Question

如果A＝1110/2221,B=3332/6665,那么A与B中较大的数是

Answer 1

A = (2221-1111) / (4443-2222)

B = (2221+1111) / (4443+2222)

A : B

= (2221-1111) / (4443-2222) : (2221+1111) / (4443+2222)

= (2221-1111) * (4443+2222) : (2221+1111) * (4443-2222)

= (2221*4443 + 2221*2222 - 1111*4443 - 1111*2222) :

(2221*4443 -2221*2222 + 1111*4443 - 1111*2222)

显然,因

2221*2222 - 1111*4443 = 1111*(2221*2 - 4443) ……①

-2221*2222 + 1111*4443 = 1111*(-2221*2 + 4443) ……②

①0,② > ①

则比例式 A : B < 1

A < B