Name (or proof) of $\frac{a}{b} - 1 = \frac{a-b}{b}$

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).

• Get a common denominator. Feb 9 '21 at 19:28
• I doubt this particular equation has a name, as it's an extremely simple rewrite of an expression as a single fraction. Feb 9 '21 at 19:29
• 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. Feb 9 '21 at 19:33
• I agree with @Randall ... you can call it "common denominator" if you need a name. Feb 9 '21 at 19:37
• @nimo23 why is one "roundabout" and the other "elegant"? This is just subtracting fractions as in grade school. 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.