Can someone tell me the name of the equation (or the proof) which I show here:

The equation is always valid:

$$\frac{a}{b} - 1 = \frac{a-b}{b}$$

I used $(a-b)/b$ to calculate the difference in percentage between $a$ and $b$. But it seems, that I can also use $(a/b) - 1$ (which return always the same result).

  • 2
    $\begingroup$ Get a common denominator. $\endgroup$
    – Randall
    Feb 9 '21 at 19:28
  • $\begingroup$ I doubt this particular equation has a name, as it's an extremely simple rewrite of an expression as a single fraction. $\endgroup$ Feb 9 '21 at 19:29
  • $\begingroup$ No official name for this? Most people tend to use the roundabout (a-b)/b to calcualte the percentage difference, I think because they are not aware of the elegant equivalent equation (a/b) - 1. $\endgroup$
    – nimo23
    Feb 9 '21 at 19:33
  • $\begingroup$ I agree with @Randall ... you can call it "common denominator" if you need a name. $\endgroup$
    – GEdgar
    Feb 9 '21 at 19:37
  • $\begingroup$ @nimo23 why is one "roundabout" and the other "elegant"? This is just subtracting fractions as in grade school. $\endgroup$
    – Randall
    Feb 9 '21 at 19:38

Its just $\frac{a}{b}-1=\frac{a}{b}-\frac{b}{b}=\frac{a-b}{b}$ as @Randall mentioned.


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