Алгебра § 1. Вычисления. Обыкновенные и десятичные дроби. Выполните действия

Решение:

Выполним действия с обыкновенными и десятичными дробями согласно номерам.

1. \( \frac{7}{15} + \frac{1}{15} + \frac{6}{15} = \frac{7+1+6}{15} = \frac{14}{15} \)
2. \( \frac{13}{23} - \frac{4}{23} - \frac{1}{23} = \frac{13-4-1}{23} = \frac{8}{23} \)
3. \( 2\frac{1}{2} + 7 = 2.5 + 7 = 9.5 = 9\frac{1}{2} \)
4. \( 8\frac{7}{5} + 4\frac{2}{7} = \frac{47}{5} + \frac{30}{7} = \frac{47 \cdot 7 + 30 \cdot 5}{35} = \frac{329 + 150}{35} = \frac{479}{35} = 13\frac{24}{35} \)
5. \( 4 - \frac{3}{7} = \frac{28}{7} - \frac{3}{7} = \frac{25}{7} = 3\frac{4}{7} \)
6. \( 4\frac{3}{5} - 1\frac{4}{5} = \frac{23}{5} - \frac{9}{5} = \frac{14}{5} = 2\frac{4}{5} \)
7. \( 8\frac{1}{5} + 2\frac{4}{5} - 3 = \frac{41}{5} + \frac{14}{5} - 3 = \frac{55}{5} - 3 = 11 - 3 = 8 \)
8. \( 9\frac{1}{6} + 3\frac{5}{18} = \frac{55}{6} + \frac{59}{18} = \frac{55 \cdot 3 + 59}{18} = \frac{165 + 59}{18} = \frac{224}{18} = \frac{112}{9} = 12\frac{4}{9} \)
9. \( 10\frac{5}{8} - 2\frac{7}{16} = \frac{85}{8} - \frac{39}{16} = \frac{85 \cdot 2 - 39}{16} = \frac{170 - 39}{16} = \frac{131}{16} = 8\frac{3}{16} \)
10. \( 8\frac{5}{9} + 3\frac{5}{6} = \frac{77}{9} + \frac{23}{6} = \frac{77 \cdot 2 + 23 \cdot 3}{18} = \frac{154 + 69}{18} = \frac{223}{18} = 12\frac{7}{18} \)
11. \( 12\frac{5}{12} - 8\frac{7}{18} = \frac{149}{12} - \frac{151}{18} = \frac{149 \cdot 3 - 151 \cdot 2}{36} = \frac{447 - 302}{36} = \frac{145}{36} = 4\frac{1}{36} \)
12. \( 5\frac{11}{12} - 2\frac{1}{6} - 1\frac{1}{4} = \frac{71}{12} - \frac{13}{6} - \frac{5}{4} = \frac{71 - 13 \cdot 2 - 5 \cdot 3}{12} = \frac{71 - 26 - 15}{12} = \frac{30}{12} = \frac{5}{2} = 2\frac{1}{2} \)
13. \( 2\frac{7}{9} - 1\frac{5}{18} + 5\frac{1}{2} = \frac{25}{9} - \frac{23}{18} + \frac{11}{2} = \frac{25 \cdot 2 - 23 + 11 \cdot 9}{18} = \frac{50 - 23 + 99}{18} = \frac{126}{18} = 7 \)
14. \( \frac{1}{2} - \frac{4}{7} = \frac{7 - 8}{14} = -\frac{1}{14} \)
15. \( \frac{17}{26} - \frac{13}{34} = \frac{17 \cdot 17 - 13 \cdot 13}{442} = \frac{289 - 169}{442} = \frac{120}{442} = \frac{60}{221} \)

Ответ: 1. \(\frac{14}{15}\) 2. \(\frac{8}{23}\) 3. \(9\frac{1}{2}\) 4. \(13\frac{24}{35}\) 5. \(3\frac{4}{7}\) 6. \(2\frac{4}{5}\) 7. 8 8. \(12\frac{4}{9}\) 9. \(8\frac{3}{16}\) 10. \(12\frac{7}{18}\) 11. \(4\frac{1}{36}\) 12. \(2\frac{1}{2}\) 13. 7 14. \(-\frac{1}{14}\) 15. \(\frac{60}{221}\)