Вопрос:

Вычислите: в) $$2\frac{5}{12} - \frac{7}{8}$$; г) $$11\frac{1}{2} - 3\frac{11}{18}$$; д) $$9\frac{2}{11} - 7\frac{5}{9}$$; e) $$2\frac{6}{25} - 1\frac{7}{10}$$; ж) $$3\frac{1}{2} - 2\frac{3}{4}$$; з) $$12\frac{5}{12} - 9\frac{13}{18}$$

Ответ:

Решения:

в) $$2\frac{5}{12} - \frac{7}{8} = \frac{29}{12} - \frac{7}{8} = \frac{29\cdot2}{12\cdot2} - \frac{7\cdot3}{8\cdot3} = \frac{58}{24} - \frac{21}{24} = \frac{58-21}{24} = \frac{37}{24} = 1\frac{13}{24}$$

Ответ: $$1\frac{13}{24}$$

г) $$11\frac{1}{2} - 3\frac{11}{18} = \frac{23}{2} - \frac{65}{18} = \frac{23\cdot9}{2\cdot9} - \frac{65}{18} = \frac{207}{18} - \frac{65}{18} = \frac{207-65}{18} = \frac{142}{18} = \frac{71}{9} = 7\frac{8}{9}$$

Ответ: $$7\frac{8}{9}$$

д) $$9\frac{2}{11} - 7\frac{5}{9} = \frac{101}{11} - \frac{68}{9} = \frac{101\cdot9}{11\cdot9} - \frac{68\cdot11}{9\cdot11} = \frac{909}{99} - \frac{748}{99} = \frac{909-748}{99} = \frac{161}{99} = 1\frac{62}{99}$$

Ответ: $$1\frac{62}{99}$$

e) $$2\frac{6}{25} - 1\frac{7}{10} = \frac{56}{25} - \frac{17}{10} = \frac{56\cdot2}{25\cdot2} - \frac{17\cdot5}{10\cdot5} = \frac{112}{50} - \frac{85}{50} = \frac{112-85}{50} = \frac{27}{50}$$

Ответ: $$\frac{27}{50}$$

ж) $$3\frac{1}{2} - 2\frac{3}{4} = \frac{7}{2} - \frac{11}{4} = \frac{7\cdot2}{2\cdot2} - \frac{11}{4} = \frac{14}{4} - \frac{11}{4} = \frac{14-11}{4} = \frac{3}{4}$$

Ответ: $$\frac{3}{4}$$

з) $$12\frac{5}{12} - 9\frac{13}{18} = \frac{149}{12} - \frac{175}{18} = \frac{149\cdot3}{12\cdot3} - \frac{175\cdot2}{18\cdot2} = \frac{447}{36} - \frac{350}{36} = \frac{447-350}{36} = \frac{97}{36} = 2\frac{25}{36}$$

Ответ: $$2\frac{25}{36}$$

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