730. Выполните действия. 1)7\frac{1}{2}-4\frac{5}{8}+1\frac{3}{4} 2)5\frac{2}{3}+1\frac{7}{9}-4\frac{5}{6}+2; 3) 10-3\frac{9}{10}+7\frac{4}{5}-6\frac{1}{2}; 4) 15\frac{3}{8}+2\frac{3}{4}-10\frac{7}{12}+3; 5)(8\frac{1}{6}-2\frac{2}{3})-(1\frac{7}{9}+2\frac{1}{2})+(4\frac{2}{3}-1\frac{5}{18}); 6)17\frac{1}{18}-(8\frac{3}{4}+5\frac{1}{2}); 7)75\frac{1}{5}-(\frac{42}{50}-5\frac{3}{4}-19\frac{1}{25}); 8)(9\frac{1}{24}+3\frac{7}{8})-(5\frac{3}{4}+1\frac{1}{2})-3\frac{5}{6}.

1. 1) 7\frac{1}{2}-4\frac{5}{8}+1\frac{3}{4}

   Приведем дроби к общему знаменателю 8:

   7\frac{1}{2} = 7\frac{4}{8}; 4\frac{5}{8}; 1\frac{3}{4} = 1\frac{6}{8}

   7\frac{4}{8}-4\frac{5}{8}+1\frac{6}{8} = (7 - 4 + 1) + (\frac{4}{8} - \frac{5}{8} + \frac{6}{8}) = 4 + \frac{5}{8} = 4\frac{5}{8}

2. 2) 5\frac{2}{3}+1\frac{7}{9}-4\frac{5}{6}+2

   Приведем дроби к общему знаменателю 18:

   5\frac{2}{3} = 5\frac{12}{18}; 1\frac{7}{9} = 1\frac{14}{18}; 4\frac{5}{6} = 4\frac{15}{18}

   5\frac{12}{18}+1\frac{14}{18}-4\frac{15}{18}+2 = (5 + 1 - 4 + 2) + (\frac{12}{18} + \frac{14}{18} - \frac{15}{18}) = 4 + \frac{11}{18} = 4\frac{11}{18}

3. 3) 10-3\frac{9}{10}+7\frac{4}{5}-6\frac{1}{2}

   Приведем дроби к общему знаменателю 10:

   3\frac{9}{10}; 7\frac{4}{5} = 7\frac{8}{10}; 6\frac{1}{2} = 6\frac{5}{10}

   10-3\frac{9}{10}+7\frac{8}{10}-6\frac{5}{10} = (10 - 3 + 7 - 6) + (-\frac{9}{10} + \frac{8}{10} - \frac{5}{10}) = 8 - \frac{6}{10} = 7\frac{4}{10} = 7\frac{2}{5}

4. 4) 15\frac{3}{8}+2\frac{3}{4}-10\frac{7}{12}+3

   Приведем дроби к общему знаменателю 24:

   15\frac{3}{8} = 15\frac{9}{24}; 2\frac{3}{4} = 2\frac{18}{24}; 10\frac{7}{12} = 10\frac{14}{24}

   15\frac{9}{24}+2\frac{18}{24}-10\frac{14}{24}+3 = (15 + 2 - 10 + 3) + (\frac{9}{24} + \frac{18}{24} - \frac{14}{24}) = 10 + \frac{13}{24} = 10\frac{13}{24}

5. 5) (8\frac{1}{6}-2\frac{2}{3})-(1\frac{7}{9}+2\frac{1}{2})+(4\frac{2}{3}-1\frac{5}{18})

   Приведем дроби к общему знаменателю:

   8\frac{1}{6} = 8\frac{3}{18}; 2\frac{2}{3} = 2\frac{12}{18}; 1\frac{7}{9} = 1\frac{14}{18}; 2\frac{1}{2} = 2\frac{9}{18}; 4\frac{2}{3} = 4\frac{12}{18}; 1\frac{5}{18}

   (8\frac{3}{18}-2\frac{12}{18})-(1\frac{14}{18}+2\frac{9}{18})+(4\frac{12}{18}-1\frac{5}{18}) = (5\frac{9}{18}) - (3\frac{23}{18}) + (3\frac{7}{18}) = 5\frac{9}{18} - 3\frac{23}{18} + 3\frac{7}{18} = (5 - 3 + 3) + (\frac{9}{18} - \frac{23}{18} + \frac{7}{18}) = 5 - \frac{7}{18} = 4\frac{11}{18}

6. 6) 17\frac{1}{18}-(8\frac{3}{4}+5\frac{1}{2})

   Приведем дроби к общему знаменателю 36:

   17\frac{1}{18} = 17\frac{2}{36}; 8\frac{3}{4} = 8\frac{27}{36}; 5\frac{1}{2} = 5\frac{18}{36}

   17\frac{2}{36}-(8\frac{27}{36}+5\frac{18}{36}) = 17\frac{2}{36} - (13\frac{45}{36}) = 17\frac{2}{36} - 14\frac{9}{36} = 3 - \frac{7}{36} = 2\frac{29}{36}

7. 7) 75\frac{1}{5}-(\frac{42}{50}-5\frac{3}{4}-19\frac{1}{25})

   Приведем дроби к общему знаменателю 100:

   75\frac{1}{5} = 75\frac{20}{100}; \frac{42}{50} = \frac{84}{100}; 5\frac{3}{4} = 5\frac{75}{100}; 19\frac{1}{25} = 19\frac{4}{100}

   75\frac{20}{100}-(\frac{84}{100}-5\frac{75}{100}-19\frac{4}{100}) = 75\frac{20}{100} - (\frac{84}{100} - 24\frac{79}{100}) = 75\frac{20}{100} + 24\frac{-5}{100} = 99\frac{15}{100} = 99\frac{3}{20}

8. 8) (9\frac{1}{24}+3\frac{7}{8})-(5\frac{3}{4}+1\frac{1}{2})-3\frac{5}{6}

   Приведем дроби к общему знаменателю 24:

   9\frac{1}{24}; 3\frac{7}{8} = 3\frac{21}{24}; 5\frac{3}{4} = 5\frac{18}{24}; 1\frac{1}{2} = 1\frac{12}{24}; 3\frac{5}{6} = 3\frac{20}{24}

   (9\frac{1}{24}+3\frac{21}{24})-(5\frac{18}{24}+1\frac{12}{24})-3\frac{20}{24} = 12\frac{22}{24} - 6\frac{30}{24} - 3\frac{20}{24} = (12 - 6 - 3) + (\frac{22}{24} - \frac{30}{24} - \frac{20}{24}) = 3 - \frac{28}{24} = 3 - 1\frac{4}{24} = 2 - \frac{4}{24} = 1\frac{20}{24} = 1\frac{5}{6}

Ответ: 1) 4\frac{5}{8}; 2) 4\frac{11}{18}; 3) 7\frac{2}{5}; 4) 10\frac{13}{24}; 5) 4\frac{11}{18}; 6) 2\frac{29}{36}; 7) 99\frac{3}{20}; 8) 1\frac{5}{6}