52. Выполните вычитание: 1) \(3\frac{1}{16} - \frac{1}{8};\) 2) \(7\frac{9}{20} - 5\frac{17}{30};\) 3) \(4\frac{2}{7} - 1\frac{4}{9};\) 4) \(8\frac{5}{36} - 1\frac{43}{108};\) 5) \(9\frac{7}{9} - 4\frac{5}{6};\) 6) \(6\frac{7}{32} - 2\frac{11}{48}.\)

Выполним вычисления:

1. \(3\frac{1}{16} - \frac{1}{8} = 3 + \frac{1}{16} - \frac{1}{8} = 3 + \frac{1}{16} - \frac{1 \cdot 2}{8 \cdot 2} = 3 + \frac{1}{16} - \frac{2}{16} = 3 - \frac{1}{16} = 2\frac{16}{16} - \frac{1}{16} = 2\frac{16 - 1}{16} = 2\frac{15}{16}\)
2. \(7\frac{9}{20} - 5\frac{17}{30} = 7 - 5 + \frac{9}{20} - \frac{17}{30} = 2 + \frac{9 \cdot 3}{20 \cdot 3} - \frac{17 \cdot 2}{30 \cdot 2} = 2 + \frac{27}{60} - \frac{34}{60} = 2 - \frac{7}{60} = 1\frac{60}{60} - \frac{7}{60} = 1\frac{60 - 7}{60} = 1\frac{53}{60}\)
3. \(4\frac{2}{7} - 1\frac{4}{9} = 4 - 1 + \frac{2}{7} - \frac{4}{9} = 3 + \frac{2 \cdot 9}{7 \cdot 9} - \frac{4 \cdot 7}{9 \cdot 7} = 3 + \frac{18}{63} - \frac{28}{63} = 3 - \frac{10}{63} = 2\frac{63}{63} - \frac{10}{63} = 2\frac{63 - 10}{63} = 2\frac{53}{63}\)
4. \(8\frac{5}{36} - 1\frac{43}{108} = 8 - 1 + \frac{5}{36} - \frac{43}{108} = 7 + \frac{5 \cdot 3}{36 \cdot 3} - \frac{43}{108} = 7 + \frac{15}{108} - \frac{43}{108} = 7 - \frac{28}{108} = 6\frac{108}{108} - \frac{28}{108} = 6\frac{108 - 28}{108} = 6\frac{80}{108} = 6\frac{20}{27}\)
5. \(9\frac{7}{9} - 4\frac{5}{6} = 9 - 4 + \frac{7}{9} - \frac{5}{6} = 5 + \frac{7 \cdot 2}{9 \cdot 2} - \frac{5 \cdot 3}{6 \cdot 3} = 5 + \frac{14}{18} - \frac{15}{18} = 5 - \frac{1}{18} = 4\frac{18}{18} - \frac{1}{18} = 4\frac{18 - 1}{18} = 4\frac{17}{18}\)
6. \(6\frac{7}{32} - 2\frac{11}{48} = 6 - 2 + \frac{7}{32} - \frac{11}{48} = 4 + \frac{7 \cdot 3}{32 \cdot 3} - \frac{11 \cdot 2}{48 \cdot 2} = 4 + \frac{21}{96} - \frac{22}{96} = 4 - \frac{1}{96} = 3\frac{96}{96} - \frac{1}{96} = 3\frac{96 - 1}{96} = 3\frac{95}{96}\)

Ответ: 1) \(2\frac{15}{16}\); 2) \(1\frac{53}{60}\); 3) \(2\frac{53}{63}\); 4) \(6\frac{20}{27}\); 5) \(4\frac{17}{18}\); 6) \(3\frac{95}{96}\)