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March 1st, 2016, 09:06 PM  #1 
Senior Member Joined: Nov 2015 From: USA Posts: 107 Thanks: 6  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 (A1/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? 
March 3rd, 2016, 12:06 AM  #2 
Math Team Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 
Your formula doesn't make a lot of sense. Say $A = 80%$. Then $Z = 1  80 + \dfrac{1}{80} < 0$. How does that work?

March 4th, 2016, 06:20 AM  #3 
Senior Member Joined: Nov 2015 From: USA Posts: 107 Thanks: 6 
How exactly did you derive that from my formula? What it should be, Z=1(A1/A) Z=1(801/80) z=1(79/80) z=1(.9875) z=.0125 If you get something else, then a mistake was made somewhere. 
March 4th, 2016, 06:27 AM  #4 
Senior Member Joined: Nov 2015 From: USA Posts: 107 Thanks: 6 
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. 
March 4th, 2016, 06:00 PM  #5  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  Quote:
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Last edited by Country Boy; March 4th, 2016 at 06:02 PM.  
March 4th, 2016, 07:01 PM  #6 
Senior Member Joined: Nov 2015 From: USA Posts: 107 Thanks: 6 
The error I refered to I guess wasn't clear, I didn't include a pair parenthesis, so try this, Z = 1 ((A1)/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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