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a) \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\) (dấu chấm là dấu nhân)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
\(=1-\frac{1}{7}\)
\(=\frac{6}{7}\)
b) \(\frac{19}{13}+\frac{14}{6}+\frac{1}{9}+\frac{4}{6}+\frac{7}{13}+\frac{17}{9}\)
\(=\left(\frac{19}{13}+\frac{7}{13}\right)+\left(\frac{14}{6}+\frac{4}{6}\right)+\left(\frac{1}{9}+\frac{17}{9}\right)\)
= 2 + 3 + 2
= 7
a,
\(\frac{14}{6}+\frac{1}{9}+\frac{19}{13}+\frac{17}{9}+\frac{7}{13}+\frac{4}{6}\)
\(=\left(\frac{14}{6}+\frac{4}{6}\right)+\left(\frac{1}{9}+\frac{17}{9}\right)+\left(\frac{19}{13}+\frac{7}{13}\right)\)
\(=\frac{18}{6}+\frac{18}{9}+\frac{26}{13}\)
\(=3+2+2\)
\(=7\)
b,
\(\frac{995}{997}x\frac{990}{993}x\frac{997}{990}x\frac{993}{995}x\frac{97}{95}\)
\(=\frac{995x990x997x993x97}{997x993x990x995x95}\)
\(=\frac{97}{95}\)
(Cùng triệt tiêu 995 ; 990 ; 997 ; 993 )
a) 47,54+18,72+5,13-17,54-7,72+4,87=(47,54-17,54)+(18,72-7,72)+(4,87+5,13)=30+11+10=51
b)4/7+7/13+17/9+19/13-8/9+17/7=(4/7+17/7)+(7/13+19/13)+(17/9-8/9)=3+2+1=6
\(\frac{4}{6}+\frac{7}{13}+\frac{17}{9}+\frac{19}{13}+\frac{1}{9}+\frac{14}{6}\)
\(=\left(\frac{4}{6}+\frac{14}{6}\right)+\left(\frac{7}{13}+\frac{19}{13}\right)+\left(\frac{17}{9}+\frac{1}{9}\right)\)
\(=3+2+2=7\)
4/6 + 7/13 + 17/9 + 19/13 + 1/9 + 14/6. = ( 4/6 + 14/6 ) + ( 7/13 + 19/13 ) + ( 17/9 + 1/9 ). = 18/6 + 26/13 + 18/9. = 3 + 2 + 2 = 7.
a/ \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}=\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}=\)
= 1-1/8 = 7/8
b/ = (17/9+1/9)+(19/13+7/13)+(14/6+10/6) = 18/9 + 26/13 + 24/6 = 2+2+4 = 8
14/6 + 1/9 + 19/13 + 17/9 + 7/13 + 4/6 = (14/6 + 4/6) + (1/9 + 17/9) + (19/13 + 7/13)
= 18/6 + 18/9 + 26/13
= 3 + 2 + 2
= 7