I need a name for (a-b) = - (b-a)?

Question

I'm collecting together a list of math ideas that are later used in higher science courses.  One of the ideas is (a-b) = -(b-a).

The operation is fairly simple.

If a=33 and b=11:

(33-11) = -(11-33)
(22) = -(-22)
22 = 22

I need an official name for this (example: I consider "associative law of addition" to be an official name).  I'm in a catch 22 because I can't google this without knowing the name.  

I specifically need a name for this idea, not the name of something related or the name of something leading to it.

Thank you.

Rita the dog · Accepted Answer

I don't think this has a name.  There are two things involved.  First that for any number c, -c = (-1) c.  And second that (-1)(b-a) = a-b which, in fact, is the distributive law of multiplication over addition.  Note, use c = b-a above to get -(b-a) = (-1)(b-a).

Jared · Answer

I would say distribution because you show equality by distributing the negative:

-(b - a) = -b + -(-a) = -b + a

From there is equal due to commutivity of addition.

? · Answer

Something with negative. Like "the negative parenthetical law"

Anonymous · Answer

i could be wrong....but i think this is called algebra.

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I need a name for (a-b) = - (b-a)?

4 Answers