Выполни вычисления в заданиях с дробями

Конечно, давай решим эти примеры вместе! Сейчас я тебе всё подробно объясню, и ты увидишь, что это совсем не сложно. **1. Вычислите:** a) $2 - \frac{3}{4} = \frac{8}{4} - \frac{3}{4} = \frac{5}{4} = 1\frac{1}{4}$ б) $10 - \frac{9}{10} = \frac{100}{10} - \frac{9}{10} = \frac{91}{10} = 9\frac{1}{10}$ в) $12\frac{7}{9} - 10\frac{3}{4} = \frac{115}{9} - \frac{43}{4} = \frac{460}{36} - \frac{387}{36} = \frac{73}{36} = 2\frac{1}{36}$ г) $10\frac{7}{9} - 4\frac{16}{27} = \frac{97}{9} - \frac{124}{27} = \frac{291}{27} - \frac{124}{27} = \frac{167}{27} = 6\frac{5}{27}$ д) $13\frac{8}{21} - 12\frac{1}{4} = \frac{281}{21} - \frac{49}{4} = \frac{1124}{84} - \frac{1029}{84} = \frac{95}{84} = 1\frac{11}{84}$ е) $4\frac{5}{12} - 2\frac{3}{7} = \frac{53}{12} - \frac{17}{7} = \frac{371}{84} - \frac{204}{84} = \frac{167}{84} = 1\frac{83}{84}$ ж) $7\frac{27}{100} - 4\frac{23}{25} = \frac{727}{100} - \frac{123}{25} = \frac{727}{100} - \frac{492}{100} = \frac{235}{100} = 2\frac{35}{100} = 2\frac{7}{20}$ з) $17\frac{3}{5} - 12 = \frac{88}{5} - \frac{60}{5} = \frac{28}{5} = 5\frac{3}{5}$ и) $4\frac{2}{5} - \frac{3}{5} = \frac{22}{5} - \frac{3}{5} = \frac{19}{5} = 3\frac{4}{5}$ **2. Вычислите:** a) $7 - \frac{21}{31} = \frac{217}{31} - \frac{21}{31} = \frac{196}{31} = 6\frac{10}{31}$ б) $101 - \frac{101}{102} = \frac{10302}{102} - \frac{101}{102} = \frac{10201}{102} = 100\frac{1}{102}$ в) $21\frac{5}{8} - 20\frac{5}{6} = \frac{173}{8} - \frac{125}{6} = \frac{519}{24} - \frac{500}{24} = \frac{19}{24}$ г) $25\frac{7}{24} - 19\frac{5}{9} = \frac{607}{24} - \frac{176}{9} = \frac{1821}{72} - \frac{1408}{72} = \frac{413}{72} = 5\frac{53}{72}$ д) $17\frac{7}{11} - 8\frac{2}{3} = \frac{194}{11} - \frac{26}{3} = \frac{582}{33} - \frac{286}{33} = \frac{296}{33} = 8\frac{32}{33}$ е) $23\frac{7}{9} - 22\frac{5}{6} = \frac{214}{9} - \frac{137}{6} = \frac{428}{18} - \frac{411}{18} = \frac{17}{18}$ ж) $11\frac{8}{11} - 8\frac{11}{13} = \frac{129}{11} - \frac{115}{13} = \frac{1677}{143} - \frac{1265}{143} = \frac{412}{143} = 2\frac{126}{143}$ з) $14\frac{31}{45} - 14 = \frac{661}{45} - \frac{630}{45} = \frac{31}{45}$ и) $5\frac{7}{10} - \frac{9}{10} = \frac{57}{10} - \frac{9}{10} = \frac{48}{10} = 4\frac{8}{10} = 4\frac{4}{5}$ **3. Вычислите:** a) $25\frac{3}{4} - (12\frac{5}{9} - 4\frac{7}{8} + 1\frac{5}{12}) = 25\frac{3}{4} - (\frac{113}{9} - \frac{39}{8} + \frac{17}{12}) = 25\frac{3}{4} - (\frac{904}{72} - \frac{351}{72} + \frac{102}{72}) = 25\frac{3}{4} - \frac{655}{72} = \frac{103}{4} - \frac{655}{72} = \frac{1854}{72} - \frac{655}{72} = \frac{1199}{72} = 16\frac{47}{72}$ б) $(5\frac{5}{12} + 8\frac{7}{15}) + (16\frac{7}{24} - 9\frac{5}{56}) = (\frac{65}{12} + \frac{127}{15}) + (\frac{391}{24} - \frac{509}{56}) = (\frac{325}{60} + \frac{508}{60}) + (\frac{5474}{336} - \frac{3054}{336}) = \frac{833}{60} + \frac{2420}{336} = \frac{833}{60} + \frac{605}{84} = \frac{5831}{420} + \frac{3025}{420} = \frac{8856}{420} = \frac{2214}{105} = 21\frac{9}{105} = 21\frac{3}{35}$ в) $17\frac{2}{3} + 4\frac{3}{8} - 19\frac{5}{9} - (6\frac{1}{36} - 5\frac{3}{16}) = \frac{53}{3} + \frac{35}{8} - \frac{176}{9} - (\frac{217}{36} - \frac{83}{16}) = \frac{53}{3} + \frac{35}{8} - \frac{176}{9} - (\frac{868}{144} - \frac{747}{144}) = \frac{53}{3} + \frac{35}{8} - \frac{176}{9} - \frac{121}{144} = \frac{20304}{1152} + \frac{5040}{1152} - \frac{22528}{1152} - \frac{968}{1152} = \frac{18648}{1152} = \frac{2331}{144} = 16\frac{27}{144} = 16\frac{3}{16}$ **4. Вычислите:** a) $(3\frac{13}{74} + 1\frac{5}{6}) = (\frac{235}{74} + \frac{11}{6}) = (\frac{705}{222} + \frac{407}{222}) = \frac{1112}{222} = \frac{556}{111} = 5\frac{1}{111}$ б) $(16\frac{3}{5} + 17\frac{7}{10}) = (\frac{83}{5} + \frac{177}{10}) = (\frac{166}{10} + \frac{177}{10}) = \frac{343}{10} = 34\frac{3}{10}$ в) $20 - (13\frac{3}{8} + \frac{7}{24}) = 20 - (\frac{107}{8} + \frac{7}{24}) = 20 - (\frac{321}{24} + \frac{7}{24}) = 20 - \frac{328}{24} = \frac{480}{24} - \frac{328}{24} = \frac{152}{24} = \frac{38}{6} = 6\frac{2}{6} = 6\frac{1}{3}$