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Multiplying positive and negative numbers

Basics of multiplication with negative numbers

Multiplying positive and negative numbers

Discussion and questions for this video
Can anyone think of any ways to connect multiplying two negative numbers with a real-world application? or how to actually SUPPORT WWHHYY two negatives produce a positive with multiplying/dividing?
Real world example (more or less):
A company wanted to encourage sales of its "fuzzy wigets" by offering a $3 rebate to the first 1000 customers to send in the rebate forms. The company's financial computer input was set up so that the total rebates were calculated as a negative number and money was allocated for the amount needed.

-3 x 1000 = -3000 $3000 allocated for rebate use only.

Unfortunately, the printer had problems and no rebate forms were printed, so no rebates were given. In order to use the program to re-allocate the money, the number of customers not using the rebate program had to be entered as a negative number.

-3 x -1000 = 3000

$3000 could now be reallocated for other uses.
At 3:59, why doesn't -1 times 0 equal -0 ? Why is it just 0?
0 isn't negative, and it isn't positive either. It's a neutral number.
if you can multiply negative can you divide them?
You can, and dividing negatives is actually very similar. Dividing a negative by a positive (and vice versa) gives you a negative. Dividing a negative with a negative gives you a positive. Hope this helps! :)
what happens if the equations is positive x positive x Negative

posted 11:20 ET USA
The product would be negative; Positive times negative is a negative, and another positive number won't change that:
why when we multiply or divide two negative number it is always positive?
The two negative signs cancel each other out to become positive. Or they cross to make a positive sign.
what helped me is to make a triangle and put two negative sign at bottom and a positive sign at the top and when I got two negative signs I would cover up the bottom negative signs and the positive sign at the top would show and Id know that it was a positive example 3x(-9)=negative cause Id cover up a positive cause positive 3 and cover up a negative cause negative 9 and it would be a negative -27
No. If you know how to multiply and put in negative # signs, it is only too easy.
neg times neg pos_ pos times pos pos_ neg times pos neg_ pos times neg neg?
how can I remember all of this? do you have a idea or any suggestions?
Two `like` signs become a positive, and two `unlike` signs become a negative.
what would -5 x 1 be? 1 x any other number is that number but i do not know if that works for negatives.
Yes, it works for negatives, too. 1 is a pretty cool number.
If you did negative 1 or positive 1, how would you know what 1 it is? Because 1*1=1 . Would that 1 be a positive or negative 1?
That's why you have the (-) sign before a number and in your case if one of the ones is negative, you will see -1
i am always getting confused with if you multiply a negative and a positive and a negative = what and a negative and negative or a positive and a positive = what ? same with division
This has always made it easier for me to remember --
positive = love
negative = hate
If you love love or hate hate, then you are positive.
If you love hate or hate love, then you are negative.
This also works for addition and subtraction for getting the signs correct.
Example: 6 + -4 =
The "plus negative" can be looked at as loving hate ("negative" or simply changing the sign to minus), so you are actually subtracting the 4 from the 6. The answer, of course, being 2.
I hope this helps.
I just thought that two lines like in -2 x-3 and their are two lines in a positive sign like in +6 so that is my way of looking at it.
At 3:17, how is it that a negative times a negative is a positive?
Just an example that might be helpful:
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!" (positive).
What if it was a positive times a positive times a negative? Or a negative times a negative times a positive? Like -6 x 23 x -17.
If you have an odd number of negative numbers being multiplied, then the product will be negative. If you have an even number of negative numbers being multiplied, then the product will be positive.
e.g. -1 x -1 x -1 x -1 x -1 (There are five -1 is this problem, five is odd) = -1
e.g. -1 x -1 x -1 x -1 (There are four -1 is this problem, four is even) = 1
do you have any practice on mutiplying positive and negative numbers ?
yes i am the top person on multiplication in my school with positive and negatives # (numbers) 9x5=45 or just do this 9+9+9+9+9=45 and for negatives is love and hate.

for example -9 x 5 =-45 because u hate to love so it = hate
-9 x -9 = 81 because u hate to hate so it = love
hate = - and love= +
How come if it's negative times positive, it's negative, and if it's positive times negative, it's still negative? Or is it the same with the normal multiplication?
If it's negative times positive yes, it's negative but when it's positive times negative times positive it's negative too.(Does not matter which way just like it is in normal multiplication.Your right.)
so I don't get why negative + negative = a positive
Actually, it's negative x negative.

I don't really get it either, but that's how it works.
I'm having trouble remembering
+ x + = +
- x - = ?
I can never remembering what combinations equal what. Any story thingys that help you remember? I know the previous person said "Does my saying work; If a Bad thing happens to a bad person (-x - -x) its a good thing (answer would be a positive)?" But I need every other combination and the answers to it you know:
Negative times positive equals what?
Positive times negative equals what?
Count up the number of negatives that are being multiplied or divided. If you have an even number of negatives, your answer will be positive. If you have an odd number of negatives, your answer will be negative.

The order in which they are multiplied does not matter.
hi everyone!! how can you add the neg times a pos
If you have a "neg times a pos" then it will be a negative. Calculate the number (which will be negative) then add as usual.
Hi.Can anybody tell me how to use a timestamp?please.
Hi Abhimanyu!
Say you are referring to 2:15 in a video then all you have to do is type 2 : 1 5.
(Without the spaces in between the numbers☺).
I hope that helped!
So on the chart on the bottom it doesn't say what is a negative times a positive or is it the same as a positive times negative?
Yes. With multiplication, the order doesn't matter (the commutative property of multiplication), so a negative times a positive is the same thing as a positive times a negative.
why isnt zero a defined number????
zero is defined number, but deviding by zero isn't.
At 2:39, could someone demonstrate how this works on the number line? Negative numbers to the left of zero, positive numbers to the right.
I can't do a video to show you, but I can explain it and if you draw it on a number line, you can see for yourself how it works.
The expression was -2 * -3.

Let me first explain how you would represent -2 * 3 on the number line.
-2 means go left 2 postions. Start at zero and go left two postions and then go left two more postions and then go left two more positons. You are now at -6.

Ok, now lets do 2 * -3. Two is positive so it means go right two postions. The minus on the second number means opposite, So, start at 0 and go the opposite of right two postions and go opposite of right right more postions and go opposite of right two more positions. And again you are at -6.

Now lets do -2 * -3. The negative on the two means go right. The negative on the three means go opposite.
So start at zero. Go the opposite of right two positons and go the opposite or right two more postons and go the opposite of right two more postions. You are now at 6.
So -2*-3 = 6 and you have shown it on a number line.
I hope that helps.
So a negative times a negative is a positive?
Yep, thats right! Good job on figuring that out! :)
sal said 3*-2 is -2 plus it self 3 times: -2 + -2 + -2.
how do you do 3 plus itself -2 times?
so if I understand this correctly - 0 x -1 = 0 instead of -0? is there ever a case where 0 will be negative as opposed to positive? I'm thinking I understand that 0 is always 0 and never negative - am I right?
0 is neither a positive or a negative number. This is because numbers are classified as whether or not they are larger or smaller than 0. It would be like saying 0>0 or 0<0, which is not correct because 0=0. Just remember 0 as a kind of placeholder on a number line.
how do you do this? its confusing me and Im not exactly a math person but im not bad at it. Can anyone help me on this? IT IS VERY CONFUSING!
What u need help on cause I can help u??
But there is no video about multiplying 3 different numbers that are negative, but if there is tell me about it please kinda confused.
You can multiply two of the numbers and get the answer. Multiply that answer by the third number.
Here's an example: Multiply (-3)(-4)(-2)
First multiply -3 by -4 = 12
Then multiply the answer 12 by -2 = -24
So the answer is -24.
Hope this helps.
What about -10 times -4 times -2 do all of them cancel out?
No, if you're multiplying an odd number of negative values then your final answer will be negative.
Would brackets have any effect on these equations or no?
I don't think it would, most of the problems he does here are single-step (just a * b), instead of multi steps where you use the order of operations(bedmas)(a+c*b/d-e), since brackets only real purpose are to tell you to do this first, before you do anything else, a pair of brackets wouldn't change anything.
Hope this helped
why is it that a negative times a positive and a positive times a negative?
watch the 2nd video then you will know
why is it so tricky?
Well, I guess because it has negative numbers involved. To make it easy, all you need to remember is that positive x positive = positive, negative x negative = positive and positive x negative = negative. After you memorise that, it will hopefully become easier :)
At 0:32 he starts telling us about positives and negatives. Does my saying work; If a Bad thing happens to a bad person (-x - -x) its a good thing (answer would be a positive)?
Mathematically, we would get a neutral or positive. We wold probably represent it more as an addition problem in math, but the abstract concept of a negative negative will always give a positive still stands in your saying. :)

It's kind of saying like : I will not not do something...

Interesting Question. :)
i did and i still dont get it
At 1:12 , your saying that - X + = -?
while - X - = +.
I don't understand that.
Can you please explain it?
Why would you cancel out when you can act like it is not even there at all and how can -1x0=0 I thought you said that a neg.+pos.=neg so shouldn't it be a neg. instead of a pos. ?
Anytime you multiply or divide by zero it is always zero. 0x1=0 and 0x-1 is still 0.
dis is confusing people i knew how to do it but know i don't Llf..............
So I was wondering, can you or can you not use a number line?...
if a question ask you to use a number line or if it dosent but you can use it to help you
i mean why does 2 Negatives = a positive?
If you multiplied -1 times 1 would would be the answer?
At 0:44 Sal says that -2 * 3 = -6, or -2+-2+-2 couldn't we write this as -2+(-2)+(-2)? Thanks!
So, neg. x neg. and pos. x pos. = pos., while neg. x pos. and pos. x neg. = neg.?
Are you sure its right i got a diffreant answer Just Kiddin
why doesn't -1 times 0 equal -0 ? Why is it just 0?
There is no such thing as "-0". It is just known as 0.

Anything multiplied by 0 is 0.
If I had a negetive times a positive what will happen ?
A negative times a positive will make the product (answer) a negative. I can't explain it as good as Sal but there is a video by him on what happens when two negatives multiply. The video can answer your question better than I can. Here is the URL code for the video: https://www.khanacademy.org/math/arithmetic/absolute-value/mult_div_negatives/v/why-a-negative-times-a-negative-is-a-positive
at 1:43 i dont understand:( HELP!!!!!!!!!!!!!!
three groups of -2. what do you get?

Im new and i was wondering how to make a video and put it up??
I'm not sure that's possible..
In general, we're just students here...
the people making the videos are employed to do so..
Can someone demonstrate how this works on the number line?
You can think of it this way: If someone you like asks you to dance, that's good (positive). If someone you like doesn't ask you to dance, that's bad (negative). If someone you don't like asks you to dance, that's bad. If someone you don't like doesn't ask you to dance, that's good.
i always remember negative x's negative = positive and positive x's positive = positive
Negative x's positive = negative
Same for division
there is a rule for positive and negitive numbers which is " if the signs are the same the answer is positive but if the signs are opposite the answer is negitive" but i have a multiplication question which is ' -8 x 0 = 0 ' but that then should be a negitive number acording to the rule can someone please explain why this is
zero is just zero, it can't be negative or positive.
at 5:17 do you multiply positive numbers the same way you multiply regular numbers..? if so do the positive numbers cancel out and the awnser become negative..?
ok but what I don't understand is how negative x negative =positive but positive x positive =positive how does that work..? shouldn't it be positive x positive =negative...?
cna yoy post word problerms on the samr?
at 2:39 can some please exsplain to me haw the number line gose ? negative # to the left zero,positive # to right
math is fun, when ur programming games... (my opinion here) :)
I don't get the exercise because I always have to like, do for example: 1 x -1 and It always changes weirdly. If someone could tell me what I have to do, It would be greatly appreciated. Thank you.
How come the product and quotient of two negative numbers are positive while you have to copy the sign in addition and subtraction?
is there an excersise for this lesson?
at 0:10 I dint under stand any thing
sumtimes i cant find the lessons i need and i keep trying but its just not there
hav any tips?
why is there no practicing the consept? o.o
Why do two negatives create a positive
because it is always opposite
Why do to negatives make a positive when multiplying but not when adding because multiplying is just repeated addition?
You've got that statement sort of correct. Multiplying isn't exactly repeated addition. Negatives make a positive when multiplying because the negatives cancel each other out and leave you with just the numbers. Negatives stay negatives when adding because the negative signs don't cancel out here. You keep the sign and add the numbers.
Is -2 x -2 =4;yes or no?
Yes, it is. -2 x -2 is 4 since they are both negative. Negative times a negative is always a positive.
What if you multiply more than 2 numbers? Like -2*-3*4? Or 5*3*-7? Or -6*-9*-8? How would you work that out?
Left to right, so multiply the first two together, and then multiply that answer with the third number.
So if it is one negative number, multiplying with another positive number is that positive? or negative? I don't understand which one.
No, multiplying numbers with different signs always yields negative. The same signs is always positive.
-1 x -1 = 1
1 x 1 = 1
-1 x 1 = -1
1 x -1 = -1
so will a neg.+ neg.+ pos. will thae awnser be a pos. or a neg.
If you're adding them:

(negative number)+(negative number)+(positive number) = ?

then the answer can be either positive or negative depending on the particular numbers. If you are multiplying:

(negative number) x (negative number) x (positive number) = (positive number)

then the answer will always be a positive number.
How would you multiply 3 numbers? Ex. (-1/2)X(-1/2)X(-1/2)=?

Would it equal +1/8 or -1/8?
The product of 3 negatives would be negative.
If you have an even number of negative factors it's positive.
If you have an odd number of negative factors it's negative.
Why are ± used and how?
It is used to change 7 to -7 or vise versa It is used to change a positive to a negative or vise versa
this stupid comper aintworkin
this video really helped me

but I have a question when you multiply a negative and a positive do you get a negative
yes correct. the negative cancels out the positive so its a negative number.
How to model (-4)(-4) using counters?
I think there should be a video bout it.
Does -2 x 3=2 x -3
Yes, I think its just an extension of the communitive property.
I am so lost....
in simpilar words can somebody explain the formula?
(if that makes ANY SINCE)
Anything times a positive is a positive. But if a negative times a positive is going to equal a negative. The negative is always dominate... GET IT NOW :)
I don't get how -1 times -1 is +1
the negatives cancel each other out which gives you a positive.
at 2:27 it basically sums it up, negative times negative equals positive, and negative times negative times equals positive (same signs equal positive, different signs equal negative)
I really liked how you explained that to me and other users! :)
i thought this video was really helpful cuz in the beginning of the year i was not so good at this stuff
Could you be more specific and make a video just on dividing negative numbers? I could only find one in the search with multiplying. Thanks!
When Sal does -1x-1=1 I don't get 1 I get -2
Thank alt but no i didn't add
why is that 2 negative a positive?
how does Negative Times a Negative works on the number line?
a negative number times a negative number would equal a positive; so on the number line you would mark it as a positive number
what is 0.5147 times any number would be ?
People I need help with this question: Expand the following 3(5+4)-2(3-1)= This is the way I would do it but I think it is incorrect: 3x5= 15 3x4= 12 add the two results together: 27

Then -2(3-1) -2x3= -6 -2x1= -2 subtract the two results= -8 now I have 27 and -8 here is where I get stuck, is the answer 19? Need some help this question is part of a assignment which I need to hand in by 15/10/2012 after two days. If someone can point which videos or section I need to go to would be helpful. Thanks
Why is it that when you multiply two negative numbers, they cancel each other out?
I think this is easier to understand intuitively using division first. Suppose you have (-$8) in your bank account and you want to divide it equally into groups of (-$2). You would have (-$2)+(-$2)+(-$2)+(-$2) = (-$8). That is, there are four equal groups. So a negative divided by a negative is a positive (-8/-2 = 4).

Now let's consider multiplying (-3)x(2). Draw out a number line and put a dot at 0. (-3)x(2) tells you that you add -3 two times. So from zero you go to the left three places to get to -3 (you've added -3 once), then left another three places to get to -6 (you've added -3 twice) so the answer is (-3)x(2) = (-6).

What if that 2 was negative (i.e. (-3)x(-2) = ?)? Then you would add -3 to itself two times _in the opposite direction_. So on the number line we start at zero, and instead of moving left, we move right 3 places to get to +3 (-3 has been added -1 times), then we move another 3 places to the right (-3 has been added -2 times total) to get to +6. That is, (-3)x(-2) = 6, and a negative multiplied by a negative is a positive (the negatives "cancel each other out").

Does that make sense?
6:01 Is it the same with multiplying a negative number with a four digit poositive number?
does it have the same rule as as if you add and subtract negative numbers where you can change it like this: If you take 4 + -5 = -1 but adding a negative is the same thing as subtracting a positive so 4 - 5 = -1: can you do that with multiplying?
No not really. But you can change 4x-5=-20 to (-5)4=20.
is it posable to put exponents on negitve numbers
Yes, negative numbers can be raised to both positive and negative powers.
this is too easy . . . wheres the harder stuff?
you can search up what you want to learn in the search bar that says "search for a video or topic"
how do you get a positive times a negative = a negative
take -2x 4 for example.
-2x4= -2+-2+-2+-2
-2+-2+-2+-2= -8

Look to the video "Adding Negative Numbers" if my explanation made no sense.
at 2:30 how many times can it go in to it
i dont get negative numbers can someone plese help i cant get this
i thought the when the neg is bigger its alway a neg
^-^ yay positive and negative ! hazahhhh
Report a mistake in the video

At 2:33, Sal said "single bonds" but meant "covalent bonds."

Report a mistake in the video

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