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\(\dfrac{6}{7}\cdot\dfrac{8}{9}+\dfrac{7}{9}\cdot\dfrac{2}{7}-\dfrac{18}{21}\cdot\dfrac{1}{9}+\dfrac{7}{9}\cdot\dfrac{3}{7}\)
\(=\dfrac{6}{7}\cdot\dfrac{8}{9}-\dfrac{6}{7}\cdot\dfrac{1}{9}+\dfrac{7}{9}\left(\dfrac{2}{7}+\dfrac{3}{7}\right)\)
\(=\dfrac{6}{7}\left(\dfrac{8}{9}-\dfrac{1}{9}\right)+\dfrac{7}{9}\cdot\dfrac{5}{7}\)
\(=\dfrac{7}{9}\left(\dfrac{6}{7}+\dfrac{5}{7}\right)=\dfrac{7}{9}\cdot\dfrac{11}{7}=\dfrac{11}{9}\)
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`!`
\(a,\dfrac{8}{9}\times\dfrac{7}{5}-\dfrac{7}{9}\times\dfrac{2}{5}+\dfrac{2}{9}\\ =\dfrac{8}{9}\times\left(\dfrac{7}{5}-\dfrac{2}{5}\right)+\dfrac{2}{9}\\ =\dfrac{8}{9}\times\dfrac{5}{5}+\dfrac{2}{9}\\ =\dfrac{8}{9}+\dfrac{2}{9}\\ =\dfrac{10}{9}\)
\(b,\dfrac{5}{9}\times\dfrac{1}{4}+\dfrac{4}{9}\times\dfrac{3}{12}\\ =\dfrac{5}{9}\times\dfrac{1}{4}+\dfrac{4}{9}\times\dfrac{1}{4}\\ =\dfrac{1}{4}\times\left(\dfrac{5}{9}+\dfrac{4}{9}\right)\\ =\dfrac{1}{4}\times\dfrac{9}{9}\\ =\dfrac{1}{4}\)
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1+1+2+2+3+3+4+4+5+5+6+6+7+7+8+9+8+9+10+12+13+14+15+16+17+18+19+20+30+1000000=10000274
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a,
\(\frac{8}{3}+\frac{17}{9}+\frac{19}{13}+\frac{1}{3}+\frac{7}{13}+\frac{1}{9}\)
\(=\left(\frac{8}{3}+\frac{1}{3}\right)+\left(\frac{17}{9}+\frac{1}{9}\right)+\left(\frac{19}{13}+\frac{7}{13}\right)\)
\(=3+2+2\)
\(=7\)
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1/9 + 2/8 + 3/7 + 4/6 + 5/5 + 6/4 + 7/3 + 8/2 + 9/1
=1/9 + 2/8 + 3/7 + 4/6 + 5/5 + 6/4 + 7/3 + 8/2 + 9/1
=9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1/1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
=1/1