"Opposite Numbers"

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John Whitaker

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OPPOSITE NUMBERS: My "Complete Idiot's Guide To Algebra" p.9, states: "The opposite of a number is indicated by a lone negative sign out in front of it. For example, the opposite of -3 would be written like this: -(-3). The value of a number's opposite is simply the number multiplied by -1. Therefore, the only difference between a number and it's opposite is its sign."

They offer 2 samples; one of which is a fraction I can not duplicate here. The other is the one that puzzles me: -(4) = -4 I see the signs as the same. Can you explain what I don't see?

Thank you. John :?:
 
Seems pretty basic to me. Exactly where is your difficulty?
 
Think of a number line. Then if p is a point on that number line then –p is also on the line and is located the same distance from zero as p but on the opposite side of zero.
So what number is the same distance from zero as 3 but opposite zero? Well it is –3! Therefore –(3)=-3 and –(-4)=4 because 4 is the same distance from zero as –4 but on the other side of zero.
 
PKA Reply

I get you down to and including: “Well it is –3!” But -(3)=-3 throws me. What is the difference between –(3) and -3 ? Are they both not on the same side of zero?
John Whitaker
 
Re: PKA Reply

John Whitaker said:
What is the difference between –(3) and -3 ?
Click to expand...

They are exactly the same. It's just another way to represent it. I can represent a number such as "1" by writing "(-1)(-1)", but the result is still "1". Don't overthink it too much.
 
The reading of –(3)=-3 is “the negative of 3 is minus 3”.
The reading of –(-4)=4 is “the negative of minus 4 is 4”.
It is a matter of words.
 
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