281. Выполните вычитание:

Решение:

1. \( 4\frac{3}{16} - \frac{5}{8} = \frac{4 · 16 + 3}{16} - \frac{5 · 2}{8 · 2} = \frac{64+3}{16} - \frac{10}{16} = \frac{67}{16} - \frac{10}{16} = \frac{57}{16} = 3\frac{9}{16} \)
2. \( 6\frac{4}{9} - 3\frac{6}{7} = \frac{6 · 9 + 4}{9} - \frac{3 · 7 + 6}{7} = \frac{54+4}{9} - \frac{21+6}{7} = \frac{58}{9} - \frac{27}{7} = \frac{58 · 7}{9 · 7} - \frac{27 · 9}{7 · 9} = \frac{406}{63} - \frac{243}{63} = \frac{163}{63} = 2\frac{37}{63} \)
3. \( 10\frac{11}{24} - 8\frac{19}{36} = \frac{10 · 24 + 11}{24} - \frac{8 · 36 + 19}{36} = \frac{240+11}{24} - \frac{288+19}{36} = \frac{251}{24} - \frac{307}{36} = \frac{251 · 3}{24 · 3} - \frac{307 · 2}{36 · 2} = \frac{753}{72} - \frac{614}{72} = \frac{139}{72} = 1\frac{67}{72} \)
4. \( 9\frac{1}{6} - 5\frac{3}{4} = \frac{9 · 6 + 1}{6} - \frac{5 · 4 + 3}{4} = \frac{54+1}{6} - \frac{20+3}{4} = \frac{55}{6} - \frac{23}{4} = \frac{55 · 2}{6 · 2} - \frac{23 · 3}{4 · 3} = \frac{110}{12} - \frac{69}{12} = \frac{41}{12} = 3\frac{5}{12} \)

Ответ: 1) \( 3\frac{9}{16} \); 2) \( 2\frac{37}{63} \); 3) \( 1\frac{67}{72} \); 4) \( 3\frac{5}{12} \).