"Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other Persons."
When this topic came up in our Section 2 class we discussed the potential reasoning behind the inclusion of this clause. As representation would be determined by population, the issue of whether or not to count slaves was made a big deal by the framers. Many northerners held that slaves were merely property and deserved no representation whatsoever. They maintained that counting slaves would put the north at a disadvantage and would in fact incentivize an increase in slave importation.
With the shift from a confederacy to a federal system, states with lower representation would lose power in Congress. Not wanting to be at a disadvantage, the southern states pressed the issue of representation because of the benefit it provided. The 3/5 rule came as a result of the conflict between the slave and free states, but it did not originate at the Convention. It actually came from the Articles of Confederation and had previously existed as a means to collect requisitions which was the source of income for Congress under the Articles. To go along with allowing increased representation in the slave states, Gouverneur Morris of Pennsylvania recommended that the clause also include the concept that taxation would be directly proportioned based on representation. As such, southern states would get the representation that they desired but would also be burdened by the additional taxes that would be incurred as a result of the compromise.
In affect the Compromise was more anti-slavery than we sometimes suggest it to be. The 3/5 rule removed whatever sectional benefit counting the slaves created. Rather than suggesting that slaves are not persons, the framers acknowledge the contrary in having them considered in both representation and direct taxation.