\(\frac{-1}{4}\cdot13\frac{9}{11}-0.25\cdot6\frac{2}{11}\)Tính nhanh nếu có thể
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\(A=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)
\(=7.\frac{1}{10.11}+7.\frac{1}{11.12}+7.\frac{1}{12.13}+...+7.\frac{1}{69.70}\)
\(=7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{69.70}\right)\)
\(=7.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)
\(=7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{3}{35}=\frac{3}{5}\)
\(A=7.\left(\frac{1}{10}-\frac{1}{70}\right)\)
\(=\frac{6}{70}\)
\(=\frac{3}{35}\)
\(9\frac{2}{9}+\frac{2}{3}+7\frac{7}{9}\)
\(=9+\frac{2}{9}+\frac{2}{3}+7+\frac{7}{9}\)
\(=\left(9+7\right)+\left(\frac{2}{9}+\frac{7}{9}\right)+\frac{2}{3}\)
\(=16+1+\frac{2}{3}\)
\(=17+\frac{2}{3}\)
\(=\frac{51}{3}+\frac{2}{3}\)
\(=\frac{53}{3}\)
\(\frac{5}{9}.\frac{10}{11}+\frac{5}{9}.\frac{14}{11}-\frac{5}{9}.\frac{15}{11}\)
\(=\frac{5}{9}\left(\frac{10}{11}+\frac{14}{11}-\frac{15}{11}\right)\)
\(=\frac{5}{9}.\frac{9}{11}\)
\(=\frac{5}{11}\)
\(\frac{0,4-\frac{2}{9}+\frac{2}{11}}{1,4-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-0,25+\frac{1}{5}}{1\frac{1}{6}-0,875+0,7}\)
\(=\frac{\frac{2}{5}-\frac{2}{9}+\frac{2}{11}}{\frac{7}{5}-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{2}{6}-\frac{2}{8}+\frac{2}{10}}{\frac{7}{6}-\frac{7}{8}+\frac{7}{10}}\)
\(=\frac{2.\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{11}\right)}{7.\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{11}\right)}-\frac{2.\left(\frac{1}{6}-\frac{1}{8}+\frac{1}{10}\right)}{7.\left(\frac{1}{6}-\frac{1}{8}+\frac{1}{10}\right)}\)
\(=\frac{2}{7}-\frac{2}{7}\)
\(=0\)
\(\frac{0,4-\frac{2}{9}+\frac{2}{11}}{1,4-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-0,25+\frac{1}{5}}{1\frac{1}{6}-0,875+0,7}=\frac{\frac{2}{5}-\frac{2}{9}+\frac{2}{11}}{\frac{7}{5}-\frac{7}{9}+\frac{7}{11}}-\frac{\frac{1}{3}-\frac{1}{4}+\frac{1}{5}}{\frac{7}{6}-\frac{7}{8}+\frac{7}{10}}\)
\(=\frac{2\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{11}\right)}{7\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{11}\right)}-\frac{\frac{1}{3}-\frac{1}{4}+\frac{1}{5}}{\frac{7}{2}\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{5}\right)}\)
\(=\frac{2}{7}-\frac{1}{\frac{7}{2}}\)
\(=\frac{2}{7}-\frac{2}{7}=0\)
Study well ! >_<
= \(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{18}\)\(\frac{1}{18}\)
= \(\frac{1}{3}-\frac{1}{18}\)
= \(\frac{5}{18}\)
Có:
\(A=2010\cdot\left(\frac{\frac{1}{6}+0.25-\frac{1}{8}}{1+1\frac{1}{2}-\frac{3}{4}}+\frac{0.4-\frac{2}{9}+\frac{2}{11}}{3-\frac{15}{9}+1\frac{4}{11}}\right)\)
\(=2010\cdot\left(\frac{\frac{1}{6}+\frac{1}{4}-\frac{1}{8}}{\frac{3}{3}+\frac{3}{2}-\frac{3}{4}}+\frac{\frac{2}{5}-\frac{2}{9}+\frac{2}{11}}{\frac{15}{5}-\frac{15}{9}+\frac{15}{11}}\right)\)
\(=2010\cdot\left[\frac{\frac{1}{2}\cdot\left(\frac{1}{3}+\frac{1}{2}-\frac{1}{4}\right)}{3\cdot\left(\frac{1}{3}+\frac{1}{2}-\frac{1}{4}\right)}+\frac{2\cdot\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{11}\right)}{15\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{11}\right)}\right]\)
\(=2010\cdot\left(\frac{\frac{1}{2}}{3}+\frac{2}{15}\right)\)
\(=2010\cdot\left(\frac{\frac{5}{2}}{15}+\frac{2}{15}\right)\\ =2010\cdot\left(\frac{\frac{5}{2}+2}{15}\right)\)
\(=2010\cdot\frac{\frac{9}{2}}{15}\\ =\frac{2010\cdot\frac{9}{2}}{15}\\ =\frac{1005\cdot9}{15}\\ =201\cdot3\\ =603\)
\(\frac{-1}{4}\cdot13\frac{9}{11}-0,25\cdot6\frac{2}{11}\)
\(=-0,25\cdot13\frac{9}{11}-0,25\cdot6\frac{2}{11}\)
\(=-0,25\cdot\left(13\frac{9}{11}+6\frac{2}{11}\right)\)
\(=-0,25\cdot\left[\left(13+6\right)+\left(\frac{9}{11}+\frac{2}{11}\right)\right]\)
\(=-0,25\cdot\left[19+1\right]\)
\(=-0,25\cdot20\)
\(=-5\)