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Properties of subtraction? 
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#1
Jul2507, 02:56 PM

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: [tex]m=\frac{y1y2}{x1x2}[/tex] You can switch the terms around so that it would be y2y1, x2x1 right? Also for the distance formula: [tex]\sqrt{(x1x2)^{2}+(y1iy2)^{2}[/tex] Btw, the numbers are suppose to be subscripts. 


#2
Jul2507, 03:05 PM

Mentor
P: 8,316

No, subtraction does not commute, but you could say something like [itex]xy=yx[/itex].
The reason you can swap the terms in the first equation you give is, since y1<y2 and x1<x2, swapping both the values of x on the top and y on the bottom will introduce a minus sign in both the numerator and denominator, which will cancel. In the distance formula, you are squaring the difference between x1 and x2, and y1 and y2, which will make sure the answer is always positive. 


#3
Jul2507, 03:08 PM

P: 2,046

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 nonzero real number is positive.
P.S. For subsripts, use underscore, as in x_1. [tex]x_1[/tex] 


#4
Jul2607, 02:23 AM

HW Helper
P: 1,422

Properties of subtraction?
3  2 = 1 whereas: 2  3 = 1. Well, 1 and 1 are, of course, different. So, no, subtraction is not commutative. :) 


#5
Jul2607, 02:53 AM

Sci Advisor
HW Helper
P: 4,300

But you can also see that
[tex]3  2 =  (2  3)[/tex] which you can read as shorthand for [tex]1 \times (2  3).[/tex] Now this does always hold and explains why the formulas in your first post work out:



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