multiplying negatives

heatherthet said:
Why does a negative times a negative equal a positive?
Click to expand...
What else could it equal? :wink:
 
Yes. It does.
Here's a trick I learned in Pre-Algebra

Okay you know how the tic-tac-toe board looks like, rigth?

On the top left write P and on the middle write P on the bottom right write P
on the rest write N's.

(I suggest you write it down in your notes)


I like being helpful..so yeah.
 
GlennJ said:
… Here's a trick I learned in Pre-Algebra …
Click to expand...


Thanks for the chuckle, Glenn.

(I'm curious to know the "trick" that you use for recalling the sign of a positive times a positive.) :twisted:

Here's the "trick" about the sign of a product of two factors that I learned in pre-algebra:

Same signs: positive
Different signs: negative

 
I know that a negative times a negative equals a positive, I know the rules.

My questions is why? What's the theory behind it?
 
heatherthet said:
My questions is why? What's the theory behind it?
Click to expand...
Perhaps it's looked at this way:
-(2 times -4)
remove - 4 twice
say you remove -4 twice from -20; so you're left with -12 : a positive effect :idea:
guess it's time for me to hit the sack...
 
heatherthet said:
I know that a negative times a negative equals a positive, I know the rules.

My questions is why? What's the theory behind it?
Click to expand...

We know that

-2 + 2 = 0

Suppose we multiply both sides of the above statement by -4:

-4(-2 + 2) = -4*0

We know that the product of 0 and any number is 0, so

-4(-2 + 2) = 0

Use the distributive property on the left side:

(-4)*(-2) + (-4)*(2) = 0

And it's rather easy to demonstrate that (-4)*2 = -8; if you start at 0 on the number line and move 4 units to the left (that's -4) TWO times, you will surely end up at -8. So,

(-4)*(-2) + (-8) = 0
The only way this statement can be true is for (-4)*(-2) to be the OPPOSITE of -8, or + 8.

If that doesn't convince you, than I don't know what WILL.
 
heatherthet said:
My questions is why? What's the theory behind it?
Click to expand...


Yes, Heather; we understand your question. Denis already responded to your question, some time ago.

Are you now telling us that, in all of the information provided by Denis, you still cannot find a satisfactory answer?

(Perhaps, you never tried. I dunno.)

 
You're right, I didn't look at the links on google that Denis posted. Thank you Denis.

My actual situation is that my math teacher assigned us a project in which we had to find a math help website and ask the tutors "why does a negative times a negative equal a positive". Then we are supposed to give her the responses and explanations we received from the website, so that is why I asked again.

Thank you for your help though! The google link was the most helpful bit of information.
 
heatherthet said:
You're right, I didn't look at the links on google that Denis posted. Thank you Denis.

My actual situation is that my math teacher assigned us a project in which we had to find a math help website and ask the tutors "why does a negative times a negative equal a positive". Then we are supposed to give her the responses and explanations we received from the website, so that is why I asked again.

Thank you for your help though! The google link was the most helpful bit of information.
Click to expand...

You didn't look at the links provided, I guess.

You didn't read my response either, I guess.

That is how I explained to my students WHY a negative times a negative gives a positive result. THEY got it.

Oh well.
 
heatherthet said:
… my math teacher assigned us a project in which we had to find a math help website and ask the tutors "why does a negative times a negative equal a positive". Then we are supposed to give her the responses and explanations we received from the website …
Click to expand...


OIC. We're Guinea pigs.

And the reason that you asked again is why? Instead of simply reporting Denis' response, it seems to me that you're interpreting the project instructions as "repeatedly ask the tutors the same question until you decide to stop" ? :roll:

Are we done now?

 
"Minus time minus equals plus
The reason for this, we won't discuss!"

Axiom : The definition of negation : x + (-x) = (-x) + x = 0.

Theorem 1 : -(-y) = y.
Proof : Letting x = -y in the definiton of negation, -y + (-(-y)). Letting x = y in the definition of negation gives (-y) + y = 0. Therefore, -y + (-(-y)) = -y + y, so (by the cancellation law) -(-y) = y.

Axiom : The distributive law : a(b+c) = ab+ac
Axiom : Multiplication by zero : a.0 = 0.

Theorem 2 : a(-b) = -ab.
Proof : Let c = -b in the distributive law.
Then 0 = a.0 = a(b+(-b)) = ab + a(-b)
Therefore, a(-b) = -(ab), from the definitaion of negation.

Axiom : The commutative law : xy = yx.

Theorem : (-a)(-b) = ab.
Proof :
From Theorem 2, (-a)(-b) = -((-a)b)
From the commutative law, this equals -(b(-a))
From Theorem 2 again, this equals -(-(ba))
From the commutative law again, this is -(-(ab))
From Theorem 1, this is ab. Therefore, (-a)(-b) = ab.
 
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