View Full Version : "Opposite Numbers"
05-09-2006, 10:25 AM
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 :?:
05-09-2006, 10:30 AM
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.
05-09-2006, 11:55 AM
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?
05-09-2006, 11:58 AM
What is the difference between (3) and -3 ?
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.
05-09-2006, 12:54 PM
aHA! I thinkI have it. Thanks. John
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