Question

insert the rational number between 2/3 and 3/4

Answer 1

First we will take a common denominator.
The LCM of 3 and 4 is 12.
So 2/3=8/12
     3/4=9/12
Now a rational number between 8/12 and 9/12 is very easy  to find.
you can choose either of the numbers in between.
And remember the number of rational numbers between any 2 rational number's is infinite

Answer 2

(2/3+3/4)/2. So, (2/3+3/4)/2 = 17/12/2 = 17/24. This is the 1 rational number between 2/3 and 3/4. { By applying the formula :- (a+b)/2 }