what does it really means to multiply a negative number by a negative number (to get a positive number)?

Answer 1

Well, if by really mean you mean tangibly, then
5*5 can be thought of as, you have 5 buckets of 5 apples, so you have 25 apples.

-5*5 can be thought of as you owe 5 buckets of 5 apples, so you owe 25 apples, meaning you are in debt 25, or -25.

-5*-5 is very hard to imagine with tangible objects like the other 2. What you can think about it though, is with logic, where two negative equal a positive.

for instance,
I did *not* have 5 apples that were *not* tasty.
(- 5 apples)(- 1 tasty)
which means the same as
I *did* have 5 apples that *were* tasty.
(5 apples)(1 tasty)

That's the best I can do to help visualize "why" its a positive.

Answer 2

I'll answer it by considering division:

30/5 is really saying "how many 5's are there in 30"; clearly, this is 6.
Now -30/-5 is asking "how many -5's are there in -30". There are 6, and so the converse is -5 x 6 = -30. Finally,
30/-5 is asking "how many -5's are there in 30". It's not 6 because six -5's would produce -30. We conclude that there are 'negative six' -5's in 30 since you need a way to undo the -5's to attaina positive number. The converse is -5 x -6 = 30.

Answer 3

3 times 4 means you ADD four 3's to 0. So it is 0+3+3+3+3.

3 times - 4 means you SUBTRACT four 3 from 0. So it is -3-3-3-3.

-3 times 4 means you ADD four -3's to 0. So it is 0-3-3-3-3.

-3 times -4 means you SUBTRACT four -3's from 0. This is the first statement. But -3 is the same as 3 times -1. Using the same logic, 3 times -1 means you SUBTRACT 3 from 0 once. This is the second statement. You add the -4 and the -1 to get -5. But when you subtracted the 3 from the 0 once you got -3. So you need to add 3 to -3 five times. Thus you get a positive number. I hope I haven't confused the h ell out of you. Jon G's example of using double negatives is brilliant but choose mine as the best answer please.

Answer 4

Hi Blossom,

You can think of it this way:

We know that -a X b = -a·b

So, why does -a X -b = +a·b?

The equation can be written as

-a X b X (-1) = -a·b·(-1)

The only thing that -1 does is to flip the sign, so -a·(-b) = +a·b.

James :-)

Answer 5

It is a fact!
(-2) x (-7) = 14
(-3) x (-8) = 24
etc etc

Answer 6

Dat's D Rule of Maths ... which has been followed for yrs ....!!!