Q:

What should I study to fully understand the rules of division between two real numbers

I'm struggling to explain to a child the rules of division, why we add 0's , decimal points, and when we do those things. I know how to do it by memory, but I can't justify those steps.  ( I think it is called long division. ) I need to understand the rules.  All the material that I found so far are for kids, I feel like I need a more mature view about this algorithm. Thank you

A:

I would highly recommend Sybilla Beckmann's book "Mathematics for Elementary Teachers".
This is a college level book specifically addressing all of your questions:  they "why's" of elementary school mathematics.  Included are explanations of the meaning of the 4 basic operations, why the standard algorithms for computing these operations make sense, etc.

