Negative times negative?? If i can write 3*3=9 as 3+3+3=9 How do i write for the -, like (-3)*(-3)=9?

Galery

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Mar 7, 2019
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If i can write, for example 3*3=9 as this 3+3+3=9
How do i write for the -, like (-3)*(-3)=9 how do i write the equation as the first one?
 

Dr.Peterson

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You can't, really. It is only for natural number multipliers that you can equate multiplication with repeated addition.

But you can come close.

Multiplying -3 by 3 can be thought of as starting with 0 and doing 3 additions of -3: 0 + -3 + -3 + -3 = -9. Multiplying -3 by -3 can be thought of as undoing 3 additions of -3: 0 - -3 - -3 - -3 = 9, just as subtraction can be thought of as undoing an addition, and adding a negative number as undoing an addition of a positive number.
 

Jomo

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Dec 30, 2014
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Here is how I think of it. -3 is the additive inverse of 3.
So -3 = -(3)(the additive inverse of 3)
Now (-3)(-3) = -(3)(-3) = -{(3)(-3)} ie the additive inverse of (3)*(-3) which is the additive inverse of -9 (-9 is obtained by repeated addition of -3) which is 9
 
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