2.251 Найдите разность: a) $$1-\frac{4}{17}$$; б) $$5-\frac{7}{13}$$; в) $$6-5\frac{6}{11}$$; г) $$4\frac{5}{9}-3$$; д) $$4\frac{9}{16}-2\frac{3}{14}$$; e) $$11\frac{7}{31}-9\frac{11}{64}$$; ж) $$17\frac{2}{3}-6\frac{7}{8}$$; з) $$24\frac{7}{15}-15\frac{5}{12}$$.

a) $$1-\frac{4}{17} = \frac{17}{17} - \frac{4}{17} = \frac{17-4}{17} = \frac{13}{17}$$

б) $$5-\frac{7}{13} = \frac{5 \cdot 13}{13} - \frac{7}{13} = \frac{65}{13} - \frac{7}{13} = \frac{65-7}{13} = \frac{58}{13} = 4\frac{6}{13}$$

в) $$6-5\frac{6}{11} = \frac{6 \cdot 11}{11} - \frac{5 \cdot 11 + 6}{11} = \frac{66}{11} - \frac{61}{11} = \frac{66-61}{11} = \frac{5}{11}$$

г) $$4\frac{5}{9}-3 = \frac{4 \cdot 9 + 5}{9} - \frac{3 \cdot 9}{9} = \frac{41}{9} - \frac{27}{9} = \frac{41-27}{9} = \frac{14}{9} = 1\frac{5}{9}$$

д) $$4\frac{9}{16}-2\frac{3}{14} = \frac{4 \cdot 16 + 9}{16} - \frac{2 \cdot 14 + 3}{14} = \frac{73}{16} - \frac{31}{14} = \frac{73 \cdot 7}{16 \cdot 7} - \frac{31 \cdot 8}{14 \cdot 8} = \frac{511}{112} - \frac{248}{112} = \frac{263}{112} = 2\frac{39}{112}$$

e) $$11\frac{7}{31}-9\frac{11}{64} = \frac{11 \cdot 31 + 7}{31} - \frac{9 \cdot 64 + 11}{64} = \frac{348}{31} - \frac{587}{64} = \frac{348 \cdot 64}{31 \cdot 64} - \frac{587 \cdot 31}{64 \cdot 31} = \frac{22272}{1984} - \frac{18197}{1984} = \frac{4075}{1984} = 2\frac{107}{1984}$$

ж) $$17\frac{2}{3}-6\frac{7}{8} = \frac{17 \cdot 3 + 2}{3} - \frac{6 \cdot 8 + 7}{8} = \frac{53}{3} - \frac{55}{8} = \frac{53 \cdot 8}{3 \cdot 8} - \frac{55 \cdot 3}{8 \cdot 3} = \frac{424}{24} - \frac{165}{24} = \frac{259}{24} = 10\frac{19}{24}$$

з) $$24\frac{7}{15}-15\frac{5}{12} = \frac{24 \cdot 15 + 7}{15} - \frac{15 \cdot 12 + 5}{12} = \frac{367}{15} - \frac{185}{12} = \frac{367 \cdot 4}{15 \cdot 4} - \frac{185 \cdot 5}{12 \cdot 5} = \frac{1468}{60} - \frac{925}{60} = \frac{543}{60} = \frac{181}{20} = 9\frac{1}{20}$$