3. Вычислите: 1) 5 2 + ( −4 1 6 1 7 3 + 7 2 + 3 8 ); 1 1 7 5 20 2)2 3 ⋅ 14 −7 8 + 2 + 3 ; 3)4 1 4 −( 5−3 3 5 4 + 8 ); 4) −2+( 11 5 24 + 6 ): 15 2 16 5

Ответ: -1.

1. 1) \[\frac{5}{2} + (-4\frac{1}{3} + \frac{6}{7} + 2\frac{1}{3} + \frac{7}{8}) = \frac{5}{2} + ((\frac{-13}{3} + \frac{6}{7} + \frac{7}{3} + \frac{7}{8}) = \frac{5}{2} + ((\frac{-13 \cdot 7 \cdot 8}{3 \cdot 7 \cdot 8} + \frac{6 \cdot 3 \cdot 8}{7 \cdot 3 \cdot 8} + \frac{7 \cdot 7 \cdot 8}{3 \cdot 7 \cdot 8} + \frac{7 \cdot 3 \cdot 7}{8 \cdot 3 \cdot 7}) = \frac{5}{2} + (\frac{-728}{168} + \frac{144}{168} + \frac{392}{168} + \frac{147}{168}) = \frac{5}{2} + \frac{-728 + 144 + 392 + 147}{168} = \frac{5}{2} + \frac{-45}{168} = \frac{5}{2} - \frac{45}{168} = \frac{5 \cdot 84}{2 \cdot 84} - \frac{45}{168} = \frac{420}{168} - \frac{45}{168} = \frac{375}{168} = \frac{125}{56} = 2\frac{13}{56}\]
2. 2) \[2\frac{1}{3} \cdot \frac{1}{14} - 7\frac{5}{8} + \frac{2}{3} + \frac{5}{20} = \frac{7}{3} \cdot \frac{1}{14} - \frac{61}{8} + \frac{2}{3} + \frac{1}{4} = \frac{7}{42} - \frac{61}{8} + \frac{2}{3} + \frac{1}{4} = \frac{1}{6} - \frac{61}{8} + \frac{2}{3} + \frac{1}{4} = \frac{1 \cdot 4}{6 \cdot 4} - \frac{61 \cdot 3}{8 \cdot 3} + \frac{2 \cdot 8}{3 \cdot 8} + \frac{1 \cdot 6}{4 \cdot 6} = \frac{4}{24} - \frac{183}{24} + \frac{16}{24} + \frac{6}{24} = \frac{4 - 183 + 16 + 6}{24} = \frac{-157}{24} = -6\frac{13}{24}\]
3. 3) \[4\frac{1}{4} - (5 - 3\frac{3}{4}) : \frac{5}{8} + \frac{2}{3} = \frac{17}{4} - (5 - \frac{15}{4}) : \frac{5}{8} + \frac{2}{3} = \frac{17}{4} - (\frac{20}{4} - \frac{15}{4}) : \frac{5}{8} + \frac{2}{3} = \frac{17}{4} - \frac{5}{4} : \frac{5}{8} + \frac{2}{3} = \frac{17}{4} - \frac{5}{4} \cdot \frac{8}{5} + \frac{2}{3} = \frac{17}{4} - \frac{1 \cdot 2}{1 \cdot 1} + \frac{2}{3} = \frac{17}{4} - 2 + \frac{2}{3} = \frac{17}{4} - \frac{2 \cdot 12}{1 \cdot 12} + \frac{2}{3} = \frac{17}{4} - \frac{24}{12} + \frac{2}{3} = \frac{17}{4} - \frac{24}{12} + \frac{2}{3} = \frac{17 \cdot 3}{4 \cdot 3} - \frac{24 \cdot 1}{12 \cdot 1} + \frac{2 \cdot 4}{3 \cdot 4} = \frac{51}{12} - \frac{24}{12} + \frac{8}{12} = \frac{51 - 24 + 8}{12} = \frac{35}{12} = 2\frac{11}{12}\]
4. 4) \[-2 + (\frac{11}{24} + \frac{5}{6}) : \frac{15}{16} - \frac{2}{5} = -2 + (\frac{11}{24} + \frac{5 \cdot 4}{6 \cdot 4}) : \frac{15}{16} - \frac{2}{5} = -2 + (\frac{11}{24} + \frac{20}{24}) : \frac{15}{16} - \frac{2}{5} = -2 + \frac{31}{24} : \frac{15}{16} - \frac{2}{5} = -2 + \frac{31}{24} \cdot \frac{16}{15} - \frac{2}{5} = -2 + \frac{31 \cdot 2}{3 \cdot 15} - \frac{2}{5} = -2 + \frac{62}{45} - \frac{2}{5} = -2 + \frac{62}{45} - \frac{2 \cdot 9}{5 \cdot 9} = -2 + \frac{62}{45} - \frac{18}{45} = -2 + \frac{62 - 18}{45} = -2 + \frac{44}{45} = \frac{-2 \cdot 45}{45} + \frac{44}{45} = \frac{-90}{45} + \frac{44}{45} = \frac{-90 + 44}{45} = \frac{-46}{45} = -1\frac{1}{45}\]

Ответ: -1.