Prove if k and m are rational numbers with k < m, there exists a rational number between k and m

Prove if k and m are rational numbers with k < m, there exists a rational number between k and m

k < m = k+k < k+m = 2k < k+m = k < k+m/2 so k < (m+k)/2

and

k < m = k+m < m+m = k+m < m+m = k+m < 2m so (k+m)/2 < m

if we let t=(k+m)/2 then t is a rational number between k and m. ~~~~