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) \(6\frac{7}{32} - 2\frac{11}{48}\)

Решение:

1. \( 3\frac{1}{16} - \frac{1}{8} = 3\frac{1}{16} - \frac{2}{16} \). Так как \( \frac{1}{16} < \frac{2}{16} \), занимаем 1 у целой части: \( (2+1)\frac{1}{16} - \frac{2}{16} = 2\frac{17}{16} - \frac{2}{16} = 2\frac{15}{16} \)


2. \( 7\frac{9}{20} - 5\frac{17}{30} = (7-5) + (\frac{9}{20} - \frac{17}{30}) = 2 + \frac{9 \times 3 - 17 \times 2}{60} = 2 + \frac{27-34}{60} = 2 + (-\frac{7}{60}) = 1 + \frac{60}{60} - \frac{7}{60} = 1\frac{53}{60} \)


3. \( 4\frac{2}{7} - 1\frac{4}{9} = (4-1) + (\frac{2}{7} - \frac{4}{9}) = 3 + \frac{2 \times 9 - 4 \times 7}{63} = 3 + \frac{18-28}{63} = 3 - \frac{10}{63} = 2 + \frac{63}{63} - \frac{10}{63} = 2\frac{53}{63} \)


4. \( 8\frac{5}{36} - 1\frac{43}{108} = (8-1) + (\frac{5}{36} - \frac{43}{108}) = 7 + \frac{5 \times 3 - 43}{108} = 7 + \frac{15-43}{108} = 7 - \frac{28}{108} = 7 - \frac{7}{27} = 6 + \frac{27}{27} - \frac{7}{27} = 6\frac{20}{27} \)


5. \( 9\frac{7}{9} - 4\frac{5}{6} = (9-4) + (\frac{7}{9} - \frac{5}{6}) = 5 + \frac{7 \times 2 - 5 \times 3}{18} = 5 + \frac{14-15}{18} = 5 - \frac{1}{18} = 4 + \frac{18}{18} - \frac{1}{18} = 4\frac{17}{18} \)


6. \( 6\frac{7}{32} - 2\frac{11}{48} = (6-2) + (\frac{7}{32} - \frac{11}{48}) = 4 + \frac{7 \times 3 - 11 \times 2}{96} = 4 + \frac{21-22}{96} = 4 - \frac{1}{96} = 3 + \frac{96}{96} - \frac{1}{96} = 3\frac{95}{96} \)