The Three-Fifths Compromise settled the disagreement at the U.S. Constitutional Convention in 1787 over how to count slaves when determining a state's population for taxation and representation purposes. This compromise is in Article 1, Section 2, Paragraph 3 of the United States Constitution.
A state's representation in the House of Representatives relies on its population. Northern delegates to the Constitutional Convention argued that slaves should not count toward representation in the legislature because, according to the law, slaves were property. This argument supposed that because property like houses and cows didn't count toward a state's population numbers, slaves shouldn't either. The Northern delegates were worried that counting slaves would increase the South's political influence. However, they did argue that slaves should count for taxation purposes, for as property, they increased the wealth of the states in which they lived.
Southern representatives argued that slaves should count for representation purposes but not to determine taxation. To resolve this impasse, delegates James Wilson and Roger Sherman turned to a compromise the James Madison had suggested as an amendment to the Articles of Confederation in 1783. Under this compromise, each slave would count as three-fifths of a person both for representation and taxation purposes.
The Three-Fifths Compromise gave the Southern states, which had a much smaller population of free people relative to the Northern states, outsize power on the national stage, allowing them to force compromises that preserved and extended slavery until the 13th Amendment outlawed the practice.