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Multiplying positive and negative numbers

Basics of multiplication with negative numbers
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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?
Thanks!!
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:
5*4*-2=-40.
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 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.
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.
neg times neg pos_ pos times pos pos_ neg times pos neg_ pos times neg neg?
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.
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
a negative times a positive is a negative and the same the other way around, and a negative times a negative and a positive times a positive is a positive. so the negative times the positive will be a negative, and that times the other negative will be a positive.
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.
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?
Let's look at the four possibilities:
1 * 1 = 1. OR positive 1 * positive 1 = positive 1.
-1 * 1 = -1, OR negative 1 * positive 1 = negative 1.
1 * -1 = -1, OR positive 1 * negative 1 = negative 1.
-1 * -1 = 1, or negative 1 * negative 1 = positive 1.
why is it that a negative times a positive and a positive times a negative?
watch the 2nd video then you will know
sal said 3*-2 is -2 plus it self 3 times: -2 + -2 + -2.
how do you do 3 plus itself -2 times?
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. :)
Sylvia.
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.
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= +
why isnt zero a defined number????
zero is defined number, but deviding by zero isn't.
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.
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.
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 a negative times a negative is a positive?
Yep, thats right! Good job on figuring that out! :)
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
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.
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.
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.
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).
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.
Would brackets have any effect on these equations or no?
Thanks!
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 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 :)
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
why is there so many videos and not enough practices am i going cazy or is there more practices with each video?
You can repeat the review the practices anytime and you'll generally spend more time with them than the videos as you go further into the future.
i mean why does 2 Negatives = a positive?
neg x neg = pos
pos x neg = neg
pos x pos = pos
thats how it works.
live with it
School standards have dropped. I am already past this in 6th.
yeah. I remember learning this in 6th.
Why neg times neg equal positive
i have no idea, even though it *is* true.
but, here is a disclaimer
_people say multiplication is repeated addition. if so, then look at this:
-5*-3
-5+-5+-5
-15_
i have no idea how it is positive, but we just stick to that.
This Is All Confusing To Me Just Integers Help Its Like Not The Same As We Learn IN School Comment Please......!
what is that whit box thing that popped up in 5:05 ?
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.
at 3:04 why do we use negative for positive.
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.
20 boys are in a class with 28 girls. What percentage are the girls?
hi, if you multiply a - # x - # = - # but if you multiply a - # x - # x - # = + # right?
Oh wow. You aiming to be a mathematician?? Tip: instead of writing # write 'n' it's a common variable, or letter used to represent an number of unknown value. :)

Okay: onto your question: if you muliptly -a * -b = -c, but if you muliptly - x * -y * -z = * u, right? _Please remember that these letters are the same thing as writing #_
I'm afraid you've gotten it mixed up... a negative number * negative number = positive number.
A positive number * negative number = negative number.

So: if you have, let's say -5 * -5, you're going to get an answer of *positive* 25.
If you have -5 * -5 * -5 you're going to get an answer of *negative* 125.

So, (using your symbols): a -# * -# = +#
and a -# * -# * -# = -#

Remember: if you have an even number of negative numbers (2, 4, 6, 10..100 etc) you will get a positive number
If you have an odd number of negative number (3, 5, 7, 111) you will get a negative number.

Those rules will be very important to know when you get into exponents!

Hope this helped,
Sylvia.
dis is confusing people i knew how to do it but know i don't Llf..............
Why when you multiply negative #s is the answer positive?
Ok. I'll try and make this as clear as possible. During the video Sal keeps saying two negatives always make a positive. But when you multiply a negative by a negative wouldn't you either get the number you are multiplying or 0?

Say I'm multiplying -6 by -7. I would go from -6 to zero. Then onward to positive 6. But then the current answer would be positive so wouldn't I subtract 6 the next time?
But you aren't adding and subtracting here, you are multiplying.
Adding 2 negatives will always give you a negative answer
Multiplying 2 negatives will always give you a positive though.
Another way of saying negative is "the opposite of".
So every time you multiply by a negative the sign will flip.
If you have 1, 3, 5, . . . negative factors in a string of multiplications, the final answer is negative.
If you have 2, 4, 6, ... negative factors the final answer will be positive.
(-2)(-3) = +6 or just 6
(-2)(-3)(-1) = -6
Using arrows on a number line helps when you are adding but not when you are multiplying.
I hope this helps.
i dont get negative numbers can someone plese help i cant get this
How can you remember if a pos x neg = ? or neg x neg =? are there any ways to remeber like P.E.M.D.A.S
This is my way of remembering it:
Both sides have the same sign? Positive Number.
Both sides have a different sign? Negative Number.
at 2:39 can some please exsplain to me haw the number line gose ? negative # to the left zero,positive # to right
Is there a place to practice Questions on a specific topic, like word probelms? If so, where is it?
a way to think of a negative times a negative is that negative sign plus negative sign the two negative lines make a positive sign or:

- + - = +
So basically if you take 2x3=6 and if you make the same equation a negative ,you will get the same answer,6?
Do you mean -(2x3)? This would equal -6.
Or do you mean -(2)x-(3)? That would equal 6.
why is there no practicing the consept? o.o
i thought this video was really helpful cuz in the beginning of the year i was not so good at this stuff
Hi, guys. I'm new on khan academy and could you tell me where can i find some exercises, please?
You can go to to *LEARN* at the top of the page and click on the *Knowledge Map* link and it will take you to the map of exercises.
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"
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.
I don't get how -1 times -1 is +1
the negatives cancel each other out which gives you a positive.
i used to think that those were hard they kinda easy if u listien and ask ouestions
How many multiplications of positive + negative integers are there with an answer of -6 ?
one negative and one positive example 3x(-2)
How do I practice this activity?
is it posable to put exponents on negitve numbers
Yes, negative numbers can be raised to both positive and negative powers.
Can this get more complicated?
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 :)
its not realy that hard to me somtimes like neg. times a poz = neg. or poz times a poz =poz or a neg times a neg =poz examples -7x1=-7 7x1=7 -7x-1=7 i think thhats how it gose
What is the difference (not meaning subtraction) between – (m3n) and (-mn)3 ? (The "3" is an exponent.) That is, what happens when a negative sign is inside verses outside of the parentheses?
if i had -3 + -5 would it be neg or pos and would i add or sub?
Here's a quick way to remember addition with negative numbers:
If the two numbers have the same sign, you add them and keep the sign. If they have different signs, you subtract them and keep the sign of the larger number. Thus,

- 3 + -5 = -8
3 + 5 = 8
- 3 + 5 = 2
3 + -5 = -2
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
what about the laws of pemdas?
negative numbers are just like positive numbers when it comes to PEMDAS.
How do you kown if it is postive or negtive number
Same sign add and keep different sign subtract keep the sign of the highest number than they be exact. Example: -3+4=1 highest number is 4 so the answer is a positive.
at 0:35 he starts talking about multiplying negatives and positives. I don't get it, why is a positive times a negative always negative?
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 thought the when the neg is bigger its alway a neg
what program are you useing please tell me
why is negative times a negative positive ?
my friend taught me if you hate (negative) to hate (negative) then you love (positive).
how do negatives times negatives cancel out?
It might help to think of multiplying by negatives to be like flipping something over. If you flip something over twice (multiply 2 negatives) it will be where it was at the start (positive)
Does sal have a video explaining why a negative x a negative is possible?
dues it work the same for + ?
No, the final sign is dependent upon which number's absolute value (distance from zero) is greater. So, if both are negative, you'll go farther negative.
You no how u did the problem and =0 doesn't that still make it -0 are just zero
Does -2 x 3=2 x -3
Yes, I think its just an extension of the communitive property.
so the neg and the neg cansasle out
thank you for the help
How come the product and quotient of two negative numbers are positive while you have to copy the sign in addition and subtraction?
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.
Is there a video on that with decimals involved ?😄😄😄
The rules are exactly the same. With multiplying and/or dividing with negative numbers here is how you do it:
Step 1: Do the math as though the negative signs were not there.
Step 2: Count up the number of negative signs. If there is an even number of negative signs, the answer is positive. If there is an odd number of negative signs, the answer is negative.
Would (-3)*(-3)*(-3) equal a positive or negative number?
Actually, it would equal -27 because (-3)*(-3)= +9, and +9* (-3) would equal -27.
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.
What is zero really some people say negative other people say neutral please like my question and answer it! :)
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.
Report a mistake in the video
Example:

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

Report a mistake in the video


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