Perform the following operations with fractions: 1/2 - 2/3 2 1/7 - 1 3/5 4/8 + 3 15/16 6/8 - 3 5/6

Решение:

Выполним вычитание дробей:

1. \( \frac{1}{2} - \frac{2}{3} = \frac{1 \cdot 3}{2 \cdot 3} - \frac{2 \cdot 2}{3 \cdot 2} = \frac{3}{6} - \frac{4}{6} = \frac{3-4}{6} = -\frac{1}{6} \)
2. \( 2 \frac{1}{7} - 1 \frac{3}{5} = \frac{2 \cdot 7 + 1}{7} - \frac{1 \cdot 5 + 3}{5} = \frac{15}{7} - \frac{8}{5} = \frac{15 \cdot 5}{7 \cdot 5} - \frac{8 \cdot 7}{5 \cdot 7} = \frac{75}{35} - \frac{56}{35} = \frac{75-56}{35} = \frac{19}{35} \)

Выполним сложение и вычитание дробей:

1. \( \frac{4}{8} + 3 \frac{15}{16} = \frac{1}{2} + \frac{3 \cdot 16 + 15}{16} = \frac{1}{2} + \frac{48 + 15}{16} = \frac{1}{2} + \frac{63}{16} = \frac{1 \cdot 8}{2 \cdot 8} + \frac{63}{16} = \frac{8}{16} + \frac{63}{16} = \frac{8+63}{16} = \frac{71}{16} = 4 \frac{7}{16} \)
2. \( \frac{6}{8} - 3 \frac{5}{6} = \frac{3}{4} - \frac{3 \cdot 6 + 5}{6} = \frac{3}{4} - \frac{18 + 5}{6} = \frac{3}{4} - \frac{23}{6} = \frac{3 \cdot 3}{4 \cdot 3} - \frac{23 \cdot 2}{6 \cdot 2} = \frac{9}{12} - \frac{46}{12} = \frac{9-46}{12} = -\frac{37}{12} = -3 \frac{1}{12} \)

Ответ: -1/6; 19/35; 71/16; -37/12.