How did the three-fifths compromise help the south preserve slavery?

The Three-Fifths compromise gave southern states disproportionate representation in the House of Representatives relative to free states, thereby helping the southern states to preserve slavery.

During the US Constitutional Convention delegates from northern states wanted House of Representatives representation to be directly proportional to the number of free inhabitants in each state. Conversely, delegates from southern states wanted representation to be proportional to both free inhabitants and slaves in each state even though slaves did not have the right to vote for their representatives. The two sides ultimately compromised and counted slaves as three-fifths of a person.

As a result, southern states with large slave populations had disproportionate representation. For example, in 1793 slave states had 47 of the 105 members of the House of Representatives, but would have had only 33 had the seats been assigned based on free populations.