1: \(\dfrac{1}{7}\cdot\dfrac{1}{3}+\dfrac{1}{7}\cdot\dfrac{1}{2}-\dfrac{1}{7}\)
\(=\dfrac{1}{7}\left(\dfrac{1}{3}+\dfrac{1}{2}-1\right)\)
\(=\dfrac{1}{7}\cdot\left(\dfrac{5}{6}-1\right)=\dfrac{1}{7}\cdot\dfrac{-1}{6}=-\dfrac{1}{42}\)
2: \(\dfrac{3}{5}\cdot\dfrac{7}{9}+\dfrac{3}{5}\cdot\dfrac{2}{9}+\dfrac{3}{5}\)
\(=\dfrac{3}{5}\left(\dfrac{7}{9}+\dfrac{2}{9}+1\right)\)
\(=\dfrac{3}{5}\left(1+1\right)=\dfrac{3}{5}\cdot2=\dfrac{6}{5}\)
3: \(21\cdot\left(\dfrac{1}{7}-\dfrac{1}{5}+\dfrac{19}{21}\right)\)
\(=21\cdot\dfrac{1}{7}-21\cdot\dfrac{1}{5}+21\cdot\dfrac{19}{21}\)
\(=3+19-\dfrac{21}{5}=22-\dfrac{21}{5}=\dfrac{22\cdot5-21}{5}=\dfrac{110-21}{5}\)
\(=\dfrac{89}{5}\)
4: \(46\cdot\left(\dfrac{1}{2}-\dfrac{7}{23}-\dfrac{27}{46}\right):\dfrac{1}{5}\)
\(=\left(23-46\cdot\dfrac{7}{23}-46\cdot\dfrac{27}{46}\right)\cdot5\)
\(=\left(23-14-27\right)\cdot5=\left(9-27\right)\cdot5=\left(-18\right)\cdot5=-90\)
5: \(75\cdot\left(\dfrac{1}{5}-\dfrac{3}{25}-\dfrac{8}{15}\right)\cdot\dfrac{1}{4}\)
\(=75\cdot\left(\dfrac{15}{75}-\dfrac{9}{75}-\dfrac{40}{75}\right)\cdot\dfrac{1}{4}\)
\(=75\cdot\dfrac{-34}{75}\cdot\dfrac{1}{4}=-\dfrac{34}{4}=-\dfrac{17}{2}\)
6: \(-34\cdot\left(\dfrac{1}{17}-\dfrac{5}{34}+\dfrac{1}{2}\right):4\)
\(=-34\cdot\left(\dfrac{2}{34}-\dfrac{5}{34}+\dfrac{17}{34}\right):4\)
\(=-34\cdot\dfrac{14}{34}:4=-\dfrac{14}{4}=-\dfrac{7}{2}\)
7: \(45\cdot\left(-\dfrac{3}{5}-\dfrac{8}{15}+\dfrac{7}{3}-\dfrac{5}{9}\right)\)
\(=45\cdot\left(-\dfrac{27}{45}-\dfrac{24}{45}+\dfrac{105}{45}-\dfrac{25}{45}\right)\)
\(=45\cdot\dfrac{105-25-27-24}{45}=105-25-27-24\)
=80-51
=29
8: \(\left(\dfrac{11}{12}-1\dfrac{5}{3}+\dfrac{1}{12}-\dfrac{1}{3}\right):\dfrac{2}{3}\)
\(=\left(\dfrac{11}{12}+\dfrac{1}{12}-1-\dfrac{5}{3}-\dfrac{1}{3}\right)\cdot\dfrac{3}{2}\)
\(=\left(1-1-2\right)\cdot\dfrac{3}{2}=-2\cdot\dfrac{3}{2}=-3\)
9: \(\left(\dfrac{7}{15}-\dfrac{7}{5}+\dfrac{8}{15}+\dfrac{2}{5}\right)\cdot\dfrac{189}{2007}\)
\(=\left(\dfrac{15}{15}-\dfrac{5}{5}\right)\cdot\dfrac{189}{2007}\)
\(=\left(1-1\right)\cdot\dfrac{189}{2007}=\dfrac{21}{223}\)
10: \(-\dfrac{5}{9}+\dfrac{14}{18}-\dfrac{4}{9}+\dfrac{2}{9}+\dfrac{1}{2007}\)
\(=\left(-\dfrac{5}{9}+\dfrac{7}{9}-\dfrac{4}{9}+\dfrac{2}{9}\right)+\dfrac{1}{2007}\)
\(=\dfrac{-5+7-4+2}{9}+\dfrac{1}{2007}=\dfrac{2-2}{9}+\dfrac{1}{2007}=\dfrac{1}{2007}\)
