Multiplying Negatives

When You Multiply ...

			Example
×	two positives you get a positive:		3 × 2 = 6
×	a positive and a negative you get a negative:		(-3) × 2 = -6
×	a negative and a positive you get a negative:		3 × (-2) = -6
×	two negatives you get a positive:		(-3) × (-2) = 6

So, a negative times a positive gives a negative ...
but multiplying two negatives gives a positive!

Why does multiplying two negative numbers make a positive?

Well, first there is the "common sense" explanation:

If I say "Eat!" I am encouraging you to eat (positive), but if I say "do not eat!" I am saying the opposite (negative).

Now if I say "Do NOT not eat", I am saying I don't want you to starve, so I am back to saying "Eat!".

So, two negatives make a positive, and if that satisifes you, then you don't need to read any more.

Direction

It is all about direction. Remember the Number Line?

Well here we have Baby Steven taking his first steps. He takes 2 paces at a time, and does this three times, so he moves 3 x 2 = 6 steps forward:

Now, Baby Steven can also step backwards (he is a clever little guy). His Dad puts him back at the start and then Steven steps backwards 2 steps, and does this three times:

Once again Steven's Dad puts him back at the start, but facing the other way. Steven takes 2 steps forward (for him!) but he is heading in the negative direction. He does this 3 times:

Back at the start again (thanks Dad!), still facing in the negative direction, he tries his backwards walking, once again taking two steps at a time, and he does this three times:

So, by walking backwards, while facing in the negative direction, he moves in the positive direction.

And That's All !