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tính: A = \(\frac{3^2}{5.14}+\frac{3^2}{7.18}+\frac{3^2}{9.22}+\frac{3^2}{11.26}+\frac{3^2}{13.30}\)
\(\frac{3^2}{5.14}+\frac{3^2}{7.18}+\frac{3^2}{99.22}+\frac{3^2}{11.26}+\frac{3^2}{13.30}\)
\(=\frac{9}{5.14}+\frac{9}{7.18}+\frac{9}{9.22}+\frac{9}{11.26}+\frac{9}{13.30}\)
\(=\frac{9}{2}.\left(\frac{4}{10.14}+\frac{4}{14.18}+\frac{4}{18.22}+\frac{4}{22.26}+\frac{4}{26.30}\right)\)
\(=\frac{9}{2}.\left(\frac{1}{10}-\frac{1}{14}+\frac{1}{14}-\frac{1}{18}+...+\frac{1}{26}-\frac{1}{30}\right)\)
\(=\frac{9}{2}.\left(\frac{1}{10}-\frac{1}{30}\right)\)
\(=\frac{9}{2}.\left(\frac{3}{30}-\frac{1}{30}\right)\)
\(=\frac{9}{2}.\frac{2}{30}\)
\(=\frac{9}{30}\)
\(=\frac{3}{10}\)
Chúc bạn học tốt !!!
a )
\(\frac{-4}{9}.\frac{1}{3}-\frac{4}{9}.\frac{5}{6}+\frac{3}{7}.\frac{4}{9}\)
\(=\frac{4}{9}.\left(-\frac{1}{3}-\frac{5}{6}+\frac{3}{7}\right)\)
\(=\frac{4}{9}.\left(-\frac{14}{42}-\frac{35}{42}+\frac{18}{42}\right)\)
\(=\frac{4}{9}.\frac{-31}{42}\)
\(=-\frac{62}{189}\)
b )
\(\frac{2}{3}:\frac{3}{7}-\frac{2}{3}:\frac{4}{3}+\frac{2}{3}:\frac{1}{21}\)
\(=\frac{2}{3}.\frac{7}{3}-\frac{2}{3}.\frac{3}{4}+\frac{2}{3}.21\)
\(=\frac{14}{9}-\frac{1}{2}+14\)
\(=\frac{28}{18}-\frac{9}{18}+14\)
\(=\frac{19}{18}+14\)
\(=1+14+\frac{1}{18}\)
\(=15\frac{1}{18}\)
c )
\(\left(5\frac{1}{3}+3\frac{2}{3}\right)-4\frac{1}{3}\)
\(=\left(5+3-4\right)+\left(\frac{1}{3}+\frac{2}{3}-\frac{1}{3}\right)\)
\(=4\frac{2}{3}\)
\(=\frac{14}{3}\)
a) \(-\frac{4}{9}\cdot\frac{1}{3}-\frac{4}{9}\cdot\frac{5}{6}+\frac{3}{7}\cdot\frac{4}{9}\)
\(=\left(-\frac{4}{9}\right)\cdot\frac{1}{3}+\left(-\frac{4}{9}\right)\cdot\frac{5}{6}-\left(-\frac{4}{9}\right)\cdot\frac{3}{7}\)
\(=\left(-\frac{4}{9}\right)\left(\frac{1}{3}+\frac{5}{6}-\frac{3}{7}\right)\)
\(=\left(-\frac{4}{9}\right)\cdot\frac{31}{42}=-\frac{62}{189}\)
\(A=\left(3+\frac{1}{2}-\frac{2}{3}\right)-\left(2-\frac{2}{3}+\frac{5}{2}\right)-\left(5-\frac{5}{2}+\frac{4}{3}\right)\)
\(A=3+\frac{1}{2}-\frac{2}{3}-2+\frac{2}{3}-\frac{5}{2}-5+\frac{5}{2}-\frac{4}{3}\)
\(A=\left(3-2-5\right)+\left(\frac{2}{3}-\frac{2}{3}\right)+\left(\frac{5}{2}-\frac{5}{2}\right)+\frac{1}{2}-\frac{4}{3}\)
\(A=-4+\frac{1}{2}-1-\frac{1}{3}\)
\(A=-5+\frac{1}{2}-\frac{1}{3}\)
\(A=-5+\frac{1}{6}\)
\(A=-4\frac{5}{6}\)
A =\(\frac{3^2}{5.14}+\frac{3^2}{7.18}+\frac{3^2}{9.22}+\frac{3^2}{11.26}+\frac{3^2}{13.30}\)
A =\(3^2.\left(\frac{1}{5.14}+\frac{1}{7.18}+\frac{1}{9.22}+\frac{1}{11.26}+\frac{1}{13.30}\right)\)
A =\(9.\frac{1}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)
A =\(\frac{9}{4}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
A =\(\frac{9}{4}.\left(\frac{1}{5}-\frac{1}{15}\right)\)
A =\(\frac{9}{4}.\frac{2}{15}\)
A =\(\frac{3}{10}\)