# the nature of numbers?

I am currently relearning basic math - including; fractions, decimals and percentages. I am learning from various different sources, and what gets me is that they only teach math in forms of methods. This bugs me because they teach you the 'how' and not the 'why'. There maybe a good method to divide two fractions with uncommon denominators, but there is no explanation of why the method works. I want to understand the process, not just learn it.

Question - are there any reliable educational sources that explain the logic behind the methods? Or in other words, is there a way to understand the nature of numbers and how they are calculated? In this way I can understand math, rather than just learning the methods to calculate numbers.

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Well, there's always Russell and Whitehead, Principia Mathematica. Of course, the drawback to explaining the logic behind the methods is that it took them over 500 pages to get to the proof that $1+1=2$. –  Gerry Myerson Oct 22 '12 at 11:46
In general khanacademy.org gives very good understandable lessons (and explanations) of basic mathematics. Maybe you should try this. –  André Oct 22 '12 at 12:02