# The product of integers question about why....

Hello all,

I saw a tweet this weekend and I wondered how many of you have encountered this situation.

The product of a (+) and (-) integer is negative: 3(-2) = 3 (-2)s = -2,-2,-2, = -6. None of the explanations of (-)(-) = (+) that I know are convincing to me in this intuitive way. How are you convinced that (-)(-) = (+)?

Thoughts?

Brooke

### I'm easy to convince.  …

I'm easy to convince.   Taking away a bad thing is like giving me a good thing.   I learned to draw two extra vertical lines in there and then finish with a curvy smiley face mouth that looks like I'm really happy and drunk (that's what appealed to me in seventh grade, anyway ;)) ….
If I've been using 2 cups of bird seed a day for the past seven days.... how would I figure out how much bird seed I had a week ago?   Would I have more, or less?

Brooke, I just watched an instructional video that said when multiplying two negative numbers, you factor out a -1 from each and they cancel each other leaving you with a postitive number.  See here: https://mathantics.com/lesson/integer-multiply-and-divide

I have never seen it explained/demonstrated this way.

Gayla

What would happen in the example if it was 2(-2)?

2(-2) = 2(-2)s = (-2)(-2) = +4.  Hmm.

This issue is they are changing the 3(-2) = 3(-2)s but it should be equal to (-2) + (-2) + (-2). Multiplication is repeated addition. To correct my example: 2(-2) = 2(-2)s = (-2) + (-2) = -4. Hope this might shed some light.

### Using money is always good

Another way of explaining this is if someone borrows money that person owes money.  Debt is a negative number.  Then the person who lent the money says, I cancel your debt.  It is like the borrower got extra money.  A way of explaining this to remember is:

If something good happens to someone good that is good