A difficult and critical sticking point at the Constitutional Convention was how to count a state’s population, particularly whether slaves would be counted for purposes of both representation and taxation. If slaves were considered property, they would not be counted at all; if they were considered persons, they would be counted fully — just as women, children, and others who could not vote were counted.
Ironically, Southern slave-owners, who considered slaves their property, wanted slaves to be fully counted to increase their own political power in Congress. After extended debate, the framers agreed to the three-fifths compromise — three-fifths of the total number of slaves would be included in a state’s population total (note that the framers never use the word “slaves” in the document).
After the Civil War, the formula was changed with the passage of the 13th Amendment, which abolished slavery, and Section 2 of the 14th Amendment, which specifically repealed the three-fifths rule. – The United States Constitution, What It Says, What It Means, A Hip Pocket Guide