac{6}{36}\right) = \frac{52}{72} - \frac{3}{72} - \left(\frac{29}{72} + \frac{12}{72}\right) = \frac{49}{72} - \frac{41}{72} = \frac{8}{72} = \frac{1}{9}$$
e) $$\left(\frac{7}{8} - \frac{4}{5}\right) + \left(\frac{1}{20} + \frac{1}{4}\right) + \frac{1}{2} = \left(\frac{35}{40} - \frac{32}{40}\right) + \left(\frac{1}{20} + \frac{5}{20}\right) + \frac{1}{2} = \frac{3}{40} + \frac{6}{20} + \frac{1}{2} = \frac{3}{40} + \frac{12}{40} + \frac{20}{40} = \frac{35}{40} = \frac{7}{8}$$
333. Решите уравнение:
a) $$x + \frac{4}{15} = \frac{2}{3} + \frac{2}{5}$$
$$x + \frac{4}{15} = \frac{10}{15} + \frac{6}{15}$$
$$x + \frac{4}{15} = \frac{16}{15}$$
$$x = \frac{16}{15} - \frac{4}{15}$$
$$x = \frac{12}{15} = \frac{4}{5}$$
б) $$\left(\frac{4}{5} - x\right) + \frac{13}{20} = \frac{25}{30}$$
$$\frac{4}{5} - x = \frac{25}{30} - \frac{13}{20}$$
$$\frac{4}{5} - x = \frac{50}{60} - \frac{39}{60}$$
$$\frac{4}{5} - x = \frac{11}{60}$$
$$x = \frac{4}{5} - \frac{11}{60}$$
$$x = \frac{48}{60} - \frac{11}{60}$$
$$x = \frac{37}{60}$$
в) $$y - \frac{5}{20} = \frac{5}{8} - \frac{3}{10}$$
$$y - \frac{1}{4} = \frac{25}{40} - \frac{12}{40}$$
$$y - \frac{1}{4} = \frac{13}{40}$$
$$y = \frac{13}{40} + \frac{1}{4}$$
$$y = \frac{13}{40} + \frac{10}{40}$$
$$y = \frac{23}{40}$$
г) $$\frac{2}{3} - \left(\frac{7}{9} - a\right) = \frac{1}{3}$$
$$-\left(\frac{7}{9} - a\right) = \frac{1}{3} - \frac{2}{3}$$
$$-\frac{7}{9} + a = -\frac{1}{3}$$
$$a = -\frac{1}{3} + \frac{7}{9}$$
$$a = -\frac{3}{9} + \frac{7}{9}$$
$$a = \frac{4}{9}$$
34. Найдите значение выражения:
a) $$\frac{1}{4} + 0,7 - \frac{1}{5} = 0,25 + 0,7 - 0,2 = 0,95 - 0,2 = 0,75 = \frac{3}{4}$$
в) $$\frac{4}{5} - \frac{1}{3} + 0,6 = 0,8 - \frac{1}{3} + 0,6 = 1,4 - \frac{1}{3} = \frac{14}{10} - \frac{1}{3} = \frac{42}{30} - \frac{10}{30} = \frac{32}{30} = \frac{16}{15}$$
б) $$0,8 - 0,3 - \frac{2}{5} = 0,5 - 0,4 = 0,1 = \frac{1}{10}$$
г) $$\frac{7}{9} + 0,4 - 0,6 = \frac{7}{9} - 0,2 = \frac{7}{9} - \frac{2}{10} = \frac{7}{9} - \frac{1}{5} = \frac{35}{45} - \frac{9}{45} = \frac{26}{45}$$