数学术语

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=c/d…=m/n

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

等比性质：

若a1/b1=a2/b2=a3/b3=...=an/bn 则a1/b1=a2/b2=...=(a1+a2+a3+...+an)/(b1+b2+b3+...+bn)=an/bn