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1/6+1/24+1/40+1/60的巧算过程该怎样写?
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1/6+1/24+1/40+1/60的巧算过程该怎样写?
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答案和解析
不用通分.
1/6+1/24+1/40+1/60
=1/6+(1/2)×(1/12+1/20+1/30)
=1/6+(1/2)×[1/(3×4)+1/(4×5)+1/(5×6)]
=1/6+(1/2)×(1/3-1/4+1/4-1/5+1/5-1/6)
=1/6+(1/2)×(1/3-1/6)
=1/6+(1/2)×(1/3)-(1/2)×(1/6)
=1/6+1/6-1/12
=1/3-1/12
=1/4.
1/6+1/24+1/40+1/60
=1/6+(1/2)×(1/12+1/20+1/30)
=1/6+(1/2)×[1/(3×4)+1/(4×5)+1/(5×6)]
=1/6+(1/2)×(1/3-1/4+1/4-1/5+1/5-1/6)
=1/6+(1/2)×(1/3-1/6)
=1/6+(1/2)×(1/3)-(1/2)×(1/6)
=1/6+1/6-1/12
=1/3-1/12
=1/4.
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