Name of the mathematical term $\frac{a-b}{a+b}$

Question

I calculated a kind of proportion between $a$ and $b$, not $\frac{a}{b}$ but

$$\frac{a-b}{a+b}$$

Do this mathematical term has a name? If so, it would help me to explain my calculations...

Answer 1

$${{a-b} \over {a+b}}$$ can be split into ${a \over {a+b}}$ and $-{b \over {a+b}}$. These two terms are the Percentage Fractions. The term with $a$ in the numerator could also be considered as a probability.

Answer 2

I think you could safely call this "the relative difference of $a$ and $b$," at least if both are positive.

I say "relative difference" because it's clearly related to the difference, but it's scaled by the size of the numbers: if you doubled both $a$ and $b$, you'd get the same result. (Put differently, if $a$ and $b$ are measurements, it doesn't matter whether you use a yardstick or a meter-stick to take them, because the relative difference will be the same.)

By the way, this "relative difference," if both are positive, will always be between $-1$ and $1$.

Despite this, I'm not certain that giving this thing a name is a particularly good idea, unless you need to write about it in a long paper where it's going to be used multiple times, and need to save space.