6减去2分之3间去6分之7减去12分之13减去20分之21减去30分之31.

6减去2分之3间去6分之7减去12分之13减去20分之21减去30分之31.
6减去2分之3间去6分之7减去12分之13减去20分之21减去30分之31.

6减去2分之3间去6分之7减去12分之13减去20分之21减去30分之31.
6-(3/2)-(7/6)-(13/12)-(21/20)-(31/30)
=6-1-(1/2)-1-(1/6)-1-(1/12)-1-(1/20)-1-(1/30)
=6-5-[(1/2)+(1/6)+(1/12)+(1/20)+(1/30)]
=1-[1/1*2+1/2*3+1/3*4+1/4*5+1/5*6]
=1-[1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6]
=1-(1-1/6)
=1-5/6
=1/6

6-3/2-7/6-13/12-21/20-31/30
=6-(1+1/2)-(1+1/6)-(1+1/12)-(1+1/20)-(1+1/30)
=1-1/2-1/6-1/12-1/20-1/30
=1/6

6-3/2-7/6-13/12-21/20-31/30
=1-1/2-1/6-1/12-1/20-1/30
=1/3-1/6-1/12-1/20-1/30
=1/6-1/12-1/20-1/30
=1/12-1/20-1/30
=1/(3*4)-1/(4*5)-1/(5*6)
=1/3-1/4-(1/4-1/5)-(1/5-1/6)
=1/3-1/6
=1/6

奥数题：6减去2分之3间去6分之7减去12分之13减去20分之21减去30分之31。要有过程
6-3/2-7/6-13/12-21/20-31/30
=6-(1+1/2)-(1+1/12)-(1+1/20)-(1+1/30)
=6-1-1/2-1-1/12-1-1/20-1-1/30
=2-1/2-1/12-1/20-1/30
=2-(30/60+5/60+3/60+2/60)
=2-2/3=4/3

6-3/2-7/6-13/12-21/20-31/30
=12/2-3/2-7/6-13/12-21/20-31/30
=9/2-7/6-13/12-21/20-31/30
=27/6-7/6-13/12-21/20-31/30
=20/6-13/12-21/20-31/30
=40/12-13/12-21/20-31/30
=27/12-21/20-31/30
=9/4-21/20-31/30
=45/20-21/20-31/30
=24/20-31/30
=12/10-31/30
=36/30-31/30
=5/30
=1/6

6-3/2-7/6-13/12-21/20-31/30
=6-(1+1/2)-(1+1/6)-(1+1/12)-(1+1/20)-(1+1/30)
=6-1-1/2-1-1/6-1-1/12-1-1/20-1-1/30
=-(1/2+1/6+1/12+1/20+1/30)
=-[(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)]
=-[1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6]
=-[1-1/6]
=-5/6

6-3/2-7/6-13/12-21/20-31/30
=29/2-(7/6+13/12)-(21/20+31/30)
=2/9-27/12-(63+62)/60
=9/2-9/4-25/12
=9/4-25/12
=(27-25)/12
=2/12
=1/6

6-3/2-7/6-13/12-21/20-31/30
=6-(1+1/2)-(1+1/6)-(1+1/12)-(1+1/20)-(1+1/30)
=6-1-1/2-1-1/6-1-1/12-1-1/20-1-1/30
=1-(1/2+1/6+1/12+1/20+1/30)
=1-[(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5...

全部展开

6-3/2-7/6-13/12-21/20-31/30
=6-(1+1/2)-(1+1/6)-(1+1/12)-(1+1/20)-(1+1/30)
=6-1-1/2-1-1/6-1-1/12-1-1/20-1-1/30
=1-(1/2+1/6+1/12+1/20+1/30)
=1-[(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)]
=1-[1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6]
=1-[1-1/6]
=1-5/6
=1/6
奥数的简便方法应该是这样的~就是绕开通分
希望回答对你有帮助

收起