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March 1st, 2016, 09:06 PM   #1
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Percentage Transformation

I discovered ages ago that any percentage value has a counterpart.

Let us say we have a number family, X, Y, and Z.

Z is what percentage Y is of X. The thing with this number family, is that while knowing any two, the third is easy discern, X and Y can not be swapped.

Well, it is quite often that I might know Z and one of the others, I might also want to know Z if Y and X were reversed.

Basically, if Y is 125% of X, then X is what percentage of Y?

If you know X or Y, you can find the other, flip them, then find Z again. But I have found the relationship between the two percentages.

So now, there is a number family of four, X, Y, Z, and A. Z is the percentage Y is of X, and A is the percentage X is of Y.

Z = 1- (A-1/A)

No need for a reversal as you can swap A and Z and it still works (which makes sense of course).
So what do you all think of this? Neat right?
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March 3rd, 2016, 12:06 AM   #2
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Your formula doesn't make a lot of sense. Say $A = 80%$. Then $Z = 1 - 80 + \dfrac{1}{80} < 0$. How does that work?
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March 4th, 2016, 06:20 AM   #3
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How exactly did you derive that from my formula?

What it should be,
Z=1-(A-1/A)
Z=1-(80-1/80)
z=1-(79/80)
z=1-(.9875)
z=.0125

If you get something else, then a mistake was made somewhere.
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March 4th, 2016, 06:27 AM   #4
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Hmm, I see two mistakes, one mine one yours. I normally do programming math, so I forgot that division would be done before subtraction outside of programming.

Your mistake was adding rather than subtracting, but could have been a typo.
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March 4th, 2016, 06:00 PM   #5
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Quote:
Originally Posted by MystMage View Post
I discovered ages ago that any percentage value has a counterpart.

Let us say we have a number family, X, Y, and Z.

Z is what percentage Y is of X. The thing with this number family, is that while knowing any two, the third is easy discern, X and Y can not be swapped.
That is true of any "non-commutative" binary operation.

Quote:
Well, it is quite often that I might know Z and one of the others, I might also want to know Z if Y and X were reversed.

Basically, if Y is 125% of X, then X is what percentage of Y?
You have swapped Y and Z here! If Y is 125% of X Then Y= 1.25X. To find solve for X, divide by 1.25= 5/4. X= Y/1.25= (4/5)Y= 0.80Y. X is 80% of X.

Quote:
If you know X or Y, you can find the other, flip them, then find Z again. But I have found the relationship between the two percentages.
Yes, if Y is a% of X then then X is 1/a % of Y.

Quote:
So now, there is a number family of four, X, Y, Z, and A. Z is the percentage Y is of X, and A is the percentage X is of Y.

Z = 1- (A-1/A)
I'm not quite sure what you mean here. Are you saying then that Y is 50% of X then X is 1- (.5- 1/.5)= 1- .5+ 2= 3- .5= 2.5 or 250% of X? That is clearly not true. If Y is 50% of X then Y= 0.50X so X= (1/.50)Y= 2.00Y or X is 200% of Y.

Quote:
No need for a reversal as you can swap A and Z and it still works (which makes sense of course).
So what do you all think of this? Neat right?
If you mean what I suggested above, it is not correct. If you do not mean that what do you mean by "Z= 1- (A-1/A)"? If Y is 30% of X, what is your "A"? What is "Z"?

Last edited by Country Boy; March 4th, 2016 at 06:02 PM.
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March 4th, 2016, 07:01 PM   #6
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The error I refered to I guess wasn't clear, I didn't include a pair parenthesis, so try this,
Z = 1- ((A-1)/A)

Of course, you doing Y=ZX works, if you know two of those values.

The equation I came up with is good if you don't know X or Y, just Z but want to see the percentage in the reverse direction.
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