2.210 Вычислите значение выражения: в) $$(14\frac{2}{3} - 5\frac{5}{9}) - (3\frac{7}{8} + 4\frac{5}{6}) + (10\frac{3}{4} - 4\frac{4}{9})$$;

Решим данное выражение по действиям:

1. $$14\frac{2}{3} - 5\frac{5}{9} = \frac{44}{3} - \frac{50}{9} = \frac{44 \cdot 3}{3 \cdot 3} - \frac{50}{9} = \frac{132}{9} - \frac{50}{9} = \frac{82}{9} = 9\frac{1}{9}$$
2. $$3\frac{7}{8} + 4\frac{5}{6} = \frac{31}{8} + \frac{29}{6} = \frac{31 \cdot 3}{8 \cdot 3} + \frac{29 \cdot 4}{6 \cdot 4} = \frac{93}{24} + \frac{116}{24} = \frac{209}{24} = 8\frac{17}{24}$$
3. $$10\frac{3}{4} - 4\frac{4}{9} = \frac{43}{4} - \frac{40}{9} = \frac{43 \cdot 9}{4 \cdot 9} - \frac{40 \cdot 4}{9 \cdot 4} = \frac{387}{36} - \frac{160}{36} = \frac{227}{36} = 6\frac{11}{36}$$
4. $$9\frac{1}{9} - 8\frac{17}{24} + 6\frac{11}{36} = \frac{82}{9} - \frac{209}{24} + \frac{227}{36} = \frac{82 \cdot 8}{9 \cdot 8} - \frac{209 \cdot 3}{24 \cdot 3} + \frac{227 \cdot 2}{36 \cdot 2} = \frac{656}{72} - \frac{627}{72} + \frac{454}{72} = \frac{656 - 627 + 454}{72} = \frac{454+29}{72} = \frac{483}{72} = \frac{161}{24} = 6\frac{17}{24}$$

Ответ: $$6\frac{17}{24}$$