Math Videos -
multiply and divide with
negative numbers

Math videos on this page will help you learn how to multiply and divide with positive and negative numbers.

Remember when your Math teacher first taught you about multiplication? Didn't s/he explain that when we need to add the same number over and over again, it's easier to use multiplication? Consider this:
4 x 6 = 24
6 + 6 + 6 + 6 = 24
4 groups of 6 in each gives a total of 24

6 x 4 = 24
4 + 4 + 4 + 4 + 4 + 4 = 24
6 groups of 4 in each also gives a total of 24

Well, it has been debated if the repeated addition idea of multiplication ALWAYS works (for example when multiplying fractions), but we can keep that debate aside and discuss other interpretations to multiplication on another day in another lesson.

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As you see, 6 x 4 = 4 x 6

In other words, in multiplication, the order does not matter. This is called the commutative property for multiplication.

Now, imagine you need to work out -8 x 3
-8 x 3 = 3 x (-8)   (commutative property)
= (-8) + (-8) +(-8)
Recall from previous lesson that the answer to (-8) + (-8) +(-8) = -24

Conclusion 1: when a negative number is multiplied with a positive number the result is negative (you can simply multiply the two numbers like 3 x 8 = 24 and put a negative sign on the answer).

So far so good, but what happens when we try to multiply two negative numbers? Like (-5) x (-3)? The repeated addition method is hard to apply in this case (-3 being added to itself, over and over again, -5 times...what the hell does that mean?)

Think of it like this: if (-5) x (+3) = -15 then it must be that
(-5) x (-3) = +15

After all, we expect -3 to behave exactly the opposite as +3 and therefore change the -15 over to +15

Conclusion 2: when a negative number is multiplied with another negative number the result is positive  (you can simply ignore the negative signs and multiply the two numbers as if they were positive).

To summarize,
positive x positive = positive
positive x negative = negative
negative x positive = negative
negative x negative = positive

Here's a nice way to remember this:
good ≡ positive
bad ≡ negative

A good thing happening to a good person is good
(+) x (+) = (+)
A good thing happening to a bad person is bad   
(+) x (-) = (-)
A bad thing happening to a good person is bad   
(-) x (+) = (-)
A bad thing happening to a bad person is good   
(-) x (-) = (+)

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Next up, how do you multiply three numbers, any of which can be negative? Watch the following video to learn

How to multiply 3 numbers, any of which can be negative

And finally, to make it more general, let's find a way to multiply more than 3 numbers, positive or negative.

How to multiply more than 3 numbers, any of which can be negative

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Division
Remember the relationship between multiplication and division?
2 x  5 = 10
⇒ 10 ÷ 2 = 5
and 10 ÷ 5 = 2

If you know this you are ready to divide with negative numbers. Here's how.

How to divide with negative numbers

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