Why is a negative number times a positive number always negative?

Answer 1

Take a simple multiplication question such as 2x3

It mean that there are 2 groups and these groups each have 3 things in them (or 3 groups each with 2 things)

So you add the groups up and get 6

Now if you have 2x-3 you have 2 groups and they each have -3 things in them. You add all the negatives 3s up just like you did in the last question and have -6.

It is difficult to imagine -3 things or -6 things, so just think of multiplying by a negative will reverse the sign (kind of like reversing the polarity of battery terminals). So if you reverse them one time (negative X positive) then it is opposite of what it was:

• If the number to be multiplied by is Positive, then the answer is negative : Negative X Positive = Negative.
• If the number to be multiplied by is Negative, then the answer is positive : Negative X Negative = Positive.

If you multiply a number by a positive, it does not reverse the sign: Positive x something equals the a number with the same sign as the something.