This document proves that for positive integers a, b, c, d where a/b is less than c/d, a/b will be less than (a+c)/(b+d) which will be less than c/d. It shows that given a/b < c/d, then a/b +1 < c/d +1 which implies (a+b)/b < (c+d)/d, or that a/b < (a+c)/(b+d) < c/d.

1. Let a,b,c,d be positive integers such that a/ b < c /d. Show that
a/ b < ( a + c)/ (b + d) < c/ d
Let a,b,c,d be positive integers such that a/ b < c /d. Show that
a/ b < ( a + c)/ (b + d) < c/ d
Solution
Given that : a/b < c/d,
a/b +1 < c/d +1, .===> (a+b)/b < (c+d)/d,
OR,
a/b < (a+c)/(b+d) < c/d