If you have two rational numbers, #x# and #y#, the number #(x+y)/2# is rational and satisfies #x < (x+y)/2 < y#

Explanation:

The numbers #2# and #3# are rational, so the number #(2+3)/2=5/2# is also rational and between #2# and #3#. But again, the number #(2+(5/2))/2=((4+5)/2)/2=(9/2)/2=9/4# is between #2# and #5/2#, So we have #2 < 9/4 < 5/2 < 3#, and the two fractions are #9/4# and #5/2#