等比性质：如果a/b=c/d=…=m/n(b+d+…+n≠0),那么(a+c+…+m)/(b+d+…+n)=a/b

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

合比性质：如果a/b=c/d,那么(a±b)/b=(c±d)/d

证 明：当b≠0且d≠0时

a/b=c/d

a/b+1=c/d+1

a/b+b/b=c/d+d/d

(a+b)/b=(c+d)/d