Tính nhanh :
A = \(\dfrac{3}{10}+\dfrac{3}{30}+\dfrac{3}{60}+.........+\dfrac{3}{1900}\)
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\(=\left(\dfrac{1}{21}+\dfrac{1}{210}+\dfrac{1}{2010}\right)\cdot\dfrac{10-6-3-1}{30}=0\)
\(\left(\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{1}{10}-\dfrac{1}{30}\right)\times\left(\dfrac{1}{21}+\dfrac{1}{210}+\dfrac{1}{2010}\right)\)
\(=\left(\dfrac{10}{30}-\dfrac{6}{30}-\dfrac{3}{30}-\dfrac{1}{30}\right)\times\left(\dfrac{1}{21}+\dfrac{1}{210}+\dfrac{1}{2010}\right)\)
\(=0\times\left(\dfrac{1}{21}+\dfrac{1}{210}+\dfrac{1}{2010}\right)\)
\(=0\)
\(2\dfrac{1}{3}.3=\dfrac{7}{3}.3=7.\\ \left(\dfrac{2}{5}-\dfrac{3}{4}\right)-\dfrac{2}{5}=\dfrac{2}{5}-\dfrac{3}{4}-\dfrac{2}{5}=-\dfrac{3}{4}.\\ \dfrac{-10}{11}.\dfrac{4}{7}+\dfrac{-10}{11}.\dfrac{3}{7}+1\dfrac{10}{11}.\\ =\dfrac{-10}{11}\left(\dfrac{4}{7}+\dfrac{3}{7}-1\right).\\ =\dfrac{-10}{11}.\left(1-1\right)=0.\)
1) 2\(\dfrac{1}{3}\).3=\(\dfrac{7}{3}\).3=7.
2) (2/5 -3/4) -2/5 = 2/5 -3/4 -2/5 = -3/4.
3) \(\dfrac{-10}{11}.\dfrac{4}{7}+\dfrac{-10}{11}.\dfrac{3}{7}+1\dfrac{10}{11}=\dfrac{1}{11}\left(-\dfrac{40}{7}-\dfrac{30}{7}+21\right)=\dfrac{1}{11}.\left(-10+21\right)=1\).
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