# mathematical and computing sciences question #5271

Jackson, a 17 year old male from Imphal asks on April 26, 2011,

Q:

In my algebra, I learn that (-3 X -2) = +6 but (-3 X +2) = -6, why?

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Aaron Abrams answered on April 27, 2011, A:

There are lots of ways to answer this. Here is one:

If you start with a number like say 0, and then you add -3 and then add -3 again, then you have added -3 twice, or in other words 2 times -3. And where are you? You are at -6. So this is why 2 x -3 = -6.

Then, if you want to know about something like -2 x -3, you can think of -2 as -1 x 2, and so you have -1 x 2 x -3. The last part, 2 x -3, we already figured out is -6. So you have -1 x -6, which is +6.

And here is a somewhat fancier way to think about it:

You can think of addition and multiplication as "doing something" to the number line. For instance adding 4 slides the number line to the right by 4 units. If you started at 6, then after you add 4, you are at 10. If you started at -5, you will end up at -1.