15. Выполните действия и сравните результаты. а) (12 : 3 3/5 + 2/3) * 2/3 б) (19/21 : 1 1/21) : (38/41 : 2/41) в) (13 2/7 - 5 3/14) : 2 11/51 г) (5 1/3 : 3 1/5) : (6 1/2 : 2 1/6)

а) \( (12 : 3\frac{3}{5} + \frac{2}{3}) \cdot \frac{2}{3} \)
\( 3\frac{3}{5} = \frac{18}{5} \); \( 12 : \frac{18}{5} = 12 \cdot \frac{5}{18} = \frac{10}{3} \);
\( \frac{10}{3} + \frac{2}{3} = 4 \);
\( 4 \cdot \frac{2}{3} = \frac{8}{3} \).

б) \( (\frac{19}{21} : 1\frac{1}{21}) : (\frac{38}{41} : \frac{2}{41}) \)
\( 1\frac{1}{21} = \frac{22}{21} \); \( \frac{19}{21} : \frac{22}{21} = \frac{19}{21} \cdot \frac{21}{22} = \frac{19}{22} \);
\( \frac{38}{41} : \frac{2}{41} = \frac{38}{41} \cdot \frac{41}{2} = 19 \);
\( \frac{19}{22} : 19 = \frac{19}{22} \cdot \frac{1}{19} = \frac{1}{22} \).

в) \( (13\frac{2}{7} - 5\frac{3}{14}) : 2\frac{11}{51} \)
\( 13\frac{2}{7} = \frac{93}{7} = \frac{186}{14} \); \( 5\frac{3}{14} = \frac{73}{14} \);
\( \frac{186}{14} - \frac{73}{14} = \frac{113}{14} \); \( 2\frac{11}{51} = \frac{113}{51} \);
\( \frac{113}{14} : \frac{113}{51} = \frac{113}{14} \cdot \frac{51}{113} = \frac{51}{14} = 3\frac{9}{14} \).

г) \( (5\frac{1}{3} : 3\frac{1}{5}) : (6\frac{1}{2} : 2\frac{1}{6}) \)
\( 5\frac{1}{3} = \frac{16}{3} \), \( 3\frac{1}{5} = \frac{16}{5} \); \( \frac{16}{3} : \frac{16}{5} = \frac{16}{3} \cdot \frac{5}{16} = \frac{5}{3} \);
\( 6\frac{1}{2} = \frac{13}{2} \), \( 2\frac{1}{6} = \frac{13}{6} \); \( \frac{13}{2} : \frac{13}{6} = \frac{13}{2} \cdot \frac{6}{13} = 3 \);
\( \frac{5}{3} : 3 = \frac{5}{3} \cdot \frac{1}{3} = \frac{5}{9} \).

Результаты различны: а) \( \frac{8}{3} \), б) \( \frac{1}{22} \), в) \( \frac{51}{14} \), г) \( \frac{5}{9} \).

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