# Properties of subtraction?

by lLovePhysics
Tags: properties, subtraction
 P: 167 Are there any communative properties of subtraction because there are many formulas like the slope and distance formulas where you can switch the two terms around right? For example: Slope Formula: $$m=\frac{y1-y2}{x1-x2}$$ You can switch the terms around so that it would be y2-y1, x2-x1 right? Also for the distance formula: $$\sqrt{(x1-x2)^{2}+(y1iy2)^{2}$$ Btw, the numbers are suppose to be subscripts.
 Mentor P: 8,262 No, subtraction does not commute, but you could say something like $|x-y|=|y-x|$. The reason you can swap the terms in the first equation you give is, since y1
 P: 2,048 Subtraction is not commutative. In your example of the slope formula, you're just multiplying the numerator and denominator by -1. In the case of the dist. formula, you're using the property the square of any non-zero real number is positive. P.S. For subsripts, use underscore, as in x_1. $$x_1$$
HW Helper
P: 1,422

## Properties of subtraction?

 Quote by lLovePhysics Are there any communative properties of subtraction ...
Well, as others have pointed out, the answer is no, there isn't. You can pick up a simple example and see:

3 - 2 = 1
whereas: 2 - 3 = -1.

Well, 1 and -1 are, of course, different. So, no, subtraction is not commutative. :)
 HW Helper Sci Advisor P: 4,281 But you can also see that $$3 - 2 = - (2 - 3)$$ which you can read as shorthand for $$-1 \times (2 - 3).$$ Now this does always hold and explains why the formulas in your first post work out: What happens if you multiply numerator and denominator by the same number in a fraction? What happens if you square the opposite of a number (e.g. $x^2 = x \times x$ versus $(-x)^2 = (-x) \times (-x)$.

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