Why did the founding fathers pick the number three-fifths for the Three-Fifths Compromise?

The 'Three-Fifths' in the 'Three-Fifths Compromise' refers to the fact that it was agreed that slaves would each count as three-fifths of a person. In other words, for every five slaves, three of them counted as people. After the 'Great Compromise,' having a large population would determine how many electoral votes each state would have, how many votes in the House of Representatives each state would have, and how much each state would pay in taxes. By counting slaves in their population, the South would gain more political power but would pay more in taxes, which they were willing to do. The North disagreed because they felt that slaves should not count as people because they did not have the rights that free people hold. If the South wanted these crucial additions to their population, the slaves would have to be free. Both sides disagreed, so they were forced to compromise. They agreed that slaves would count as three-fifths of a person. As far as your one-half or two-thirds comments, I do not know where you could find information as to why they settled on one number instead of another. It was the process used to decide the number of representatives that could be elected to the House of Representatives by Southern states and the distribution of tax revenue. Each slave was counted as three-fifths of a person" rather than a whole individual in an attempt to keep Southern slave owners from gaining substantial power in government and financial advantage in the apportioning of taxes. After agreeing on how many seats the House would hold would be based on population, they needed to decide if the slave population be counted. Most of the south was for the counting of slaves and most of the north was opposed. Finally the founders concluded that every free person should be counted and that 3/5 of the slaves would be counted. This 3/5 was also used in fixing the amount of money to be raised in each state by a direct tax. The southerners won the count of their slaves but they would now end up paying more for them. Representation of slaves was debated in the Continental Congress at the time of the creation of the Articles of Confederation. The North favored a 4-to-3 ratio, while southerners favored a 2-to-1 or 4-to-1 ratio. James Madison proposed a compromise-- a 5-to-3 ratio. All but two states agreed on the compromise figure. But, since the Articles required all states to approve such enactment, the issue was defeated. When the delegates to the Constitutional Convention met in 1787, they decided upon the representation of slaves and the three-fifths figure that Madison had suggested earlier. Because 3 out of 5 is a majority. 1 out of 2 is just half.