\(a,\dfrac{3}{4}+\dfrac{1}{4}.\dfrac{8}{3}=\dfrac{3}{4}+\dfrac{2}{3}=\dfrac{9}{12}+\dfrac{8}{12}=\dfrac{17}{12}\)
\(b,\dfrac{2}{3}+\dfrac{1}{3}\left(\dfrac{-1}{4}+\dfrac{1}{3}\right):\dfrac{7}{12}\)
\(=\dfrac{2}{3}+\dfrac{1}{3}.\left(\dfrac{-3}{12}+\dfrac{4}{12}\right).\dfrac{12}{7}\)
\(=\dfrac{2}{3}+\dfrac{1}{3}.\dfrac{1}{12}.\dfrac{12}{7}\)
\(=\dfrac{2}{3}+\dfrac{1}{21}\)
\(=\dfrac{14}{21}+\dfrac{1}{21}=\dfrac{15}{21}=\dfrac{5}{7}\)
\(c,\dfrac{7}{18}-2,75-\dfrac{25}{18}-\dfrac{1}{4}\)
\(=\dfrac{7}{18}-\dfrac{11}{4}-\dfrac{25}{18}-\dfrac{1}{4}\)
\(=\left(\dfrac{7}{18}-\dfrac{25}{18}\right)-\left(\dfrac{11}{4}+\dfrac{1}{4}\right)\)
\(=\dfrac{-18}{18}-\dfrac{12}{4}\)
\(=-1-3\)
\(=-4\)
\(d,\dfrac{3}{5}.\dfrac{7}{13}-1\dfrac{1}{2}-\dfrac{3}{5}.\dfrac{-6}{13}\)
\(=\dfrac{3}{5}.\left(\dfrac{7}{13}-\dfrac{-6}{13}\right)-1\dfrac{1}{2}\)
\(=\dfrac{3}{5}.\dfrac{13}{13}-\dfrac{3}{2}\)
\(=\dfrac{3}{5}-\dfrac{3}{2}\)
\(=\dfrac{6}{10}-\dfrac{15}{10}\)
\(=\dfrac{-9}{10}\)
\(e,5\dfrac{7}{8}-\left(1,25+4\dfrac{7}{8}\right)\)
\(=\dfrac{47}{8}-\dfrac{5}{4}-\dfrac{39}{8}\)
\(=\left(\dfrac{47}{8}-\dfrac{39}{8}\right)-\dfrac{5}{4}\)
\(=\dfrac{8}{8}-\dfrac{5}{4}\)
\(=1-\dfrac{5}{4}=\dfrac{-1}{4}\)
\(S=\dfrac{3}{1.3}+\dfrac{3}{3.5}+...+\dfrac{3}{97.99}\)
\(2S=3.\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{97.99}\right)\)
\(2S=3.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(2S=3.\left(1-\dfrac{1}{99}\right)\)
\(2S=3.\dfrac{98}{99}\)
\(2S=\dfrac{98}{33}\)
\(S=\dfrac{98}{33}:2\)
\(S=\dfrac{49}{33}\)
