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Multiplying positive and negative numbers

Here we explain some rules of thumb regarding the multiplication of positive and negative numbers.

Multiplying positive and negative numbers

Discussion and questions for this video
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:
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.
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.
Can somebody explain what -2 x -3 "means"? Like 2 x 3 means 2+2+2.
-2 means that it is a number below 0, if you add to negatives then you will get a positive or a number above 0. The answer to this question would be 6 because you added two negatives, this makes a positives. If you have the equation -2 + +3 this would be -6 because if their is one negative number in a equation it automatically turns into a negative answer!
So when you multiply 0 with any number, positive or negative, you get 0? Is that right?
yes zero multiply by any number is all ways zero - or +
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.
When Sal said any number times 0=0, does any number include infinity? Is infinity even a number, just an expression, or something else?
The way I see it is that if we must have a number, we must be able to finish counting e.g. 10 apples, 7 cars, etc. Given infinity, we cannot finish counting-agree? So, technically, infinity is not a number at all. It is just the idea of something so big that we cannot finish counting.
If I'm not mistaken some branches of math (calculus e.g.) treat infinity as a number but math with infinity is quite complicated I think.
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 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.
How about neg + neg + pos?
Multiplying two negatives and a positive would give you a positive, but by adding them it depends on the size of the numbers.
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
why neg -neg = to pos ?
Well, negative times negative and negative divided by negative both equal positive, as Anthony said, but your statement is actually incorrect. A negative number minus a lower negative number equals a positive number, since - negative= add positive, and the absolute value of the lower negative number is greater. However, a negative number minus a higher negative number equals a less negative number, but still negative, since the absolute value of the higher negative number is lesser.
Why is that if you mulitiply a negative number by 0, it doesnt equal -0. At 4:10 it explains it but it still doesnt make any sense!
Zero is neither positive, nor negative. But, anything times zero is zero because if you have nothing, then more of nothing is still nothing.
This actually helped a lot! Thank you! <3
Yay, glad this helped you! But next time, please post comments like these in the "Tips and Thanks" section, not the comments section. : )
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.
neg times neg pos_ pos times pos pos_ neg times pos neg_ pos times neg neg?
Yup. You can think of it like this: when one is positive and the other one is negative (or vice-versa), they are different, right? They "disagree", so the answer is immediately negative. When both of them are positive (or negative), they are identical, they "agree", therefore the answer is positive :) hope it helped ;)
what number do you have to multiply with a negative to make it a postive! simplest form please!
You can multiply any negative with another negative to get a positive!
What does he mean by 1 x 0 =0
when you multiple in the zeros by any number your answer will always be zero
Other than the divide symbol, the forward slash, the underline bar (between the numerator and denominator), and the colon (for ratios) can also indicate division.
What about fractions? How does that work? Dividing and multiplying fractions? I know with regular fractions that you would just want the denominators to be the same, would the math work the same way? just being either a negative or positive? Is it weird that I find multiplication of negatives and positives easier than adding and subtracting negatives from positives?
The same rule applies to fractions. If you multiply a negative fraction by a positive fraction, your result will be a negative fraction. If you multiply two negative fractions, your result will be a positive fraction. If you multiply two positive fractions, your result will be a positive fraction.

It doesn't really matter what kind of numbers you're dealing with (fractions, decimals, or integers). Just remember that a positive and a negative give a negative; a negative and a negative give a positive; and a positive and a positive give a positive.

Multiplying and dividing fractions are quite simple. To multiply fractions, you multiply the numerators and the denominators together, and then simplify your product. To divide fractions, you flip the second fraction over and multiply. For example:

1/2 divide by 1/4=1/2 times 4/1=4/2=2.

There are lots of videos on this topic on Khan Academy.
In your videos can u give at least one challenging problem because I want to see if I understand the concept. Thank u so much for what u did u really helped me in my academics.
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!
@ 4:07 how does 0 times -1 = o and not -o?
0 is a neutral number. If you put zero on a number line, it would be the middle of all the numbers.
So same signs positive, opposite sides negative. Am I getting the point?
Yes, you are correct!
-1 * 1 = -1
1 * 1 = 1
-1 * -1 = 1
Is there a counterexample for my assumption that 1 multiplied by any number equals that number?
No. Your statement is a rule, therefore thus far it has not been proven wrong. In other words, there is not counterexample.
Zero is neither negative nor positive. However, in a math problem you can have something like 2 - 0 = 2.
does commutative property work with negative numbers??
Yes. Commutative property works always, thats why it's so cool.
How does a negative times a negative equals a positive number, or a negative divided a negative equals a positive number?
Think of the sign of a number as a light bulb. When the number is positive the bulb is on, when it's negative the bulb is off.

When you multiply by a positive number you do not touch the light switch. When you multiply by a negative number you flip the light switch.

So if a number is positive (then it's light is on) and you multiply by a negative number, do the multiplication (for the numbers) and flip the switch once (for the sign)... flip the switch once, the light goes out, the answer is negative.

If you then multiply that number by another negative number, the multiply the values and flip the switch... you get a number and the light goes on, so the answer is positive.

So 2 x (-3) bulb is initially on,, 2 x 3 = 6, hit switch once, bulb goes off, answer is -6

-6 x -4, bulb is initially off, 6 x 4 = 24, hit switch once, bulb comes back on, answer is 24

It may not make a lot of sense at this point, but it is a rule you can always use. Understanding is always better, but having a rule you can use sometimes has suffice until understand develops.
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.
So a negative times a negative is a positive?
Yes, a negative times a negative is a positive
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. :)
would the product of -2 and 3 the same as -3 and 2?
Yes, in multiplying different symbols this would equal the same answer.
If there are an odd number of negatives, the product will be negative.
If there are an even number of negatives, the product will be positive.
I hope that 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 :)
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
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.
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.
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.
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.
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= +
Shouldn't -1 divided by 0 equal -1??
No, anything divided by 0 is undefined.

Essentially you are asking how many groups of 0 do I need to get -1, and there is no valid answer to that question.
heller my name id madea how wer durn
This is not a question. ;)
Do you have a question on the video or concept?
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!
Why is math so mind-blowing?
Why do I continue to ask so many questions.
Why is math so confusing?
1) Because it's awesome.
2) Because you are naturally curious.
3) Because you are working hard and you care.
Keep up the good work! You can do it!
What if you add negative with a negative?
Add the 2 numbers, keep the common sign. Example: -2 + (-7) = -9
Here is topic that has videos on this subject: http://www.khanacademy.org/math/pre-algebra/negatives-absolute-value-pre-alg/add-subtract-negatives-pre-alg
Salman Khan says in the video that -2 + -2 equals -4. Don't the negative signs cancel out and make it +4?
That being said, wouldn't the answer to -2 + -2 + -2 be +2?

I'm asking because when finding 10 to the -6th power, for example, you would break it down like:

10 x -6 x -6 x -6 x -6 x -6 x -6
10 x -6 = -60
-60 x -6 x -6 x -6 x -6 x -6
The negative signs in -60 x -6 cancel out, making the answer positive.
-60 x -6 = +120... and et cetera.

Is it just different while doing an exponent problem?
If you look at a number line for this problem, you are starting at -2. When you add -2 the negative signs do not actually cancel. You move 2 to the left of -2. Also 10 to the -6th power actually equals 1/(10 x 10 x 10 x 10 x 10 x 10). You can see a video on negative exponents here https://www.khanacademy.org/math/algebra/exponent-equations/alg-integer-exponents/v/introduction-to-negative-exponents
What if you have a negative*neg*pos*neg*pos what would be the symbol?
The product will be a negative number.
*An odd number of negative numbers multiplied together will always give a negative product*. Here 3 negative numbers are multiplied resulting in the product to be negative.
If there are *an even number of negative numbers being multiplied together then the product will be positive*.
why isnt zero a defined number????
zero is defined number, but deviding by zero isn't.
what if i have 2 negative numbers and 1 positive number?
You multiply it in order. Let's say we have this equation:

-2 * 5 * -3 (negative 2 times 5 times negative 3)
You first do -2 times 5. Which equals -10. Then you multiply that by -3. So the answer to that problem is 30 :)
So just keep multiplying in the order given.
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.
Thats great! But this sould be in tips&thanks! :D
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.
why is it that a negative times a positive and a positive times a negative?
watch the 2nd video then you will know
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.
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
Can someone demonstrate how this works on the number line?
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
how does this guy have the time to do all this?!
It's his job. This is his business and he changed the world for better and for always! And, its easy to do this when you already know the material and most importantly when you are driven by the idea of changing something for better :) I hope this link will answer more of your questions about Sal :)
How do you divide negative numbers!?
if you are talking about both the numerator and the denominator are negative then -8/-4 then your answer will be 2/1 or 2.as you divided -8/-4 then you will also cancel the numerator's negative sign with the denominator negative sign.thus,you reached at +2/1 or +1.
if your numerator is negative (-8/4) then your answer will be _2/1 or _2.in this problem you don't have negative denominator but do have negative numerator that is why you wasn't able to cancel negative sign.
i hope it work.............
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 don't get what he meant at 0:04
How would you write out a *pos* times a *neg* number?
At 0:42, he explained how to write out *-2 x 3*:
`-2 x 3 = -2 + -2 + -2 = -6`
How would you write out the *3 x -2*?
Because if you were to write it out like above:
`3 x -2 = 3 ?`
Then what? Do you subtract the numbers, like:
`3 x -2 = 3 - 3 = 0`
You are _not_ supposed to get *0*.
Are you having trouble with a calculator? If so, try enclosing the negative number in parentheses: 3 x (-2) = (-6). Otherwise, there may be a negative number button that you need to use.
School standards have dropped. I am already past this in 6th.
yeah. I remember learning this in 6th.
In each positive question make sure there must be 2 negative and one positive. XD
at 7 secins it stop`t at first
Hi, guys. I'm new on khan academy and could you tell me where can i find some exercises, please?
Here https://www.khanacademy.org/math . I hope you will find this link useful :)
what about the laws of pemdas?
negative numbers are just like positive numbers when it comes to PEMDAS.
So a positive+positive is positive neg+neg is negative. I understand that a positive times pos is positive but how is it that a negative times negative is positive? Ex: -2 x -4=8 . How is that possible! Is it because -2 goes into 8 4 times meaning positive?
I'm confused
Same sign is always positive, different sign is always negative. That's mean
+ times + = +
- times - = +
(see same sign)
+ times - = -
- times + = -
(different sign)
Does a positive and a negitive equal a negitive and why?
A positive times a negative DOES equal a negative. Why? Well, here:

Say we're multiplying 5 and -3. 5 is just 5, but we can write -3 as -1*3. So we have: -1*3*5 The 3*5 part is easy, it's just 15. Then we have to multiply by -1, and if we add -1 to itself 15 times, we get -15. Hope that helps!
i used to think that those were hard they kinda easy if u listien and ask ouestions
Thankkss again for this video :)
The only problem that I am having is I will watch some of the videos and they do not fill in green as watched. I do not understand this because some of the videos are pretty long and my Instructor checks the site to see if I watched so she might think I am not watching when I am in fact watching.
thanks :) I appreciate the feedback
i thought the when the neg is bigger its alway a neg
How many multiplications of positive + negative integers are there with an answer of -6 ?
one negative and one positive example 3x(-2)
Negitive 1 times a negitive 5 is negitive 5 right ?
Do you mean -1 X -5=?
-1 X -5 = 5
Does -2 x 3=2 x -3
Yes, I think its just an extension of the communitive property.
Why is it when they are both negative then you just regularly multiply but when one is negative and the other isn't you have to have a negative answer?
At 2:48 why does pos times neg have to be neg? is there a reason for that?
If you tell yourself that Multiplication is the same as repeated addition, then:
4x -9
is the same as saying "four times -9", or:
-9 + -9 + -9 + -9 -> -9-9-9-9 = -36
sal I really think your viedo really help me
Is timesing, a negative and a negative basically timesing a positive and a postive...? eg. -1 x -1 = 1, -3 x -3 = 9?
Yes, multiplying a negative and a negative will always give you a positive result.
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
you should do cross multplication :)
i dont like demicals but i am getting used to it if aby of you can give me inves about it that would me good thanks
Decimals are really good to learn about
i hope u know about place value system in which "0" is the place value holder
similarly this just an extension of the place value system for fractions which as no greatest common divisor
for an example
there is no number which divides them
but using decimals u can do it and u will end up with 1/2 which is
equal to 0.5 and here according to place value system the place value system of 5 is 1/10 and many numbers of great importance like "golden number",pi
etc which are frequently used are based on this concept.
i hope this worked
so if 2 x 3 = then if they were negative would it be -6 (the problem:-3 x -2) and how would it equal a positive
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