Bài 6: Tính
a, (6\(\dfrac{4}{9}\) + 3\(\dfrac{7}{11}\)) - 4\(\dfrac{4}{9}\)
b, -1\(\dfrac{1}{3}\) - 2\(\dfrac{5}{6}\) . \(\dfrac{6}{11}\) + 3 : 5%
c, \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) + \(\dfrac{2}{7.9}\) + ... + \(\dfrac{2}{97.99}\)
d, \(\dfrac{5}{7}\)\(\dfrac{5}{11}\) + \(\dfrac{5}{7}\) . \(\dfrac{2}{11}\) - \(\dfrac{5}{7}\). \(\dfrac{14}{11}\)
a) \(\left(6\dfrac{4}{9}+3\dfrac{7}{11}\right)-4\dfrac{4}{9}\)
\(=6+\dfrac{4}{9}+3+\dfrac{7}{11}-4-\dfrac{4}{9}\)
\(=\left(6+3-4\right)+\left(\dfrac{4}{9}-\dfrac{4}{9}\right)+\dfrac{7}{11}\)
\(=5+\dfrac{7}{11}\)
\(=\dfrac{62}{11}\)
b) \(-1\dfrac{1}{3}-2\dfrac{5}{6}.\dfrac{6}{11}+3:5\%\)
\(=-\dfrac{4}{3}-\dfrac{17}{6}.\dfrac{6}{11}+3:\dfrac{1}{20}\)
\(=-\dfrac{4}{3}-\dfrac{17}{11}+60\)
\(=-\dfrac{95}{33}+60\)
\(=\dfrac{1885}{33}\)
c) \(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{97.99}\)
\(=\dfrac{5-3}{3.5}+\dfrac{7-5}{5.7}+\dfrac{9-7}{7.9}+...+\dfrac{99-97}{97.99}\)
\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{97}-\dfrac{1}{99}\)
\(=\dfrac{1}{3}-\dfrac{1}{99}\)
\(=\dfrac{32}{99}\)
d) \(\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{2}{11}-\dfrac{5}{7}.\dfrac{14}{11}\)
\(=\dfrac{5}{7}.\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)\)
\(=\dfrac{5}{7}.\left(-\dfrac{7}{11}\right)\)
\(=-\dfrac{5}{11}\)
`a)(6 4/9+3 7/11)-4 4/9`
`=(6+4/9+3+7/11)-4-4/9`
`=6+4/9+3+7/11-4-4/9`
`=(6-4+3)+(4/9-4/9)+7/11`
`=5+7/11`
`=55/11+7/11`
`=62/11`
_
`b)-1 1/3-2 5/6 . 6/11+3:5%`
`=-4/3-17/6 . 6/11+60`
`=-4/3-17/11+60`
`=1885/33`
_
`c)2/3.5+2/5.7+2/7.9+..+2/97.99`
`=1/3-1/5+1/5-1/7+1/7-1/9+...+1/97-1/99`
`=1/3-1/99`
`=32/99`
_
`d)5/7 . 5/11+5/7 . 2/11-5/7 . 14/11`
`=5/7(5/11+2/11-14/11)`
`=5/7 . (-7)/11`
`=-5/11`
