52. Выполните вычитание:

Решение:

1. \( 3\frac{1}{16} - \frac{1}{8} = \frac{3 \cdot 16 + 1}{16} - \frac{1 \cdot 2}{16} = \frac{49 - 2}{16} = \frac{47}{16} = 2\frac{15}{16} \)
2. \( 7\frac{9}{20} - 5\frac{17}{30} = \frac{7 \cdot 20 + 9}{20} - \frac{5 \cdot 30 + 17}{30} = \frac{149}{20} - \frac{167}{30} = \frac{149 \cdot 3}{60} - \frac{167 \cdot 2}{60} = \frac{447 - 334}{60} = \frac{113}{60} = 1\frac{53}{60} \)
3. \( 4\frac{2}{7} - 1\frac{4}{9} = \frac{4 \cdot 7 + 2}{7} - \frac{1 \cdot 9 + 4}{9} = \frac{30}{7} - \frac{13}{9} = \frac{30 \cdot 9}{63} - \frac{13 \cdot 7}{63} = \frac{270 - 91}{63} = \frac{179}{63} = 2\frac{53}{63} \)
4. \( 8\frac{5}{36} - 1\frac{43}{108} = \frac{8 \cdot 36 + 5}{36} - \frac{1 \cdot 108 + 43}{108} = \frac{288 + 5}{36} - \frac{108 + 43}{108} = \frac{293}{36} - \frac{151}{108} = \frac{293 \cdot 3}{108} - \frac{151}{108} = \frac{879 - 151}{108} = \frac{728}{108} = \frac{182}{27} = 6\frac{20}{27} \)
5. \( 9\frac{7}{9} - 4\frac{5}{6} = \frac{9 \cdot 9 + 7}{9} - \frac{4 \cdot 6 + 5}{6} = \frac{81 + 7}{9} - \frac{24 + 5}{6} = \frac{88}{9} - \frac{29}{6} = \frac{88 \cdot 2}{18} - \frac{29 \cdot 3}{18} = \frac{176 - 87}{18} = \frac{89}{18} = 4\frac{17}{18} \)
6. \( 6\frac{7}{32} - 2\frac{11}{48} = \frac{6 \cdot 32 + 7}{32} - \frac{2 \cdot 48 + 11}{48} = \frac{192 + 7}{32} - \frac{96 + 11}{48} = \frac{199}{32} - \frac{107}{48} = \frac{199 \cdot 3}{96} - \frac{107 \cdot 2}{96} = \frac{597 - 214}{96} = \frac{383}{96} = 3\frac{95}{96} \)

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) \( 3\frac{95}{96} \).