The Three Fifths Compromise
The South's argument
Slaves should be counted for the purposes of representation in Congress. The also did not want to free their slaves as they felt that the southern economy was too dependent on the slave trade to survive without it. Most southerners were farmers and felt they needed slave labor to run their farms efficiently.
How the country felt about slavery at this time.
Many northern states had outlawed slavery within their borders by 1787. They wanted to end slavery in all states but the south argued that they needed their slaves to run their plantations/farms. The north wanted to give broad powers to congress to regulate trade between the states and other countries. This made the south nervous as they were afraid that congress would put an end to slavery.
The Slave debate
Northern and Southern states disagreed on how slaves should be counted for the purposes of representation in Congress. The southern states wanted them to be counted so their representation in Congress would be greater. The northern states argued that this was unfair as the southern states did not recognize the rights of slaves in their states to vote.
Other Southern concerns
The South also feared that giving Congress broad powers to regulate commerce between the states would lead to them taxing exports of goods like rice and tobacco to other countries.
The North's argument
People in the north did not want slaves to be counted as they knew this would give the south unfair representation. They insisted unless slaves were made free citizens and given the right to vote that they should be taxed like any other property.
How the delegates worked it out
The compromise stated that Congress could regulate trade with two exceptions. 1. Congress could not tax goods that were to be exported to other countries and 2. Congress could not interfere with the slave trade or end slavery for 20 years or until 1808. They further agreed to the Fugitive Slave clause which gave the South the full right to reclaim any slave that had gone to another state seeking freedom.
The Three-fifths Compromise
The delegates to the Constitutional Convention finally agreed to the Three Fifths Compromise, that slaves should be counted at three fifths of their real number (every 5 slaves would be counted as 3). The Three Fifths Compromise resolved the issue of counting slaves towards population in regards to representation in the House of Representatives.