Negative + Negative = Positive

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kimba

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I understand the subject RULE, but it makes no sense to me.

If I owe Kathy 6 apples, and Mary 5 apples but I have no apples then the equation is -6 + - 5, I owe 11 apples, but with the rule negative plus negative equals positive I HAVE 11 apples. Can anyone explain to me how this makes sense?
 
It doesn't make sense, in large part because it isn't true. While the product of two negatives is a positive, the sum of two negatives is another negative.
 
Can you define the difference between "product" and "sum"?

I am a person that must understand: why. Why does -6 + - 5 = 11 not -11? I am facing a wall moving beyond this point if I do not understand the rule, I can memorize the rule, but without it making sense, as I try to move on, this will cause no end of problems.
 
kimba said:
Can you define the difference between "product" and "sum"?

I am a person that must understand: why. Why does -6 + - 5 = 11 not -11? I am facing a wall moving beyond this point if I do not understand the rule, I can memorize the rule, but without it making sense, as I try to move on, this will cause no end of problems.
Click to expand...

Stapel clarified your point, the sum of -6 + (-5) = -11 (negative)

The product of -6 x (-5) = +30 positive
 
kimba said:
Can you define the difference between "product" and "sum"?

I am a person that must understand: why. Why does -6 + - 5 = 11 not -11? I am facing a wall moving beyond this point if I do not understand the rule, I can memorize the rule, but without it making sense, as I try to move on, this will cause no end of problems.
Click to expand...

The reason you are facing a wall is because your understanding is correct, but the rule you are trying to fit into it is wrong.

Wrong : NEGATIVE + NEGATIVE = POSITIVE.

Correct : NEGATIVE x NEGATIVE = POSITIVE.

Correct : NEGATIVE + NEGATIVE = NEGATIVE.

You are wise to try to understand rules, not just memorise them. Keep it up!
 
Re: Negative x Negative = Positive

DrMike said:
Correct : NEGATIVE x NEGATIVE = POSITIVE.
Click to expand...

I'm curious, why a negative times a negative a positive? how would you explain that to a 3rd grader without simply saying, its a rule so do it? Any one have any good methods?
 
Re: Negative x Negative = Positive

mse.myers said:
DrMike said:
Correct : NEGATIVE x NEGATIVE = POSITIVE.
Click to expand...

I'm curious, why a negative times a negative a positive? how would you explain that to a 3rd grader without simply saying, its a rule so do it? Any one have any good methods?
Click to expand...

We recently had a LONG discussion about this topic on these boards.

Third graders typically do NOT deal with negative numbers, so I would not even attempt an explanation at the third-grade level.

A Google search for "why is the product of two negative numbers positive?" will probably turn up WAY more information than you'll even care to look through.
 
If the temperature is 3 degrees and it drops to -4 degrees, what is the temperature drop?
We find the difference by subtracting the lower temperature from the upper one.

3-(-4) has to be 7 degrees since it takes a 3 degree drop to get to zero and a further 4 degree drop to get to -4.
Therefore 3 -(-4) is definately 3+4 because of that.

That is why negative and negative together in that way is positive.

If the temperature dropped by 4 degrees 3 times, the overall drop is 12 degrees.
We are successively subtracting 4, so we can write -4-4-4 = 3(-4) which we know is -12
reflecting the 12 degree drop.
Same thing if I have 25 apples and I give 3 each to 4 people,
I will have 20 -(4)(3) = 20-12=8 left

How do we multiply two negative numbers? say -3 by -4 ?
Well 3(-4) is subtract 4 three times, -12.
-{3(-4)} can be written (-3)(-4) which is "Do the opposite of subtract 4 three times",
in other words "Add 4 three times" or "Add 3 four times".
Addition and subtraction are opposites.

This is what we mean by (-)(-)= + and -- = +
Multiplying two negatives is the same as multiplying the positives of those values.
Subtracting a negative is the same as adding the positive of it.

-6+(-5) = (-1)(6+5) =(-1)(11)= -11
6-(-5) = 6+5 =11 the difference between 6 degrees and minus 5 degrees.
It's obvious logically.
Then you put that logic into math code.
So, you must understand what the math language means in English
 
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