Why did the framers decide only 9 of 13 states would need to ratify the constitution, rather than 13 of 13 needed for the articles of confederation?

Because they believed in majority rule. They felt that the majority of the people's approval was enough.

Plus, it was much easier for all 13 former colonies to accept the Articles of Confederation than the Constitution because it basically just handed the states governmental power and told them to cooperate with all of the other states. The Constitution, however, sought to take away some of the powers they had received such as the ability to regulate their own taxes. Understandably, it would be much more difficult to get a unanimous vote for for the Constitution due to this so the 9/13 rule seemed more reasonable.

(even though the Constitution ultimately ended up getting ratified unanimously)