The three fifths compromise settled an arguement over

There were many conflicts over representation in the south. The constitutional convention agreed to count the three-fifths compromise. This counted slaves as population for purposes of representation and taxation. (Even though slaves couldn't vote, the slaveholders vote would now hold more weight) there were more "citizens" in the northern states, so the south felt underrepresented.

 How the population of states would be counted in regard to states that permitted slavery.  

Details:

At the Constitutional Convention in 1787, the Three-Fifths Compromise was a way of accounting (somewhat) for the population of slaves in states that permitted slavery.  For taxation and representation purposes, the question was whether slaves should count in the population figures.  (They were not considered voting citizens at that time.)   The Three-Fifths Compromise said that three out of every five slaves could be counted when determining a state's population size for determining how many seats that state would receive in the House of Representatives.

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they thoght they were going to nuke each other