Prove by induction given any two fractions ab and cd with b

Prove by induction: given any two fractions a/b and c/d (with b and d positive) it holds that (a+c)/(b+d) lies in between a/b and c/d.

Solution

ans) supose let take: a/b, c/d

       if a,b,c,d=1,2,3,4.

    all are positives.

        then a/b=1/2=0.5

        and c/d=3/4 =0.75.

      and a+c=4,b+d=6

           (a+c)/(b+d)=4/6=2/3=0.66

from above we can tell.any two fractions a/b and c/d (with b and d positive) it holds that (a+c)/(b+d) lies in between a/b and c/d.

supose.a=-1,b=2,c=-3,d=4

            a/b=-1/2 =0.5,

            c/d=-3/4=-0.75

           a+c=-4

          b+d=6

          (a+c)/(b+d)=-4/6=-0.66

so these two fractions a/b and c/d (with b and d positive) it holds that (a+c)/(b+d) lies in between a/b and c/d.