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`1/7+5/6+4/7+3/6+2/7+4/6`
`=(1/7 + 4/7 + 2/7 )+(5/6 + 3/6 +4/6)`
`= 7/7 + 12/6`
`=1+2`
`=3`
`1/7+5/6+4/7+3/6+2/7+4/6`
`=(1/7+4/7+2/7)+(5/6+3/6+4/6)`
`=7/7+12/6`
`=1+2`
`=3`
![](https://rs.olm.vn/images/avt/0.png?1311)
(1/2+1/3+1/4+1/5+1/6+1/7)−(1/3+1/4+1/5+1/6+1/7+1/8)
= (1/2+1/8 )+(1/4+1/6 )+(1/6+1/4)−(1/3+1/7 )-(1/5 + 1/5 )
= 1/10 +1/10 +1/10 +1/10 -1/10
= 4/10 = 2/5
k mk na <3
1/2 + ( 1/3 - 1/3 ) + ( 1/4 - 1/4 ) + ( 1/5 -1/5 ) + ( 1/6 - 1/6 ) + ( 1/7 - 1/7 ) + 1/8
= 1/2 + 0 + 1/8
= 5/8
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\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\)
\(=1-\dfrac{1}{8}=\dfrac{7}{8}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1/10+2/9+3/8+4/7+5/6+1/6+3/7+5/8+7/9+9/10
=(1/10+9/10)+(2/9+7/9)+(3/8+5/8)+(4/7+3/7)+(5/6+1/6)
=1+1+1+1+1
=5
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{3}{7}:\dfrac{1}{5}+\dfrac{6}{7}:\dfrac{1}{5}-\dfrac{2}{7}:\dfrac{1}{5}=\dfrac{3}{7}\times5+\dfrac{6}{7}\times5-\dfrac{2}{7}\times5=5\times\left(\dfrac{3}{7}+\dfrac{6}{7}-\dfrac{2}{7}\right)=5\times\dfrac{7}{7}=5\times1=5\)
3/7:1/5+6/7:1/5-2/7:1/5
= \(\left(\dfrac{3}{7}+\dfrac{6}{7}-\dfrac{2}{7}\right):\dfrac{1}{5}\)
= 1 : \(\dfrac{1}{5}\)
= 5