it is a Compromise, which stipulates that three/fifths of the slave population would be counted for purposes of representation.
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Northern states opposed it, Southern States were in favor. Finally they compromised, and agreed that 5 slaves would be counted as 3 citizens.
William Paterson believed that slaves could vote for taxes paid by state but only 3/5 of the slaves should be counted for determining but not for determining representation in the national legislature. :)
The Southerners wanted more representatives in the House of Representatives, so they wanted slaves to count as people in order to inflate their numbers. The Northerners argued that since slaves had no rights to elect those representatives, they should not be counted (in order to give Northerners more relative representation). This debate was what resulted in the Three-Fifths Compromise, wherein slaves were counted as three-fifths of a person.
The invention of the cotton gin by Eli Whitney in 1793 led to a major increase in the number of slaves in the United States. The first census in 1790 counted 697,897 slaves, but by 1810 that number had grown 1.2 million slaves and increase of about 70%!
Slaves were not granted liberty in the U.S. Constitution. In fact, parts of the Constitution solidified their less-than-free position. The Constitution strengthened the power of slave states in several important respects. Through the Fugitive Clause, for example, governments of free states were required to help recapture runaway slaves who had escaped their masters' states. Equally disturbing was the three-fifths compromise, established for determining representation in the lower house of the legislature. Slave states wanted to have additional political power based on the number of human beings that they held as slaves. Delegates from free states wouldn't allow such a blatant manipulation of political principles, but the inhumane compromise that resulted meant counting enslaved persons as three-fifths of a free person for the sake of calculating the number of people a state could elect to the House of Representatives. The Constitution also allowed slaves to be imported into the United States until 1808.