2.247 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) $$11\frac{7}{32}-9\frac{11}{64}$$; ж) $$17\frac{2}{3}-6\frac{7}{8}$$; з) $$24\frac{7}{15}-15\frac{5}{12}$$.

Решим примеры на вычитание дробей:

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

Ответ: $$ \frac{13}{17}$$

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

Ответ: $$4\frac{6}{13}$$

в) $$6 - 5\frac{6}{11} = 6 - \frac{5 \cdot 11 + 6}{11} = 6 - \frac{55 + 6}{11} = 6 - \frac{61}{11} = \frac{6 \cdot 11}{11} - \frac{61}{11} = \frac{66}{11} - \frac{61}{11} = \frac{66 - 61}{11} = \frac{5}{11}$$

Ответ: $$\frac{5}{11}$$

г) $$4\frac{5}{9} - 3 = \frac{4 \cdot 9 + 5}{9} - 3 = \frac{36 + 5}{9} - 3 = \frac{41}{9} - 3 = \frac{41}{9} - \frac{3 \cdot 9}{9} = \frac{41}{9} - \frac{27}{9} = \frac{41 - 27}{9} = \frac{14}{9} = 1\frac{5}{9}$$

Ответ: $$1\frac{5}{9}$$

д) $$4\frac{9}{16} - 2\frac{3}{14} = \frac{4 \cdot 16 + 9}{16} - \frac{2 \cdot 14 + 3}{14} = \frac{64 + 9}{16} - \frac{28 + 3}{14} = \frac{73}{16} - \frac{31}{14} = \frac{73 \cdot 7}{16 \cdot 7} - \frac{31 \cdot 8}{14 \cdot 8} = \frac{511}{112} - \frac{248}{112} = \frac{511 - 248}{112} = \frac{263}{112} = 2\frac{39}{112}$$

Ответ: $$2\frac{39}{112}$$

е) $$11\frac{7}{32} - 9\frac{11}{64} = \frac{11 \cdot 32 + 7}{32} - \frac{9 \cdot 64 + 11}{64} = \frac{352 + 7}{32} - \frac{576 + 11}{64} = \frac{359}{32} - \frac{587}{64} = \frac{359 \cdot 2}{32 \cdot 2} - \frac{587}{64} = \frac{718}{64} - \frac{587}{64} = \frac{718 - 587}{64} = \frac{131}{64} = 2\frac{3}{64}$$

Ответ: $$2\frac{3}{64}$$

ж) $$17\frac{2}{3} - 6\frac{7}{8} = \frac{17 \cdot 3 + 2}{3} - \frac{6 \cdot 8 + 7}{8} = \frac{51 + 2}{3} - \frac{48 + 7}{8} = \frac{53}{3} - \frac{55}{8} = \frac{53 \cdot 8}{3 \cdot 8} - \frac{55 \cdot 3}{8 \cdot 3} = \frac{424}{24} - \frac{165}{24} = \frac{424 - 165}{24} = \frac{259}{24} = 10\frac{19}{24}$$

Ответ: $$10\frac{19}{24}$$

з) $$24\frac{7}{15} - 15\frac{5}{12} = \frac{24 \cdot 15 + 7}{15} - \frac{15 \cdot 12 + 5}{12} = \frac{360 + 7}{15} - \frac{180 + 5}{12} = \frac{367}{15} - \frac{185}{12} = \frac{367 \cdot 4}{15 \cdot 4} - \frac{185 \cdot 5}{12 \cdot 5} = \frac{1468}{60} - \frac{925}{60} = \frac{1468 - 925}{60} = \frac{543}{60} = 9\frac{3}{60} = 9\frac{1}{20}$$

Ответ: $$9\frac{1}{20}$$