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why is a negative times a negative a positive number

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why is a negative times a negative a positive number

Guest Oct 13, 2014

#5
+81022
+5

The first "-" was supposed to be a dash......I can see how that is confusing....I'll edit that !!!

Thanks for pointing it out, Melody !!!

CPhill  Oct 13, 2014
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#1
+91454
+5

this can be demonstrated in many ways.

Normally I wiould show you with number patterns.

Today I'll try something different - logic

Say you borrow 'parcel' of \$3 from your mum.  You borrow 5 parcels of \$3 altogether.

If you owe someone money than this is a negative amount  that you have (really don't have)

So you now have      5*-\$3 = -\$15

Now you want to get rid of this debt you want to SUBTRACT this debt (get rid of it). Then you will have nothing (and owe nothing)

so    -15-(-15)=-15+15=0

(5*-3)-5*-3=0

but      20-2 is the same as  20+(-2)

that is

(5*-3)+(-5*-3)=0

-15+ [    ]=0

well 15 has to go in the box so -5*-3=+15

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I expect that is about as clear as mud.   LOL

I don't think i will try to explain it that way again.

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I have answered differently in the next post.

You can comment on my answer if you are there.  Think about it a little first though.

Melody  Oct 13, 2014
#2
+91454
+5

3*2=6

3*1=3

3*0=0

continuing the pattern

3*-1=-3

3*-2=-6

etc

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now

-2*3= -6       I just did that one

-2*2=-4

-2*1=-2

-2*0=0

continuing the pattern

-2*-1=-2

-2*-2=-4

hence a neg times by a negative is a positive

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Is that more help?

Melody  Oct 13, 2014
#3
+81022
+5

I like to explain it in this manner:

Suppose we have a  30 gallon bucket half full of water that has a hole in the bottom.. And water leaks out of the bucket at one gallon per minute  →   (-1) gallon per minute.

And suppose that time going forward is positive, and time going backward is negative.

So, five minutes from now, the bucket will contain (-1)*(5) = -5 gallons less than it does now.

But, 10 minutes ago, the bucket contaned (-1)*(-10) = 10 gallons more than it does now.

So, in the first case, a negative times a positive is a negative. And in the second case, a negative times a  negative is a positive !!!!

CPhill  Oct 13, 2014
#4
+91454
+5

Where did the -(-1) come from Chris?

I like the rest of the explanation.

Melody  Oct 13, 2014
#5
+81022
+5

The first "-" was supposed to be a dash......I can see how that is confusing....I'll edit that !!!

Thanks for pointing it out, Melody !!!

CPhill  Oct 13, 2014
#6
+91454
0

Melody  Oct 13, 2014

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