25+8+9=?
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\(A=\dfrac{9}{8}-\dfrac{8}{9}+\dfrac{3}{24}+\dfrac{1}{4}-\dfrac{5}{16}+\dfrac{19}{25}-\dfrac{1}{9}+\dfrac{2}{25}-\dfrac{1}{81}\)
\(=\dfrac{9}{8}+\dfrac{1}{4}-\dfrac{5}{16}+\dfrac{1}{8}-\dfrac{8}{9}-\dfrac{1}{9}-\dfrac{1}{81}+\dfrac{19}{25}+\dfrac{2}{25}\)
\(=\dfrac{10}{8}+\dfrac{1}{4}-\dfrac{5}{16}-1-\dfrac{1}{81}+\dfrac{21}{25}\)
\(=\dfrac{20+4-5}{16}-\dfrac{82}{81}+\dfrac{21}{25}\)
\(=\dfrac{19}{16}-\dfrac{82}{81}+\dfrac{21}{25}\)
\(=\dfrac{32891}{16\cdot81\cdot25}\)
b: \(B=-\dfrac{1}{3}-\dfrac{8}{35}-\dfrac{2}{9}-\dfrac{1}{35}+\dfrac{4}{5}-\dfrac{4}{9}+\dfrac{3}{7}\)
\(=\dfrac{-1}{3}-\dfrac{2}{9}-\dfrac{4}{9}-\dfrac{8}{35}-\dfrac{1}{35}+\dfrac{4}{5}+\dfrac{3}{7}\)
\(=\dfrac{-3-2-4}{9}+\dfrac{-9}{35}+\dfrac{28+15}{35}\)
\(=-1+\dfrac{-9+43}{35}=-1+\dfrac{34}{35}=-\dfrac{1}{35}\)
\(\frac{22}{25}.\left(\frac{5}{11}-\frac{8}{9}\right)-\frac{8}{9}\left(\frac{27}{4}-\frac{22}{25}\right)\)
\(\frac{22}{25}.\left(\frac{5}{11}-\frac{8}{9}\right)-\frac{8}{9}.\left(\frac{27}{4}-\frac{22}{25}\right)=\frac{22}{25}.\frac{5}{11}-\frac{22}{25}.\frac{8}{9}-\frac{8}{9}.\frac{27}{4}+\frac{8}{9}.\frac{22}{25}=\frac{2}{5}-\frac{6}{1}=\frac{-28}{5}\)
\(\dfrac{25x8+25x9+25-25x5}{99+98+97+96}\)
\(=\dfrac{25x\left(8+9+1-5\right)}{390}\)
\(=\dfrac{25x13}{390}\)
\(=\dfrac{25x13}{13x30}\)
\(=\dfrac{5}{6}\)
\(A=\frac{9}{8}-\frac{8}{9}+\frac{3}{25}+\frac{1}{4}-\frac{5}{16}+\frac{19}{25}-\frac{1}{9}+\frac{2}{25}-\frac{1}{81}\)
\(A=\left(\frac{9}{8}+\frac{1}{4}-\frac{5}{16}\right)-\left(\frac{8}{9}+\frac{1}{9}-\frac{1}{81}\right)+\left(\frac{3}{25}+\frac{19}{25}+\frac{2}{25}\right)\)
\(A=\frac{17}{16}-\frac{80}{81}+\frac{24}{25}\)
\(A=\frac{33529}{32400}\)
25+8+9=33+9=42
25+8+9=25+17=42
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