SOLUTION: Something makes no sense to me, or rather seems to be circular reasoning. My book say that to subtract signed numbers we add the opposite, so, a-b = a+(-b) but then a little furt

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Question 1132383: Something makes no sense to me, or rather seems to be circular reasoning.
My book say that to subtract signed numbers we add the opposite, so,
a-b = a+(-b) but then a little further down it says that a+(-b) usually simplifies to a-b
so we have a-b= a+(-b) which simplifies to a-b
why bother with the middle step at all if given a-b?
and why simplify a+(-b) if it is in the form we want for the operation?
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The numbers can be represented as addition or subtraction on a number line. Your book is probably preparing you to understand Additive Inverse.

a+(-a)=0, and a and -a are additive inverses of each other.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
they're just trying to tell you that the operations are equivalent.

a + (-b) is the same as a - (+b)

+b is usually written as just b (the + is implied).

therefore a + (-b) is equivalent to a - b and a - b is equivalent to a + (-b).

you'll get the same answer regardless of which operation is done first.

as long as you understand what they're talking about, then don't worry about it.