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### Course: Arithmetic (all content) > Unit 4

Lesson 8: Multiplying & dividing negative numbers- Multiplying positive & negative numbers
- Multiplying numbers with different signs
- Why a negative times a negative makes sense
- Signs of expressions
- Dividing positive and negative numbers
- Multiplying and dividing negative numbers
- Multiplying negative numbers
- Why a negative times a negative is a positive
- Simplifying complex fractions
- Simplify complex fractions
- Multiplying negative numbers review
- Dividing negative numbers review

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# Multiplying and dividing negative numbers

Sal explains multiplying and dividing positive and negative numbers. Created by Sal Khan.

## Want to join the conversation?

- What are the rules for adding, subtracting, multiplying and dividing negative numbers with positive numbers?(5 votes)
- Addition: + + + = +. - + - = -. for equations with different signs the number with the higher absolute value take the sign of the answer. Subtraction: and the opposite of. this means that 4 - -4 = 4 + 4. use the rules for addition. Multiplication and division: same sign positive different sign negative. 4 * -4 = -16 this is the equivalent of -4 4 times. -4/-4 = 1 this is saying how many times does -4 fit into -4 which is 1 time. Hope this helps :)(4 votes)

- who decided to have negative x negative= positive(7 votes)
- Well it is a positive because when you multiply decimals that are negative they can cancel each other out. I hope that answers your question :)(5 votes)

- He says to use the hints [ maybe in the practice]. But, if you use the hints, you don't get credit for the problem?(5 votes)
- so a negative + negative = negative?(4 votes)
- negative+negative= positive(2 votes)

- How would you solve a problem like this:

Multiply the sum of -6 and -5 by -8.

Please show all your workings so I can better understand how to do this:)(3 votes)- If you solve -6*-5 first in the equation, it becomes easier to solve:

6*5=30, and because we have two negatives the answer is positive. When we multiply 30 times -8, we have a negative times a positive, so the answer is negative. The answer to the problem is 240.(3 votes)

- so how does 2 negitives = positive. Because i get too cofused when people tell me(3 votes)
- its like addition

and division(2 votes)

- you prolly already said this but what is positive x positive?(2 votes)
- I am really not getting it so | x - | equals -1 how is it negative, in absolute value it never turns out to be a negative. This is really counfusing(2 votes)
- Can you do multiplication or division with negatives but with exponents? I always fail on this one.(2 votes)
- what are transitive property and commutative property?(1 vote)
- The transitive property can be described by the statement, "If a = b and b = c, then a = c." The commutative property can be described by the statement, "a+b = b+a."(3 votes)

## Video transcript

Welcome to the presentation
on multiplying and dividing negative numbers. Let's get started. I think you're going to find
that multiplying and dividing negative numbers are a lot
easier than it might look initially. You just have to remember a
couple rules, and I'm going to teach probably in the future
like I'm actually going to give you more intuition on
why these rules work. But first let me just teach
you the basic rules. So the basic rules are when you
multiply two negative numbers, so let's say I had negative
2 times negative 2. First you just look at each
of the numbers as if there was no negative sign. Well you say well, 2
times 2 that equals 4. And it turns out that if you
have a negative times a negative, that that
equals a positive. So let's write that
first rule down. A negative times a negative
equals a positive. What if it was negative
2 times positive 2? Well in this case, let's
first of all look at the two numbers without signs. We know that 2 times 2 is 4. But here we have a negative
times a positive 2, and it turns out that when you
multiply a negative times a positive you get a negative. So that's another rule. Negative times positive
is equal to negative. What happens if you have a
positive 2 times a negative 2? I think you'll probably guess
this one right, as you can tell that these two are pretty much
the same thing by, I believe it's the transitive property --
no, no I think it's the communicative property. I have to remember that. But 2 times negative 2, this
also equals negative 4. So we have the final rule that
a positive times a negative also equals the negative. And actually these second
two rules, they're kind of the same thing. A negative times a positive
is a negative, or a positive times a negative is negative. You could also say that as when
the signs are different and you multiply the two numbers,
you get a negative number. And of course, you already know
what happens when you have a positive times a positive. Well that's just a positive. So let's review. Negative times a
negative is a positive. A negative times a
positive is a negative. A positive times a
negative is a negative. And positive times each
other equals positive. I think that last little bit
completely confused you. Maybe I can simplify
it for you. What if I just told you if when
you're multiplying and they're the same signs that gets
you a positive result. And different signs gets
you a negative result. So that would be either, let's
say a 1 times 1 is equal to 1, or if I said negative 1 times
negative 1 is equal to positive 1 as well. Or if I said 1 times negative
1 is equal to negative 1, or negative 1 times 1 is
equal to negative 1. You see how on the bottom two
problems I had two different signs, positive 1
and negative 1? And the top two problems,
this one right here both 1s are positive. And this one right here
both 1s are negative. So let's do a bunch of problems
now, and hopefully it'll hit the point home, and you also
could try to do along the practice problems and also give
the hints and give you what rules to use, so that
should help you as well. So if I said negative 4 times
positive 3, well 4 times 3 is 12, and we have a
negative and a positive. So different signs
mean negative. So negative 4 times
3 is a negative 12. That makes sense because we're
essentially saying what's negative 4 times itself three
times, so it's like negative 4 plus negative 4 plus negative
4, which is negative 12. If you've seen the video on
adding and subtracting negative numbers, you probably
should watch first. Let's do another one. What if I said minus
2 times minus 7. And you might want to pause the
video at any time to see if you know how to do it and
then restart it to see what the answer is. Well, 2 times 7 is 14, and we
have the same sign here, so it's a positive 14 -- normally
you wouldn't have to write the positive but that makes it a
little bit more explicit. And what if I had -- let me
think -- 9 times negative 5. Well, 9 times 5 is 45. And once again, the signs are
different so it's a negative. And then finally what if it I
had -- let me think of some good numbers -- minus
6 times minus 11. Well, 6 times 11 is 66 and
then it's a negative and negative, it's a positive. Let me give you a
trick problem. What is 0 times negative 12? Well, you might say that the
signs are different, but 0 is actually neither
positive nor negative. And 0 times anything
is still 0. It doesn't matter if the thing
you multiply it by is a negative number or
a positive number. 0 times anything is still 0. So let's see if we can apply
these same rules to division. It actually turns out that
the same rules apply. If I have 9 divided
by negative 3. Well, first we say
what's 9 divided by 3? Well that's 3. And they have different signs,
positive 9, negative 3. So different signs
means a negative. 9 divided by negative 3
is equal to negative 3. What is minus 16 divided by 8? Well, once again, 16
divided by 8 is 2, but the signs are different. Negative 16 divided by positive
8, that equals negative 2. Remember, different signs will
get you a negative result. What is minus 54
divided by minus 6? Well, 54 divided by 6 is 9. And since both terms, the
divisor and the dividend, are both negative -- negative 54
and negative 6 -- it turns out that the answer is positive. Remember, same signs result in
a positive quotient in this example we did before,
it was product. Let's do one more. Obviously, 0 divided by
anything is still 0. That's pretty straightforward. And of course, you can't
divide anything by 0 -- that's undefined. Let's do one more. What is -- I'm just going to
think of random numbers -- 4 divided by negative 1? Well, 4 divided by 1 is 4,
but the signs are different. So it's negative 4. I hope that helps. Now what I want you to do is
actually try as many of these multiplying and dividing
negative numbers as you can. And you click on hints
and it'll remind you of which rule to use. In your own time you might want
to actually think about why these rules apply and what it
means to multiply a negative number times a positive number. And even more interesting, what
it means to multiply a negative number times a negative number. But I think at this point,
hopefully, you are ready to start doing some problems. Good luck.