Fraction of states that must agree to change the constitution

3/4

Explanation:

This rule was stated within the rule regarding constitutional amendment. (under article V).

To begin an amendment process, both houses need to approve the amendment with at least 2/3 votes among them. After that, it will be presented to the states and it needs the approval of 3/4 of the states during ratifying conventions.

The reason for this large fraction is because a change in constitution will also change the foundation the type of laws that can be passed on the state level and It will heavily affected the life of citizens on a national scale.