I don't know what tags to use for this question so if I am using the wrong ones, please suggest others.
I have a set of numbers (ex: -20, -3, 5, 8, 30). I need to make them greater than zero but preserve the ratios between them. However, if all I do is add 21 to each, the ratios change. For instance,
$5 / -20 = -0.25$
but
$26 / 1 = 26$ (added 21 to the above)
and
$8 / -20 = -0.4$
but
$29 / 1 = 29$. (added 21 to the above)
And if we divide -0.25 by -0.4 we get 0.625 while if we divide 26 by 29 we get ~0.897 so the ratios are not the same. Does anyone know how to preserve the ratios between the numbers in the set but make all the numbers positive?
Lets say we have the set {1,2,4,-8} we can see that the ratios including -8 will always be negative and the ratios not including -8 will always be positive eg. $\frac{-8}{2}=-4$ and $\frac{2}{4}=0.5$ so we cannot make -8 positive without changing the ratios, however if we ignore the negative sign using the absolute value function denoted as |x| then we don't have negatives eg. $\frac{|-8|}{|2|}=\frac{8}{2}=4=|-4|$ we will preserve the absolute values of ratios while not including negatives.