Question

Insert two rational numbers between 3/8and 7/12

Answer 1

One rational number between 3/8 and 7/12 = [(3/8) + (7/12)]/2
=[(9+14)/24]/2    {LCM of 8 and 12 is 24}
=(23/24)/2
=23/48
Another rational number can be found between 23/48 and 7/12
=[(23/48) + (7/12)]/2
=[(23 + 28)/48]/2
=(51/48)/2
=51/96
Therefore the two rational numbers between 3/8 and 7/12 are   23/48 and 51/96

Answer 2

The sophisticated way to answer such questions is make them have common denominators .

lcm of 8 and 12 is 24

multiply 3 to num and denum. so 3/8 = 9/24
multiply 2 to num and denum. so 7/12= 14/24

now ot becomes easier to find rational numbers between 9/24 and 14/24 .

Answer : 10/24 , 11/24 , 13/24 , 10.5/24 = 105/240 , 11.7/24 , etc.