等比性质

数学术语如果a／b=c／d=…=m／n(b+d+…+n≠0),那么

(a+c+…+m)／(b+d+…+n)=a／b

证明：

设a／b=c／d=…=m／n = k

则a = bk, c = dk,...m = nk

则(a+c+…+m)／(b+d+…+n) = (bk + dk +...+ nk)/(b+d+…+n) = k = a／b