The 3/5th compromise was used to determine the issue of representation between big states and small states. This resulted, along with the NJ compromise, our bi-cameral system. Small non-slave owning states were worried that big slave owning states would use slaves as residents to get more representatives.
Thus they agreed on the 3/5th compromise which allowed the entire sum of all slaves in a state to be reduced by 40% in the census. NJ compromise created the Senate.
BTW while slave owning states were ready to count slaves as “people” for the census, they argued that slaves were property, as seen in the Dread Scott Supreme Court case.