Вопрос:

Вычисли значение выражений с дробями 21.1

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Ответ ассистента

21.1 $$-(\frac{39}{18}) + (-\frac{33}{6} - (-\frac{7}{21} - \frac{33}{5})) - \frac{44}{13} = \frac{-39}{18} - \frac{33}{6} + \frac{7}{21} + \frac{33}{5} - \frac{44}{13} = $$ $$=-\frac{13}{6} - \frac{11}{2} + \frac{1}{3} + \frac{33}{5} - \frac{44}{13} = $$ $$=\frac{-13*65 - 11*195 + 1*130 + 33*78 - 44*30}{390} = $$ $$=\frac{-845 - 2145 + 130 + 2574 - 1320}{390} = $$ $$=\frac{-1606}{390} = -\frac{803}{195} \approx -4.12$$ 21.2 $$-(\frac{21}{15} + \frac{45}{18} + \frac{13}{21} + \frac{18}{20}) = -\frac{21}{15} - \frac{45}{18} - \frac{13}{21} - \frac{18}{20} = $$ $$=-\frac{7}{5} - \frac{5}{2} - \frac{13}{21} - \frac{9}{10} = $$ $$= \frac{-7*42 - 5*105 - 13*10 - 9*21}{210} = $$ $$= \frac{-294 - 525 - 130 - 189}{210} = $$ $$= \frac{-1138}{210} = -\frac{569}{105} \approx -5.42$$ 21.3 $$-(\frac{10}{4} - (-\frac{26}{5} + \frac{24}{11}) - \frac{17}{22}) = -\frac{10}{4} + (-\frac{26}{5} + \frac{24}{11}) + \frac{17}{22} = $$ $$= -\frac{5}{2} - \frac{26}{5} + \frac{24}{11} + \frac{17}{22} = $$ $$=\frac{-5*55 - 26*22 + 24*10 + 17*5}{110} = $$ $$=\frac{-275 - 572 + 240 + 85}{110} = $$ $$=\frac{-522}{110} = -\frac{261}{55} \approx -4.75$$ 21.4 $$-(\frac{22}{10} + \frac{30}{18} - \frac{11}{4}) - (-\frac{44}{20}) = -\frac{22}{10} - \frac{30}{18} + \frac{11}{4} + \frac{44}{20} = $$ $$=-\frac{11}{5} - \frac{5}{3} + \frac{11}{4} + \frac{11}{5} = $$ $$=-\frac{5}{3} + \frac{11}{4} = \frac{-5*4 + 11*3}{12} = $$ $$=\frac{-20 + 33}{12} = \frac{13}{12} \approx 1.08$$ 21.5 $$-(\frac{14}{3}) + \frac{38}{18} + (-\frac{25}{14} - \frac{14}{3}) - (-\frac{40}{9}) = -\frac{14}{3} + \frac{19}{9} - \frac{25}{14} - \frac{14}{3} + \frac{40}{9} =$$ $$= -\frac{28}{3} + \frac{59}{9} - \frac{25}{14} =$$ $$=\frac{-28*42 + 59*14 - 25*9}{126} = $$ $$=\frac{-1176 + 826 - 225}{126} = $$ $$=\frac{-575}{126} \approx -4.56$$ 21.6 $$-(\frac{4}{24} - (\frac{16}{20} - \frac{46}{12}) - \frac{7}{6}) = -\frac{1}{6} + \frac{4}{5} - \frac{23}{6} + \frac{7}{6} =$$ $$= -\frac{1}{6} + \frac{4}{5} - \frac{23}{6} + \frac{7}{6} =$$ $$=\frac{-5 + 24 - 115 + 35}{30} = $$ $$=\frac{-61}{30} \approx -2.03$$ 21.7 $$-(\frac{13}{8}) + \frac{42}{9} + \frac{5}{24} - \frac{17}{8} + \frac{17}{24} = -\frac{13}{8} + \frac{14}{3} + \frac{5}{24} - \frac{17}{8} + \frac{17}{24} =$$ $$=- \frac{30}{8} + \frac{14}{3} + \frac{22}{24} = $$ $$= - \frac{15}{4} + \frac{14}{3} + \frac{11}{12} =$$ $$=\frac{-15*3 + 14*4 + 11}{12} = $$ $$=\frac{-45 + 56 + 11}{12} = \frac{22}{12} = \frac{11}{6} \approx 1.83$$ 21.8 $$-(\frac{11}{6} - \frac{4}{20} + \frac{9}{20}) - (-\frac{35}{14}) = -\frac{11}{6} + \frac{4}{20} - \frac{9}{20} + \frac{35}{14} =$$ $$=- \frac{11}{6} - \frac{5}{20} + \frac{5}{2} = $$ $$= -\frac{11}{6} - \frac{1}{4} + \frac{5}{2} =$$ $$=\frac{-11*2 - 1*3 + 5*6}{12} =$$ $$=\frac{-22 - 3 + 30}{12} = \frac{5}{12} \approx 0.42$$

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