1. The problem statement, all variables and given/known data Check to see if the (vector space) set of rational numbers is closed under addition and scalar multiplication 2. Relevant equations The book says this holds for addition but fails for scalar multiplication. 3. The attempt at a solution Im a little confused. You can add two of the same rational number like (1/2) and (1/2) and get an integer. Now your out of the vector space. Where is my logic failing me?