Question

奥数题及答案

1949*(47分之1-1996分之1）+47*（1949分之1-1996分之1）-1996*（1949分之1+47分之1）+1003=？

Answer 1

1949×(1/47-1/1996)+47×(1/1949-1/1996)-1996×(1/1949+1/47)+1003
=1949×1/47-1949×1/1996+47×1/1949-47×1/1996-1996×1/1949-1996×1/47+1003
=(1949×1/47-1996×1/47)-(1949×1/1996+47×1/1996)+(47×1/1949-1996×1/1949)+1003
=1/47×(1949-1996)-1/1996(1949+47)+1/1949(47-1996)+1003
=1/47×(-47)-1/1996(1996)+1/1949(-1949)+1003
=-1-1-1+1003
=-3+1003
=1000

Answer 2

=1949/47-1949/1996+47/1949-47/1996-1996/1949-1996/47+1003
=(1949-1996)*(1/47)-(1949+47)*(1/1996+(47-1996)/(1949)+1003
=(-47)/(1/47)-(1996)*91/1996)+(-1949)*(1/1949)+1003
=-1-1-1+1003
=1000

Answer 3

1000