Understanding My Unusual Way of Thinking

     I've always had an unusual way of thinking, but I haven't always understood that.  One particularity of this is that I can change the way I think, going creative one second and logical the next.  Sometimes, this is a plus, but, to people who cannot work on my wavelength, it can be a bother.  It can hurt me too, if I have trouble shifting from one 'gear' to the next as it wore.  Let me show you an example.  During my years of working in retail, I have to apply various discounts and taxes to products.  While the cash register can easily handle this task, I sometimes have to estimate these amounts before keying the numbers in.  While it doesn't matter what order you perform the operations, I always put the discount in before the tax, as that is the way the register is set up.  Now, I don't remember being taught this in school.  Maybe I was absent that day, or I ignored the lesson because I was allowed to skip ahead a few chapters at times in the textbook.  Whatever the reason, I only really focused on this fact well after I was out of school.  While the order is unimportant, I have not really seen any explanation for it, probably because the long way of explaining just how to figure these totals out isn't really up to thorough examination.  For example, you want to buy something that is $10 with a 10% discount but with a newly added 10% sales tax.  Traditionally, one would be taught to first find out what 10% of $10 is [$10 x 0.1 = $1] then subtract that to the price [$10 - $1 = $9].  Next, you would find out the tax [$9 x 0.1 = $0.90] and add that to find the final total [$9 +  0.9 = $9.90].  Or, if the operations were done in the opposite order, tax first [$10 x 0.1 = $1, $10 +$1 = $11].  Then, one calculates the discount [$11 x 0.1 = $1.10] and subtracts [$11 - $1.10 = $9.90], you get the same total.  However, no one really explains why.  I don't do the math that way.  Normally, I do it like this.  When asking what a 10% discount is, you are really wondering what is left [100 - 10 = 90].  So, I multiply by 90% directly instead of subtracting 10%.  The same goes for a 10% tax [100 + 10 = 110].  This time, I multiply by 110%.  If you perform the operations this way, you still get the same totals no matter if you take the discount first or the tax first [$10 x 0.9 = $9, $9 x 1.1 = $9.90 or $10 x 1.1 = $11, $11 x 0.90 = $9.90].  Now, for those of you who forgot third grade math, this is the associative property of multiplication.  If you need to multiply three or more numbers, the order doesn't matter.  You still get the same answer [1 x 2 x 3 = {(1 x 2) x 3} or {(1 x 3) x 2} or {(2 x 3) x 1}].  So, from the example, $10 x 0.90 x 1.1 = $9.90 no matter how you multiply.  Now, if this were taught the way I think, the process makes much more sense with a strong foundation in basic math.  However, it doesn't 'show the work' as well, so I don't think this is the way it was taught in school.  At least in my time.  However, it does go to show that if someone says that their way isn't just the 'best' way but the 'only' way to achieve some solution or goal, they might be right, or it could just be their point-of-view.  Without showing exact proof, it could go either way.  There might be another way of achieving the same goal, just as fast but easier and with the same amount of proof.