Вопрос:

268. Вычислите: 1) $$\frac{3}{7} + \frac{4}{9}$$; 2) $$\frac{8}{9} - \frac{7}{8}$$; 3) $$\frac{13}{15} - \frac{2}{3}$$; 4) $$\frac{20}{21} + \frac{3}{7}$$; 5) $$\frac{17}{18} - \frac{11}{12}$$; 6) $$\frac{7}{16} + \frac{1}{6}$$; 7) $$\frac{2}{9} + \frac{5}{6}$$; 8) $$\frac{10}{21} + \frac{9}{14}$$; 9) $$\frac{7}{9} - \frac{4}{15}$$; 10) $$\frac{9}{14} - \frac{3}{7} + \frac{15}{28}$$; 11) $$\frac{1}{6} + \frac{1}{4} - \frac{1}{8}$$; 12) $$\frac{13}{18} - \frac{29}{45} + \frac{8}{15}$$

Ответ:

Решение заданий 268: 1) $$\frac{3}{7} + \frac{4}{9} = \frac{3*9}{7*9} + \frac{4*7}{9*7} = \frac{27}{63} + \frac{28}{63} = \frac{55}{63}$$ 2) $$\frac{8}{9} - \frac{7}{8} = \frac{8*8}{9*8} - \frac{7*9}{8*9} = \frac{64}{72} - \frac{63}{72} = \frac{1}{72}$$ 3) $$\frac{13}{15} - \frac{2}{3} = \frac{13}{15} - \frac{2*5}{3*5} = \frac{13}{15} - \frac{10}{15} = \frac{3}{15} = \frac{1}{5}$$ 4) $$\frac{20}{21} + \frac{3}{7} = \frac{20}{21} + \frac{3*3}{7*3} = \frac{20}{21} + \frac{9}{21} = \frac{29}{21} = 1\frac{8}{21}$$ 5) $$\frac{17}{18} - \frac{11}{12} = \frac{17*2}{18*2} - \frac{11*3}{12*3} = \frac{34}{36} - \frac{33}{36} = \frac{1}{36}$$ 6) $$\frac{7}{16} + \frac{1}{6} = \frac{7*3}{16*3} + \frac{1*8}{6*8} = \frac{21}{48} + \frac{8}{48} = \frac{29}{48}$$ 7) $$\frac{2}{9} + \frac{5}{6} = \frac{2*2}{9*2} + \frac{5*3}{6*3} = \frac{4}{18} + \frac{15}{18} = \frac{19}{18} = 1\frac{1}{18}$$ 8) $$\frac{10}{21} + \frac{9}{14} = \frac{10*2}{21*2} + \frac{9*3}{14*3} = \frac{20}{42} + \frac{27}{42} = \frac{47}{42} = 1\frac{5}{42}$$ 9) $$\frac{7}{9} - \frac{4}{15} = \frac{7*5}{9*5} - \frac{4*3}{15*3} = \frac{35}{45} - \frac{12}{45} = \frac{23}{45}$$ 10) $$\frac{9}{14} - \frac{3}{7} + \frac{15}{28} = \frac{9*2}{14*2} - \frac{3*4}{7*4} + \frac{15}{28} = \frac{18}{28} - \frac{12}{28} + \frac{15}{28} = \frac{6}{28} + \frac{15}{28} = \frac{21}{28} = \frac{3}{4}$$ 11) $$\frac{1}{6} + \frac{1}{4} - \frac{1}{8} = \frac{1*4}{6*4} + \frac{1*6}{4*6} - \frac{1*3}{8*3} = \frac{4}{24} + \frac{6}{24} - \frac{3}{24} = \frac{10}{24} - \frac{3}{24} = \frac{7}{24}$$ 12) $$\frac{13}{18} - \frac{29}{45} + \frac{8}{15} = \frac{13*5}{18*5} - \frac{29*2}{45*2} + \frac{8*6}{15*6} = \frac{65}{90} - \frac{58}{90} + \frac{48}{90} = \frac{7}{90} + \frac{48}{90} = \frac{55}{90} = \frac{11}{18}
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