Is it intuitively obvious that one quarter of 3 is the same as 3 quarters?

Yes it is elementary school level arithmetic, but does it agree with our instinct. Think of it this way. You need to divide 3 cupcakes among 4 people. Is it immediately apparent that you can do this by dividing each cupcake in quarters and giving each person 3 of them?
Here is an Excel sheet to indicate what is going on. Each row represents one cupcake and each column represents what is given to each person.