I have recently read through much of Edmund Landau's Foundations of Analysis but have wondered if there is a more intuitive order of defining fractions, division, negatives, subtraction, etc. Is there a book, website or even a video series anyone can recommend that presents such an order and clear motivation for all definitions?
For instance, I wonder if it is more intuitive to define fractions first or the operation of division.
Also, multiplying -1 by 3 makes sense: -1+-1+-1 but multiplying 3 by -1 doesn't seem as straightforward. I would like a clear motivation for defining it. Should the definition be motivated by the fact that multiplying a positive number by -1 is the same as subtracting twice the number: a * -1 = a - 2(a)