Of Geometry and an odd occurance

That odd occurance being me actually WANTING To remember Geometry!

I was helping a friend the other day with her geometry studies for her grad-entry-thingamawhatsis, and i realized just how damn much i missed doing complex math.

Quite honestly it was almost like one of those eureka moments and was VERY surprising considering that i really didn't like Geometry at all when i was taking it in high school.
(being 1 of 2 freshmen inside of a class full of juniors and seniors was not my idea of a fun time back then....)

Mental note:
Whenever doing fractions, always make sure that the first fraction doesn't cause the second to become a negative. In this case it's one of those really unusual rules in which you can do subtraction before addition.

The Problem:

(1/16) - (3/4) + 1(7/8)
(basically one-sixteenth minus three-fourths plus one seven-eights)

The first step is to simplify the problem by getting rid of the mixed number.
This can be done by multiplying the whole number by the denominator (lower half) and then adding it to the numerator (higher half).

This would be ((1)(8) + 7)/8 = 15/8

This leaves us with:
(1/16) - (3/4) + (15/8)

so now that we have everything as a fraction, we can move onto the lowest common multiple. (in order to make sure that all of them can be easily added/subtracted).

In this case the lowest common multiple for the denominators (remember the denominator is the second half) would be "16".

In order to set this up we get the following:
(1/16)(1/1) - (3/4)(4/4) + (15/8)(2/2)

This leaves us with:
(1/16) - (12/16) + (30/16)

Now we move onto the "trick" part. In normal mathmatical sequence addition is done before subtraction.
HOWEVER, one thing that i did not remember (And i was tearing out my hair thinking about it), is that this rule doesn't apply to the VERY FIRST STEP if a number will return NEGATIVE.
(In a case like this we would make the number negative first, then continue on normally.)

The wrong answer would have been 41/16.
This is only obtained if you do the addition first and the subtraction last.

the CORRECT answer is actually 19/16.

solution:
(1/16) - (12/16) + (30/16)
- (11/16) + (30/16)
= 19/16

When i kept doing this in my head i just couldn't figure out why the decimals would always end up to the equivalency of 19/16.......stupid me eh?

It wasn't until siobhan said something after i kept saying "that's weird...it keeps ending up negative.....", that i finally understood what the hell my mind kept wrapping itself around.

Doy!