Question 343893
5/7=55/77
9/11=63/77 (9/11 is bigger than 5/7)

9/11-5/7=8/77 (distance between 5/7 and 9/11)

We can have irrational numbers inbetween, by for example, adding an irrational smaller than 1 ratio of the "distance" between those 2 rational numbers to the smaller one :

IR1=5/7+8/77*1/Sqrt(2)
IR2=5/7+8/77*1/Pi