The House of Representatives shall be composed of members chosen every second Year by the People of the several States . . . 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.
While black people were whole people, they did not vote at all and did not pay taxes. The vote represented by the population of slaves (not free blacks) was counted as 3/5 of a vote. Indians who did not pay taxes didn't even get that.
It was politics, nothing to do with a black slave being only part of a person. If the north would have had its way, the vote of each slave (who weren't allowed to vote anyway) would be wholly or 5/5 non-existent.
Why did their vote (which they didn't have) count as 3/5?
The South was more sparsely populated than the North. This meant the North had an advantage in congressional representation. Therefore, the South insisted that slaves are part of the population and should count as votes because, simply, they wanted their own views to have more weight.
It didn't seem right to the north to give non-voting people who didn't pay taxes a one-for-one exchange; thus, a compromise was implemented. It allowed southern states to count each slave as 3/5 of a vote.
So despite the fact that slaves weren't voters, the political compromise allowed the southern states to count slaves within their borders for the sole purpose of increasing their congressional representation.
Counting non-voters as having 3/5 of a vote was not a true representation of the population, but it was not as inflated as it would have been if each slave counted as a full vote. The slave states still got over-represented in the Congress, just not as much.
The non-slave states would just as soon there not be any slaves at all; but failing that, they agreed to the compromise in order to hold the country together. Neither side was strong enough to withstand another war or to break away as its own country.
Once again: Free, non-slave Blacks were counted as whole votes and Indians didn't count at all as a person when it came to voting because they weren't required to pay taxes.
One Step Forward
The American Constitution gave Congress the power to ban the importation of new black slaves, which it did beginning 1808. It was a first step. The next steps forward would surely cause a war, and no one looked forward to that.
War did come. The Civil War, which pitted White against White and brother against brother and at great loss of life to the white man for the rights of Blacks, brought an end altogether to the cruel foolishness of slavery in America
from Thomas Jefferson's biography:
"Nothing more certainly written in the book of fate than that these people are to be free. Nor is it less certain that the two races, equally free, cannot live in the same government. Nature, habit, opinion has drawn indelible lines of distinction between them."
Blacks had slaves
As slaves in America were freed during the 19th century, they found themselves unable to make a living, particularly in the North. They often turned to crime causing some states to restrict the entry of Blacks into their areas. The southern Blacks fared better than those in the North as there were more opportunities for their type of labor. In New Orleans, for example, 753 Blacks owned slaves according to the 1830 census.
Throughout the early 1800's and as consciousness was raised--mostly by those of courage in Christian values such as the Quakers-- there was an ever-increasing amount of freed slaves; and many of them came to the Americas from England and offered themselves as an alternative to slave labor.