Learning math with logic

When you're taught how to do any kind of mathematics you begin with rules. Math it seems is full of rules. Rules on how to add numbers together. Start on the left side, carry the remainder, add the remainder, put the number in this column not that column, and the rules go on and on and on.The higher math you get into, the more the rules continue and the more complex they become. However, when you get into the real high math you're no longer learning rules, you're learning properties: additive, multiplicative, distribution, etc, etc, etc. No matter what mathematician you speak with they'll all tell you that the rules are merely tools. The rules are not the math, they just help you solve the problem. Is it possible to do math without rules?

The answer is a resounding yes. The easiest way to do math is logic. Most math wiz types will yell a loud and raucus "DUH" upon hearing this, because that's how they've been doing it all of their lives. These are the same kids who can't tell you how they got the answer, but the answer is right. These are the same people who failed math tests because they "did the work in their head" and not on the paper. How do they do this? Logic. How do you do math with logic? Well, here's an example: what is 25 + 45? Well, 5 and 5 is 10 and 2 and 4 is 6, so it has to be one more than adding the front numbers, and the answer is 70. The problem 5b=35 is also 5 X ? =35. You can use algebraic properties, or you can use your power of logic to come up with 7. Math wizez all over the world have written quick math tip books since the dawn of math books, and all they are teaching you is how they use logic.