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\(D=\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}\right):\left(\frac{2011}{1}+\frac{2010}{2}+...+\frac{1}{2011}\right)\)
\(\Rightarrow D=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}}{\frac{2011}{1}+\frac{2010}{2}+\frac{2009}{3}+...+\frac{1}{2011}}\)
\(\Rightarrow D=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}}{\left(\frac{2010}{2}+1\right)+\left(\frac{2009}{3}+1\right)+...+\left(\frac{1}{2011}+1\right)+1}\)
\(\Rightarrow D=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}}{\frac{2012}{2}+\frac{2012}{3}+...+\frac{2012}{2011}+\frac{2012}{2012}}\)
\(\Rightarrow D\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}}{2012\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}+\frac{1}{2012}\right)}\)
\(\Rightarrow D=\frac{1}{2012}\)
\(\left(3-\frac{1}{4}+\frac{2}{3}\right)-\left(5+\frac{1}{3}-\frac{6}{5}\right)-\left(6-\frac{7}{4}+\frac{3}{2}\right)\)
\(=3-\frac{1}{4}+\frac{2}{3}-5-\frac{1}{3}+\frac{6}{5}-6+\frac{7}{4}-\frac{3}{2}\)
\(=\left(3-5-6\right)+\left(-\frac{1}{4}+\frac{7}{4}-\frac{3}{2}\right)+\left(\frac{2}{3}-\frac{1}{3}\right)+\frac{6}{5}\)
\(=-8+\frac{1}{3}+\frac{6}{5}\)
\(=-\frac{97}{15}\)
= 3 - 1/4 +2/3 - 5 - 1/3 + 6/5 - 6 + 7/4 - 3/2
= 2/3 . -3/2 . ( 3 + 5 + 6 ) . ( 2/3 + 1/3 ) . ( -1/4 - 7/4)
= -1 . 14 . 1 . 6/4
= -14 . 1 . 6/4
= -14 . 6/4
= -84/4 = -21
b) = \(\frac{3}{4}\div\)\(\left(-\frac{1}{3}+\frac{2}{3}+\frac{1}{2}\right)\)
= \(\frac{3}{4}\div\frac{5}{6}\)
= \(\frac{9}{10}\)
c) \(\frac{16.2^3}{4}\)
\(=4.8=32\)
\(a)\left|-\frac{1}{2}\right|+3^0+\frac{1}{4}+4+2021^0.\)
\(=\frac{1}{2}+1+\frac{1}{4}+4+1\)
\(=\left(\frac{1}{2}+\frac{1}{4}\right)+\left(1+4+1\right)\)
\(=\frac{3}{4}+6=\frac{27}{4}\)
\(b)\frac{3}{4}\div\left(-\frac{1}{3}\right)+\frac{3}{4}\div\frac{2}{3}+\frac{3}{4}\div\frac{1}{2}\)
\(=\frac{3}{4}\div\left(-\frac{1}{3}+\frac{2}{3}+\frac{1}{2}\right)\)
\(=\frac{3}{4}\div\frac{5}{6}=\frac{9}{10}\)