Which fraction is in between these two?

If you are looking for the number exactly halfway between, the easiest thing to do is to take the average.

Add the numbers and divide by 2:
(3/2 + 1 3/4) / 2

Change 1 3/4 to an improper fraction:
1 3/4 → 7/4

Convert 3/2 to the same denominator
3/2 → 6/4

Add:
(6/4 + 7/4) / 2
= (13/4) / 2

Convert division by 2 into multiplication by the reciprocal:
13/4 × 1/2
= 13/8

That's as an improper fraction though they may want it as a mixed number:
1⅝

A fraction between 3/2 and 1 3/4: 
13/8