a) \(\dfrac{-1}{3}+\dfrac{7}{6}+\dfrac{3}{2}\)
\(=\left(\dfrac{-1}{3}+\dfrac{3}{2}\right)+\dfrac{7}{6}\)
\(=\left(\dfrac{-2}{6}+\dfrac{9}{6}\right)+\dfrac{7}{6}\)
\(=\dfrac{7}{6}+\dfrac{7}{6}=\dfrac{14}{6}\)
b) \(\left(-8,5\right)\cdot16,35-8,5\cdot83,65\)
\(=-8,5\cdot\left(16,35+83,65\right)\)
\(=-8,5\cdot100=-850\)
c) \(\dfrac{2^2}{1\cdot3}\cdot\dfrac{3^2}{2\cdot4}\cdot\dfrac{4^2}{3\cdot5}\cdot\dfrac{5^2}{4\cdot6}\dots\dfrac{10^2}{9\cdot11}\)
\(=\dfrac{2^2\cdot3^2\cdot4^2\cdot5^2\dots10^2}{1\cdot3\cdot2\cdot4\cdot3\cdot5\dots9\cdot11}\)
\(=\dfrac{\left(2\cdot3\cdot4\cdot5\dots10\right)^2}{\left(1\cdot2\cdot3\dots9\right)\left(3\cdot4\cdot5\dots11\right)}\)
\(=\dfrac{10\cdot2}{11}=\dfrac{20}{11}\)
\(a,-\dfrac{1}{3}+\dfrac{7}{6}+\dfrac{3}{2}\\ =-\dfrac{2}{6}+\dfrac{7}{6}+\dfrac{9}{6}\\ =\dfrac{7}{3}.\\ b,\left(-8,5\right).16,35-8,5.83,65\\ =-8,5.\left(16,35+83,65\right)\\ =-8,5.100\\ =-850.\\ c,\dfrac{2^2}{1.3}.\dfrac{3^2}{2.4}.\dfrac{4^2}{3.5}...\dfrac{10^2}{9.11}\\ =\dfrac{2.2}{1.3}.\dfrac{3.3}{2.4}...\dfrac{10.10}{9.11}\\ =2.\dfrac{10}{11}\\ =\dfrac{20}{11}\)
