280. Выполните вычитание:

Решение:

1. \( 3\frac{1}{12} - \frac{1}{6} = \frac{3 · 12 + 1}{12} - \frac{1 · 2}{6 · 2} = \frac{36+1}{12} - \frac{2}{12} = \frac{37}{12} - \frac{2}{12} = \frac{35}{12} = 2\frac{11}{12} \)
2. \( 8\frac{7}{30} - 2\frac{9}{20} = \frac{8 · 30 + 7}{30} - \frac{2 · 20 + 9}{20} = \frac{240+7}{30} - \frac{40+9}{20} = \frac{247}{30} - \frac{49}{20} = \frac{247 · 2}{30 · 2} - \frac{49 · 3}{20 · 3} = \frac{494}{60} - \frac{147}{60} = \frac{347}{60} = 5\frac{47}{60} \)
3. \( 7\frac{10}{51} - 4\frac{21}{34} = \frac{7 · 51 + 10}{51} - \frac{4 · 34 + 21}{34} = \frac{357+10}{51} - \frac{136+21}{34} = \frac{367}{51} - \frac{157}{34} = \frac{367 · 2}{51 · 2} - \frac{157 · 3}{34 · 3} = \frac{734}{102} - \frac{471}{102} = \frac{263}{102} = 2\frac{59}{102} \)
4. \( 5\frac{1}{4} - 1\frac{3}{8} = \frac{5 · 4 + 1}{4} - \frac{1 · 8 + 3}{8} = \frac{20+1}{4} - \frac{8+3}{8} = \frac{21}{4} - \frac{11}{8} = \frac{21 · 2}{4 · 2} - \frac{11}{8} = \frac{42}{8} - \frac{11}{8} = \frac{31}{8} = 3\frac{7}{8} \)

Ответ: 1) \( 2\frac{11}{12} \); 2) \( 5\frac{47}{60} \); 3) \( 2\frac{59}{102} \); 4) \( 3\frac{7}{8} \).