2004X(2.3X47+2.4)/(2.4X47-2.3)的解题思路

来源：百度知道 编辑：UC知道 时间：2024/06/14 18:35:38

2004*(2.3*47+2.4)/(2.4*47-2.3)
=2004*[(2.4-0.1)*47+2.4]/(2.4*47-2.3)
=2004*(2.4*47-4.7+2.4)/(2.4*47-2.3)
=2004*(2.4*47-2.3)/(2.4*47-2.3)
=2004

2004*(2.3*47+2.4)/(2.4*47-2.3)
=2004*(2.3*47+2.3+0.1)/(2.4*47-2.4+0.1)
=2004*(2.3*48+0.1)/(2.4*46+0.1)
=2004*(2.3*46+2.3*2+0.1)/(2.3*46+0.1*46+0.1)
=2004*(2.3*46+4.7)/(2.3*46+4.7)
=2004.

分母
2.4*47-2.3
=(2.3+0.1)*47-2.3
=2.3*4.7+4.7-2.3
=2.3*4.7+2.4
所以原式 = 2004

暂时不管2004，看右边两数相除，最好写成分数的形式

2.3*47比2.4*47小4.7
而2.4比-2.3大4.7
所以分数正好是1

答案2004

2004X(2.3X47+2.4)/(2.4X47-2.3)
=2004X(2.3X47+2.4)/(2.3X47+4.7-2.3)
=2004X(2.3X47+2.4)/(2.3X47+2.4)
=2004

因为24+23=47,可以看到题目中括号中出现的就是这几个数的倍数,
所以考虑往这方面凑
原式=2004*(23*4.7+4.7-2.3)/(2.4*47-2.3)
=2004*(24*4.7-2.3)/(24*4.7-2.3)
=2004