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问几道数学思考题(急 ⑴62又80/89×1/9⑵9又4/5+99又4/5+999又4/5+9999又4/5+4/5⑶2

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问几道数学思考题(急
⑴62又80/89×1/9
⑵9又4/5+99又4/5+999又4/5+9999又4/5+4/5
⑶2006÷2006又2006/2007
⑷1×3+2×6+3×9+4×12+5×15/1×2+2×4+3×6+4×8+5×10
⑸84又4/19×1.375+105又5/19×0.9
⑹(1+1/2) ×(1-1/2) ×(1+1/3) ×(1-1/3) ×…×(1+1/100) ×(1-1/100)
⑺(1-1/2×1/2) ×(1-1/3×1/3) ×(1-1/4×1/4) ×…×(1-1/100×1/100)
问几道数学思考题(急 ⑴62又80/89×1/9⑵9又4/5+99又4/5+999又4/5+9999又4/5+4/5⑶2
⑴62又80/89×1/9
=(63-9/89)*1/9
=63*1/9-9/89*1/9
=7-1/89
=6又88/89
⑵9又4/5+99又4/5+999又4/5+9999又4/5+4/5
=(9又4/5+1/5)+(99又4/5+1/5)+(999又4/5+1/5)+(9999又4/5+1/5)
=10+100+1000+10000
=11110
⑶2006÷2006又2006/2007
=2006/[(2006*2007+2006)/2007]
=2006/[2006*2008/2007]
=2006*[2007/(2006*2008)]
=(2006*2007)/(2006*2008)
=2007/2008
⑷1×3+2×6+3×9+4×12+5×15/1×2+2×4+3×6+4×8+5×10
=[1*3+2*(1*3)+3*(1*3)+4*(1*3)+5*(1*3)]/[1*2+2*(1*2)+3*(1*2)+4*(1*2)+5*(1*2)]
=[(1*3)*(1+2+3=4+5)]/[(1*2)*(1+2+3+4+5)]
=3/2
⑸84又4/19×1.375+105又5/19×0.9
=(21又1/19)*4*1.375+(21又1/19)*5*0.9
=21又1/19*5.5+21又1/19*4.5
=21又1/19*(5.5+4.5)
=21又1/19*10
=21*10+1/19*10
=210+10/19
=210又10/19
⑹(1+1/2) ×(1-1/2) ×(1+1/3) ×(1-1/3) ×…×(1+1/100) ×(1-1/100)
=1/2*1/2*4/3*2/3*.*101/100*99/100
=1/2*101/100
=101/200
⑺(1-1/2×1/2) ×(1-1/3×1/3) ×(1-1/4×1/4) ×…×(1-1/100×1/100)
=(1+1/2)*(1-1/2)*(1+1/3)*(1-1/3)*(1+1/4)*(1-1/4)*.*(1+1/100)*(1-1/100)
=1/2*1/2*4/3*2/3*.*101/100*99/100
=1/2*101/100
=101/200