Math: Fractions

1~ To answer why 6/7 * 7 = 6

I ended up concluding that in the essence of in the fraction 6/7 represents a number that falls short of another number.  The goal number, or the ideal number (in our heads) would be for it to be 7/7, which would make it a complete unit.  6/7 is a number falling 1 (seventh) unit short of 7/7.  When you multiply 6/7 times that denominator (which is the standard of ideal) 7, the lack is “clearly” and beautifully evident.  The number ends up being 6 (as a whole unit); the lack of 6/7, is unitly evident in 6, but you have to understand 6 not only as a unit number in itself, but you must see 6 as 7 with a lack of  1 (6 = 7 -1). 

2~ You have answered why 6/7 * 7 = 6 but that does not answer why 7 * 6/7 = 6

7 * 7/7 = 7.  7 * unit = the original number itself.  6/7 is a representation of lack, it lacks from the wholy unit 7/7. So now, when you multiply 7 times a unit whole, it will be all of seven, but when you mulitiply 7 times a representation of lack, the result will be lack of 7, how much of the lack of 7 will it be (you ask)?, well the answer lays in the symbol itself, 6/7 lacks 1 (seventh) unit out of 7/7 so the lack from 7 will be 1 unit only.

3~ You have answered why 6/7 * 7 = 6 but that still does not let me picture it physically.

To answer this I must be able to hold a visual representation of 6/7 and how it fill each step as it is being multiplied.  But 6/7 is way too complicated to hold in mind so we will first get an idea of how it is suppose to be by looking at 2/3 * 3:

[1][1][2] - [2][3][3]

With 2/3 it is easy to see how the fractions fit nicely into the integer, by the second addition, 2/3 splits equally in half between the first section and the second section; and by the third addtion, the 2/3 ends with a tightly packed symmetry to complete the section.  It is easy to see, but there is also not much to see.  But the question still stands, why do fraction additions have this property?

Now the same two whole-units: [][][] - [][][]

Can be filled by 3/3 * 2:

[1][1][1] - [2][2][2]

And by 1/3 * 6:

[1][2][3] - [4][5][6]

now 6/7 in the unit representation of wholes would be in the following order.

[1][1][1][1][1][1][2] - [2][2][2][2][2][3][3] - [3][3][3][3][4][4][4] - [4][4][4][5][5][5][5] - [5][5][6][6][6][6][6] - [6][7][7][7][7][7][7]

I think that the story in here is to describe how the god unit ends up matching up with the God unit.

The way to explain this would be to assume that the Universe is 6

({} - {} - {} - {} - {} - {})

The only reason why 7 is relevant in matching up the fraction with the Universe, is because that is what you are dividing each unit the Universe into

({[][][][][][][]} - {[][][][][][][]} - {[][][][][][][]} - {[][][][][][][]} - {[][][][][][][]} - {[][][][][][][]})

So that 7 6/7’s fit evenly into it

({[*][*][*][*][*][*][+]}  {[+][+][+][+][+][*][*]}  {[*][*][*][*][+][+][+]}  {[+][+][+][*][*][*][*]}  {[*][*][+][+][+][+][+]}  {[+][*][*][*][*][*][*]})

 but 7 really has no relevance except that it is the one you have chosen to imagine.

The Universe could have worked just as well with 6/9 * 9

({[*][*][*][*][*][*][+][+][+]} {[+][+][+][*][*][*][*][*][*]} {[+][+][+][+][+][+][*][*][*]} {[*][*][*][+][+][+][+][+][+]} {[*][*][*][*][*][*][+][+][+]} {[+][+][+][*][*][*][*][*][*]})

And even 6/4 *4

({[*][*][*][*]}  {[*][*][+][+]}  {[+][+][+][+]}  {[*][*][*][*]}  {[*][*][+][+]}  {[+][+][+][+]})

(notice how the set of sections have the numbers filled in with symmetry; this lets me know that there is a whole [where the symmetry is complete), But I am still unsatisfied with this answer because you begin by assuming that the Universe is 6.  I want my answer to start with 6/7 and only 6/7 and tell me how one would know how many times would it be necessary to accomplish the whole-unit and which whole-unit will it end up in.

So what is there to see from plain old

[1][1][1][1][1][1][*]

If we start by assuming that the Universe is from 0-1

0[][][][][][][]1

 and it has some line “randomly” drawn through the middle

0[][][][][][]X[]1

What can we learn from this randomly drawn line; how can it tell us of a symmetry that lays outside of the existence of the Universe? where and how will the symmetry be complete; and since we can not imagine what is outside our Universe of 0-1, what  will “symmetry” look like inside this Universe on its own.

6/7 - 1&5/7 - 2&4/7 - 3&3/7 - 4&2/7 - 5& 1/7 – 6

Notice that the turning point of where the fraction crosses over to its lesser half, in a body of 7 the half lies between 3 and 4 and the half of the body of 6 (as in the diagram) the half lays exactly between 2&4/7 and 3&3/7 or 18/7 and 24/7; which now would be 3 notice that when counting in units of 6/7, the fractions never touch the half of 6 (which is 3); I think this is because the god unit being used is not 1, but 6/7; but if it does not touch the half point just because it is god unit “whole” why is it still able to touch 6?

Two roads: answer why 6/7 * 7 = 6 and answer the relevance of this to any other fractions and their patterns like, the steps that a fraction like 6/7 takes as opposed to the steps a fraction like 1/7 takes.

God units and god units, there are no such things as integers (God units [integers] dont exist outside of our imagination).

Multiplication: the becoming of one another.

Lets once again look at 2/3 * 3:

[1][1][2] - [2][3][3]

 And 3/3 * 2:

[1][1][1] - [2][2][2]

And 1/3 * 6:

[1][2][3] - [4][5][6]

Now the same two whole-units: [][][] - [][][]

If you have noticed, the numerators of the fractions mulitiplied (2*3, 3*2, 1*6) yields the total number of sub-units of the sections; and the denominator, as always understood, defines the Whole-unit in terms of the sub-units.

Last Saved: 3/23/2009