Negative numbers and absolute value
Multiplying and dividing negative numbers
None
Multiplying positive and negative numbers
Learn some rules of thumb for multiplying positive and negative numbers.
Discussion and questions for this video
 We know that if we were to multiply two times three,
 that would give us positive six.
 And so we are going to think about negative numbers in this video.
 One way to think about it,
 is that I have a positive number times another positive number,
 and that gives me a positive number.
 So if I have a positive times a positive,
 that would give me a positive number.
 Now it's mixed up a little bit.
 Introduce some negative numbers.
 So what happens if I had negative two times three?
 Negative two times three.
 Well, one way to think about it
 Now we are talking about intuition in this video
 and in the future videos.
 You could view this as negative two repeatedly added three times.
 So this could be negative two plus negative two plus negative two
 Not negative six. Plus negative two.
 which would be equal to
 well, negative two plus negative two is negative four,
 plus another negative two is negative six.
 This would be equal to negative six.
 Or another way to think about it is,
 if I had two times three, I would get six.
 But because one of these two numbers is negative,
 then my product is going to be negative.
 So if I multiply, a negative times a positive,
 I'm going to get a negative.
 Now what if we swap the order which we multiply?
 So if we were to multiply three times negative two,
 it shouldn't matter.
 The order which we multiply things don't change,
 or shouldn't change the product.
 When we multiply two times three, we get six.
 When we multiply three times two, we will get six.
 So we should have the same property here.
 Three times negative two should give us the same result.
 It's going to be equal to negative six.
 And once again we say, three times two would be six.
 One of these two numbers is negative,
 and so our product is going to be negative.
 So we could draw a positive times a negative
 is also going to be a negative.
 And both of these are just the same thing with the order
 which we are multiplying switched around.
 But this is one of the two numbers are negative. Exactly one.
 So one negative, one positive number is being multiplied.
 Then you'll get a negative product.
 Now we'll think about the third circumstance,
 where both of the numbers are negative.
 So if I were to multiplyI'll just switch colors for fun here
 If I were to multiply negative two times negative three
 this might be the least intuitive for you of all,
 and here I'm going to introduce you the rule,
 in the future I will explore why this is,
 and why this makes mathematics moreall fit together.
 But this is going to be, you see, two times three would be six.
 And I have a negative times a negative,
 one way you can think about it is that negatives cancel out!
 So you'll actually end up with a positive six.
 Actually I don't have to draw a positive here.
 But I write it here just to reemphasize.
 This right over here is a positive six.
 So we have another rule of thumb here.
 If I have a negative times a negative,
 the negatives are going to cancel out.
 And that's going to give me a positive number.
 Now with these out of the way, let's just do a bunch of examples.
 I'm encouraging you to try them out before I do them.
 Pause the video, try them out, and see if you get the same answer.
 So let's try negative one times negative one.
 Well, one times one would be one.
 And we have a negative times a negative. They cancel out.
 Negative times a negative give me a positive.
 So this is going to be positive one.
 I can just write one,
 or I can literally write a plus sign there to emphasize.
 This is a positive one.
 What happened if I did negative one times zero?
 Now this might seem, this doesn't fit into any of these circumstances,
 zero is neither positive nor negative.
 And here you just have to remember anything times zero
 is going to be zero.
 So negative one times zero is going to be zero.
 Or I could've said zero times negative seven hundred and eightythree,
 that is also going to be zero.
 Now what about twolet me do some interesting ones.
 What aboutI'm looking a new color.
 Twelve times negative four.
 Well, once again, twelve times positive four would be fourtyeight.
 And we are in the circumstance where one of these two numbers,
 right over here, is negative. This one right here.
 If exactly one of the two numbers is negative,
 then the product is going to be negative.
 We are in this circumstance, right over here.
 We have one negative, so the product is negative.
 You could imagine this as repeatedly adding negative four twelve times
 And so you will get to negative fourtyeight.
 Let's do another one.
 What is seven times three?
 Well, this is a bit of a trick. There are no negative numbers here.
 This is just going to be seven times three.
 Positive seven times positive three. The first circumstance,
 which you already knew how to do before this video.
 This would just be equal to twentyone.
 Let's do one more.
 So if I were to say negative five times negative ten
 well, once again, negative times a negative.
 The negatives cancel out.
 You are just left with a positive product.
 So it's going to be five times ten. It's going to be fifty.
 The negative and the negative cancel out.
 Your product is going to be positive.
 That's this situation right over there.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

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So when you multiply 0 with any number, positive or negative, you get 0? Is that right?
Yes anything multiplying 0 is always going to be 0
You bet. Let's take 4*8 as an example. The first number (4) is what is being multiplied, and the second number (8) is how many times it's being multiplied. Multiplication itself is just taking a number and adding it to zero repeatedly. So if we take 4 and add it to zero 8 times (4*8), we would get 32. 0, 4, 8, 12, 16, 20, 24, 28, _32_. But we don't count the zero because that's multiplying it by nothing.
Now say that we take four and multiply it by absolutely nothing (0). Well, again, how many times are we adding 4 to zero? 0 times. 4 times 0 is 0. Zilch. Nada. Nothin'. Gone with the wind.
Hope this helps.
Now say that we take four and multiply it by absolutely nothing (0). Well, again, how many times are we adding 4 to zero? 0 times. 4 times 0 is 0. Zilch. Nada. Nothin'. Gone with the wind.
Hope this helps.
yes zero multiply by any number is all ways zero  or +
Yes, you are right.
yes! even though there is a neg 0 or pos 0 is still 0.
Yes and remember there is no such thing as 0.
yes it will equal 0
yes it's the multiplicative property of zero I'm learning it in my real classroom
yes because you not timing nothing
If we multiply numbers including positive and negative numbers with 0, the answer should be 0.
yes it is because 0 times anything is 0 because it is 0 of one number
anything you multiply by 0 is 0 because you multiply 1 0 times
of course. because multiplying 0 would still be 0.
Yes right :)😀
yep that is true if you multiply anything by zero you will always get zero.!
#Yup anything multiplying by 0 is always 0
yes it is because no matter what x0 it is always 0.(even negative numbers.)
Yes because since 0 is a neutral, you can't give it a negative or a positive sign, dude.
yes. use the identity property of multiplication or division
00000000000000000 zero!
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.
First, this video is about multiplying, not adding!
like he said negatives cancel out and make a positive so then it would be a positive + positive.
Also remember the order of operations.
it is pos as neg and neg cancels and pos remains
3+2+2 = 3 When adding you go from left to right. 3 +2 = 5, 5 + 2 = 3 Think of it in terms of a number line.
whatever there is more of
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.
5 x 1 IS 5, not 1
I still works the same multiplicative identity says anything multiplied by 1 will equal the factor that was multiplied by 1
the answer is 5
#yup its 5 cuz 1×any number is always the other number ;)
5*1=5 because if you multiply any number with one you get the number itself this rule works with negative numbers also
5 x 1 = 5.
If a number in the equation is a negative number, then the answer will be too.
ex.
2 x 3 = 6
If a number in the equation is a negative number, then the answer will be too.
ex.
2 x 3 = 6
5 x 1 would be 5. 5 x 1 would be 5
5x1 is absoulty 5. anything times 1 is the same number. even negatives
It is infinity if it is 0.61747247563028475... and it is and infinity number if it is the number pie
5 times 1 is 5 because any nonzero number multiplied by 1, regardless of its sign, equals that number.
are you really talkin to me
thanks that really helped
Can somebody explain what 2 x 3 "means"? Like 2 x 3 means 2+2+2.
With apologies for the late answer, but since the other answers are just telling you how to solve the equation, here's a way you can think about the topic of multiplying with negative numbers:
Basically, if you're multiplying 2 x +3 you could read it as (for example) "I have zero dollars, and from this balance, I'm removing three dollars twice".
Going further, 2 x 3 could be "I'm removing a negative three dollars twice". You can see how there's a double negative in that: You're removing (one negative) something negative (second negative).
Say you owe two people three dollars each, and you keep a record of that. Your notes tell you that you've got a 6 dollar debt, or you've got 6 dollars. Then when you pay both of them back, you're removing this debt from your notes! So you're removing 3 dollars from your notes twice, or 2 x 3 dollars. 2 x 3 works out to 6, which is the amount of dollars you paid back. In your notes, you'd put down that you paid 6 dollars, and your new balance is 0 (= you don't owe anyone anything).
Generally speaking, a way to think about negative x ______ multiplication is to think of it as a reduction. From that, one way to think about negative x negative multiplication is to think of it as debt (< one negative) reduction (< the second negative).
Basically, if you're multiplying 2 x +3 you could read it as (for example) "I have zero dollars, and from this balance, I'm removing three dollars twice".
Going further, 2 x 3 could be "I'm removing a negative three dollars twice". You can see how there's a double negative in that: You're removing (one negative) something negative (second negative).
Say you owe two people three dollars each, and you keep a record of that. Your notes tell you that you've got a 6 dollar debt, or you've got 6 dollars. Then when you pay both of them back, you're removing this debt from your notes! So you're removing 3 dollars from your notes twice, or 2 x 3 dollars. 2 x 3 works out to 6, which is the amount of dollars you paid back. In your notes, you'd put down that you paid 6 dollars, and your new balance is 0 (= you don't owe anyone anything).
Generally speaking, a way to think about negative x ______ multiplication is to think of it as a reduction. From that, one way to think about negative x negative multiplication is to think of it as debt (< one negative) reduction (< the second negative).
Please correct me if I am wrong, But adding a positive to a negative will not always give you a positive number. The positive number that you ad to the negative number MUST be larger.
ie; any number added to 3 MUST be larger than 3 to become a positive number, if you add 2 to 3 you will still have 1 and also you started talking about adding numbers when it was a multiplication question. It gets kind of confusing when someone wants to know why a neg x neg = pos. Just my thoughts when I was reading the answer and you said 2 + +3 would be 6 when it is actually +1 and because if there is one negative number in an equation it automatically turns into a negative answer is incorrect. Only in certain equations , it is not the standard for all equations.
ie; any number added to 3 MUST be larger than 3 to become a positive number, if you add 2 to 3 you will still have 1 and also you started talking about adding numbers when it was a multiplication question. It gets kind of confusing when someone wants to know why a neg x neg = pos. Just my thoughts when I was reading the answer and you said 2 + +3 would be 6 when it is actually +1 and because if there is one negative number in an equation it automatically turns into a negative answer is incorrect. Only in certain equations , it is not the standard for all equations.
Math is like a game where mathematicians have given names to a lot of things (definitions), and have choosen some rules (formally called axioms). So the formal explanation, that sometimes it may seem a little too obvious, and sometimes overly burocratic, is the following.
Let's begin with some names for stuff and a few rules:
* First, you need to know that in fact, the negative numbers are defined as such that added to its opposite number give 0. This means that (2) is defined as the number that added to 2 is equal to 0; so (2)+2 = 2+(2) = 0. And there's a rule that tells use that that opposite number always exists.
* Then you need to know that adding 0 to any number, gives the same number, so (2)+0 = 0+(2) = 2. Also multiplying anything by one doesn't change the result, so 1*X = X*1 = X.
* After that you also need to know that the "substraction" is defined as adding the opposite number, and here we can use the negative numbers, so 02 is the same as 0+(2), by the definition.
* There's also another very simple rule called "conmutativity" for addition and multiplication, for any two numbers (lets call them A and B), we know that A+B=B+A, and that A*B=B*A.
* And there's also another rule called "associativity": A+(B+C) = (A+B)+C, and also A*(B*C)=A*(B*C); here it means that it doesn't matter if you add A and B first together and then add C to the result, later, or if you begin adding B and C, and then A + the result of B+C.
* And finally the most complicated rule is called "distributivity law". Take any numbers, call them A, B, and C, and then we know that A*(B+C) = A*B + A*C. Thinking about how multiplying A*(B+C) is repeating A+A+...+A, (B+C) times, which is the same as those (A+A+...+A, b times) + (A+A+...+A, C times), it's clear that adding those number of times before multiplying is the same as adding the results of the multiplications later. There's also a video about the distributivity if you didn't understand it at first.
You probably already know that anything by 0 is 0, however it isn't a rule that comes by default in mathematics. However let's create that rule by using the previous ones:
0; changing the 0 for anything of the form AA since we know that 0=AA for any A.
=x*0x*0; adding a 0 to the first 0, since it doesn't change the result.
=x*(0+0)x*0; using the so called "distributivity law"
=(x*0+x*0)x*0; now let's use "associativity" to change the order we use for adding:
=x*0+(x*0x*0); and since we know AA is 0, let' change the x*0  x*0 for a 0:
=x*0+0; finally since adding 0 doesn't change the resul, let's take that 0:
=x*0;
=> We have "proven" that x*0=0. So from now on, anytime we see a anything multiplied by 0, we know it's 0.
So for the following step, let's create another rule by using the previous one (imagine x is any number):
(1)*x; let's use conmutativity (swapping the numbers)
=x*(1); then let's add a 0 since we know it doesn't change the result:
=x*(1)+0; and now let's change the 0 to something of the form AA, since AA=0
=x*(1)+(x*1x*1); let's use associativity for addition:
=(x*(1)+x*1)x*1; and using the rule previously called "distributivity"
=x*(1+1)x*1; we know again that 1+1=1+1=0... so:
=x*0x*1; and anything by 0 is 0 (we've just proven that), and anything by 1 is the same (a previous rule)
=0x; let's remove that useless zero
=x
=> So now we know that (1)*x = x. We can use that!
We are almost there, we need to show that the opposite of the opposite of something, is the original value, in other words x=(x).
x; adding a +0 without changing anything:
=x+0; since we know that AA=0, we change that 0 to (x)  (x):
=x+[(x)(x)]; let's use "associativity":
=[x+(x)](x); and now we have xx=0:
=0(x); by definition of substraction:
=0+((x)); removing that useless 0+:
=(x)
=> So now we have that x = (x)....
Finally! finally we can multiply (2) by (3), let's go on:
(2)*(3); by using (x)=(1)*x that we've just proven:
= (1)*2*(1)*3; then by using "conmutativity" and "associativity" several times:
= (1)*(1)*2*3; now by using the (1)*x=(x), we can change (1)*[1] for [1]
= ((1))*2*3; we also know that the opposite of the opposite is the original number:
= 1*2*3; and that multiplying by 1 doesn't change anything:
= 2*3
Hope this helps, and if you managed to understand this demonstration, you should feel pretty happy since it's thought on a University signature called "Calculus".
Let's begin with some names for stuff and a few rules:
* First, you need to know that in fact, the negative numbers are defined as such that added to its opposite number give 0. This means that (2) is defined as the number that added to 2 is equal to 0; so (2)+2 = 2+(2) = 0. And there's a rule that tells use that that opposite number always exists.
* Then you need to know that adding 0 to any number, gives the same number, so (2)+0 = 0+(2) = 2. Also multiplying anything by one doesn't change the result, so 1*X = X*1 = X.
* After that you also need to know that the "substraction" is defined as adding the opposite number, and here we can use the negative numbers, so 02 is the same as 0+(2), by the definition.
* There's also another very simple rule called "conmutativity" for addition and multiplication, for any two numbers (lets call them A and B), we know that A+B=B+A, and that A*B=B*A.
* And there's also another rule called "associativity": A+(B+C) = (A+B)+C, and also A*(B*C)=A*(B*C); here it means that it doesn't matter if you add A and B first together and then add C to the result, later, or if you begin adding B and C, and then A + the result of B+C.
* And finally the most complicated rule is called "distributivity law". Take any numbers, call them A, B, and C, and then we know that A*(B+C) = A*B + A*C. Thinking about how multiplying A*(B+C) is repeating A+A+...+A, (B+C) times, which is the same as those (A+A+...+A, b times) + (A+A+...+A, C times), it's clear that adding those number of times before multiplying is the same as adding the results of the multiplications later. There's also a video about the distributivity if you didn't understand it at first.
You probably already know that anything by 0 is 0, however it isn't a rule that comes by default in mathematics. However let's create that rule by using the previous ones:
0; changing the 0 for anything of the form AA since we know that 0=AA for any A.
=x*0x*0; adding a 0 to the first 0, since it doesn't change the result.
=x*(0+0)x*0; using the so called "distributivity law"
=(x*0+x*0)x*0; now let's use "associativity" to change the order we use for adding:
=x*0+(x*0x*0); and since we know AA is 0, let' change the x*0  x*0 for a 0:
=x*0+0; finally since adding 0 doesn't change the resul, let's take that 0:
=x*0;
=> We have "proven" that x*0=0. So from now on, anytime we see a anything multiplied by 0, we know it's 0.
So for the following step, let's create another rule by using the previous one (imagine x is any number):
(1)*x; let's use conmutativity (swapping the numbers)
=x*(1); then let's add a 0 since we know it doesn't change the result:
=x*(1)+0; and now let's change the 0 to something of the form AA, since AA=0
=x*(1)+(x*1x*1); let's use associativity for addition:
=(x*(1)+x*1)x*1; and using the rule previously called "distributivity"
=x*(1+1)x*1; we know again that 1+1=1+1=0... so:
=x*0x*1; and anything by 0 is 0 (we've just proven that), and anything by 1 is the same (a previous rule)
=0x; let's remove that useless zero
=x
=> So now we know that (1)*x = x. We can use that!
We are almost there, we need to show that the opposite of the opposite of something, is the original value, in other words x=(x).
x; adding a +0 without changing anything:
=x+0; since we know that AA=0, we change that 0 to (x)  (x):
=x+[(x)(x)]; let's use "associativity":
=[x+(x)](x); and now we have xx=0:
=0(x); by definition of substraction:
=0+((x)); removing that useless 0+:
=(x)
=> So now we have that x = (x)....
Finally! finally we can multiply (2) by (3), let's go on:
(2)*(3); by using (x)=(1)*x that we've just proven:
= (1)*2*(1)*3; then by using "conmutativity" and "associativity" several times:
= (1)*(1)*2*3; now by using the (1)*x=(x), we can change (1)*[1] for [1]
= ((1))*2*3; we also know that the opposite of the opposite is the original number:
= 1*2*3; and that multiplying by 1 doesn't change anything:
= 2*3
Hope this helps, and if you managed to understand this demonstration, you should feel pretty happy since it's thought on a University signature called "Calculus".
You are essentially doing the same multiplication as you would with positives, but negatives. Since negative numbers are very similar to positive numbers, 2*3 is essentialy 2*3, or 2+2+2.
Now to answer your question, I doubt there even is a possible way to demonstrate it. If you try to multiply backwards, You would need to multiply 2 by 4 to get to 6. You would istead of adding, you would subtract. This does not work:2(2)(2)=4. You would need to multiply by four to get to six, but 2 x 4 is obviously not 6.
I am very sorry if I misunderstood anything, please correct me if I did.
Now to answer your question, I doubt there even is a possible way to demonstrate it. If you try to multiply backwards, You would need to multiply 2 by 4 to get to 6. You would istead of adding, you would subtract. This does not work:2(2)(2)=4. You would need to multiply by four to get to six, but 2 x 4 is obviously not 6.
I am very sorry if I misunderstood anything, please correct me if I did.
Can 0 be positive or negative?
Zero is neither positive or negative, although you could say it's positive or negative. However zero is not used as a negative very often. (How often do you see 0 in a math problem?)
BOTH! 0 is a pos and a neg.
If you have zero of something you have none so you cant have a positive value since you don't have anything and it is not negative since you are not going past the negative limit. For example with money, zero is not positive since you don't have any money and it is not negative since you don't owe any money. You just don't have any money.
Zero is just zero
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
what is the sign (_9)
i do not know
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.
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.
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.
Nathan is right and another way of thinking about it is this: so let's say 10 x 4 x 2
10 x 4 would be +40. then you multiply +40 by 2 and you'll get 80
multiplying three (or any odd number of) negative numbers will always have a negative answer
10 x 4 would be +40. then you multiply +40 by 2 and you'll get 80
multiplying three (or any odd number of) negative numbers will always have a negative answer
Why negative times negative gives positive ?
2 * 3 means add 2 to itself 3 times which equals 6
but what does 1 X 1 means ?
2 * 3 means add 2 to itself 3 times which equals 6
but what does 1 X 1 means ?
Think of it as taking away a debt of $1, one time. If you take that debt away, $1 more than you did before. So 1*1=1
Sal says that negative times positive is equal to negative, but when he multiplies 12 by negative four , he doesn't put a negative sign by the fortyeight.
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
how would we multiply fractions
you do the recipricol of the problem
When you multiply fractions, the easiest way to multiply for me, is to, line of the fractions up side by side in the format of an equation and multiply the denominators be each other, and the numerators by each other. Hoped it helped! :)
What if you have parenthesis? like 3 x (4) = 3 x ?
There are parentheses around negative numbers to help separate them from the rest of the numbers and signs. A negative sign looks identical to a subtraction sign, so they want to separate them so people wouldn't get confused. Just work it like normal.
what about it
is there such thing as negative 0? like 0
No, Zero can't be a negative because it isn't a true value.
When you multiply a negative number and a negative number, does the number becomes more negative? I mean, LOL, does it go more to the left of the number line?
here is what i learned:
negative and negative is positive
positive and positive is positive
negative and positive is negative
positive and negative is negative
i hope this helps!
negative and negative is positive
positive and positive is positive
negative and positive is negative
positive and negative is negative
i hope this helps!
I recommend really focusing/understanding what he is talking about in the next lesson after that.
https://www.khanacademy.org/math/prealgebra/negativesabsolutevalueprealg/multdivnegativesprealg/v/whyanegativetimesanegativemakesintuitivesense
https://www.khanacademy.org/math/prealgebra/negativesabsolutevalueprealg/multdivnegativesprealg/v/whyanegativetimesanegativemakesintuitivesense
Why is it that two negitives equal a positive?
20150730T01:49:41Z
by
Anonymous
Because on a number line, each negative added together goes up the number line instead of down.
20150730T01:55:07Z
by
Anonymous
When Sal said any number times 0=0, does any number include infinity? Is infinity even a number, just an expression, or something else?
Infinity is an expression. No matter how many times you add, subtract, divide, or multiply, you will get either 0 or infinity. You cannot count to is, no matter if you are counting by fives, or counting by 1000s. However, you can express different occasions where you get infinity. e.g. 5/0. This makes many people believe that it is a number. However, wether it is used as an addend, or a divedend, you either get 0 or infinty. It is simply not a number.
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 countingagree? 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.
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.
adamchessulrich  Infinity is not a number. To say that it is means that it is countable. Any infinite would be in an uncountable set. The result would be an indeterminate form if you tried. So, it's like dividing by 0, you just can't do it basically.
@karsang  Calculus doesn't treat infinity as a number. It still treats it as a concept. You would be talking about limit  as a number approaches infinity for example (e.g.: an exceptionally large number).
@karsang  Calculus doesn't treat infinity as a number. It still treats it as a concept. You would be talking about limit  as a number approaches infinity for example (e.g.: an exceptionally large number).
Well, anything times 0 is always zero. This also includes infinity and millions.
I thought u said they would be negative im confused
what indacates division?
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.
When typing on your computer, it is acceptable to use a forward slash for division. In other instances a dash with a dot above and below is used.
Why is negative times a negative a positive while positive times a positive is not negative?
Something times something else with the same sign always equals a positive number. Just remember that! :)
Happy holidays!!
Happy holidays!!
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.
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.
Which video shows why a negative times a negative is a positive?
https://www.khanacademy.org/math/prealgebra/negativesabsolutevalueprealg/multdivnegativesprealg/v/whyanegativetimesanegativeisapositive
This is the link for why 2 negatives make a positive
This is the link for why 2 negatives make a positive
Why is 0 a neutral number?
Zero is the balance of a number line. It lies on neither side of negative or positive.
because it is neither negative or positive
I know that anything times 0 = 0, but isn't it just times nothing? Like 400 x 0 = 0 right? But zero is like nothing so shouldn't it be 400?
It would still be 0, because it would be multiplying 400 by nothing, therefore you would have 400 nothings, which would be 0 because it's nothing.
no it should be 0 becuse 0 is something
I am a senior citizen and I am trying to understand neg and pos math problems and I need to see examples. what is 20 minus 12? 12 minus 20? 31 x 2? 10 divided by 5? 30 plus 7 , thank you for your help.
20 minus 12 can be seen as
20  12 = 32
The answer is 32 because the absolute value of 20 is 20, and the absolute value of minus 12 is 12. All you have to do is add 20 and 12, and add the negative sign.
31 x 2 = 2 x 31
If one neg number and one pos number are being multiplied together, I usually put the neg number first, but you can most certainly have your own way of setting up a problem.
2 x 31 = 62
The answer is 62 because you are first multiplying pos 31 and pos 2 (ignore the neg sign for now). The product of 31 and 2 is 62. Now, you need to stop ignoring the neg sign on the 2 and put the neg sign beside the 62, which is 62.
10 divided by 5 is the same thing as
10 ÷ 5 = 2
If you divide pos 10 by pos 5 and ignore the neg sign beside the 10 for a moment, the answer is 2. Now you forget about ignoring the neg sign and put it beside the 2, so the answer is 2.
30 + 5 is the same as
5  30 = 25
I look at this original problem, 30 +5, as 30  5, which is 25. Then, I add the neg sign to the 25, of which is 25. I set the problem up as 30  5 first because I know that 30 = 30 and that 5 = 5. I also know that the neg sign can wait on the sidelines for a moment.
I hope that I helped you understand neg and pos math problems more.
20  12 = 32
The answer is 32 because the absolute value of 20 is 20, and the absolute value of minus 12 is 12. All you have to do is add 20 and 12, and add the negative sign.
31 x 2 = 2 x 31
If one neg number and one pos number are being multiplied together, I usually put the neg number first, but you can most certainly have your own way of setting up a problem.
2 x 31 = 62
The answer is 62 because you are first multiplying pos 31 and pos 2 (ignore the neg sign for now). The product of 31 and 2 is 62. Now, you need to stop ignoring the neg sign on the 2 and put the neg sign beside the 62, which is 62.
10 divided by 5 is the same thing as
10 ÷ 5 = 2
If you divide pos 10 by pos 5 and ignore the neg sign beside the 10 for a moment, the answer is 2. Now you forget about ignoring the neg sign and put it beside the 2, so the answer is 2.
30 + 5 is the same as
5  30 = 25
I look at this original problem, 30 +5, as 30  5, which is 25. Then, I add the neg sign to the 25, of which is 25. I set the problem up as 30  5 first because I know that 30 = 30 and that 5 = 5. I also know that the neg sign can wait on the sidelines for a moment.
I hope that I helped you understand neg and pos math problems more.
uhhhhh yesh i think uhhh
what is that number
help me with negative numbers
What do you need help with?
Guys, if you want to be good at this, memorize all the combinations. Like this:
positive x negative = negative
positive x positive = positive
positive + negative = {[(no matter what the circumstance, if your adding or subtracting, subtract the bigger number by the smaller number not considering negative signs]
Example: 10 + 20
2010 = 10
(the sign is determined by which number in the equation is bigger)
so... 10+20= 10
}
(if you didn't get this, it's ok, you'll get it eventually!!)
positive x negative = negative
positive x positive = positive
positive + negative = {[(no matter what the circumstance, if your adding or subtracting, subtract the bigger number by the smaller number not considering negative signs]
Example: 10 + 20
2010 = 10
(the sign is determined by which number in the equation is bigger)
so... 10+20= 10
}
(if you didn't get this, it's ok, you'll get it eventually!!)
54÷(−6)=? how to do this ?
First, figure out what sign the answer would have. Because the six is a negative and 54 is a positive, the answer would be negative, as that is the rule. Now, you just use your multiplication skills to figure out the answer.
P.S. the answer is 9.
P.S. the answer is 9.
Use the order of operations for this problem.
you would divide it like normal but then add the negative sign from the six
9
9
how does a negative times a negative a positve wouldn't it be negative?
Because a 'negative' symbol doesn't actually mean negative, it's more or less telling you to 'switch directions' on a number line. So a negative number multiplied by a negative number is basically canceling itself out.
that's what math wants you to think, math knows the real answers, math just is being greedy.
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!
I can help 2 k :>
It's not really confusing; you would multiply/divide the two numbers as you normally would and all you need to know is that (neg x pos = neg) (neg x neg = pos) (and of course pos x pos = pos)
example: 8 x 4 just get the answer which is 32 and then you can remember that (pos x neg = neg), so you get 32
hope this helps
example: 8 x 4 just get the answer which is 32 and then you can remember that (pos x neg = neg), so you get 32
hope this helps
A tip:
1.) a*b = a + a + ... 'b' times
2.) a*b = (a) + (a) + ... 'b' times = a  a... 'b' times
3.) a*b = a  a... 'b' times = [(a)] + [(a)] + ... 'b' times = a + a + ... 'b' times
1.) a*b = a + a + ... 'b' times
2.) a*b = (a) + (a) + ... 'b' times = a  a... 'b' times
3.) a*b = a  a... 'b' times = [(a)] + [(a)] + ... 'b' times = a + a + ... 'b' times
This is kinda hard
once you learn a bit more you will soon understand it a whole lot better!
so that means that if you have 2 x 3 x 5 x 6 = +180
yes, you did the math right. Good Job! :)
How come when you multiply a negative times a negative u also get a positive?
Wouldn't that be a negative as well?.
Wouldn't that be a negative as well?.
no just multiplication and division has those rules it is what is is and much easier than adding or subtracting integers :) if you don't get it watch the videos it helped me :)
why do you get a positive number when you multiply two negative numbers?
Because the negative ALWAYS overtakes a positive think of Star wars, like Luke overcomes Darth or something like that. Just remember that " Positives are no match for the powerful negatives" :)
why must 2 negative numbers always cancel each other out?
```if (x < 0) {Multiplying two negative numbers results in a positive number because the product of two negative numbers can be described as the additive inverse of a positive number.}``` 😁 😁 😁
don't get multiplying positive and negative numbers
if you multiply a negative number with a positive number you get a negative number, if you multiply a negative number with a negative number you get a positive number hope this helps :)
What is the math behind this?
well, think of it this way. 2 * 2. what is the answer? well, you have negative two on the number line. you multiply that, going in the same direction. (negative direction) by two. so you get four.
now, if you multiplied by 2 (so now the new problem is 2 * 2), you would change directions, again. first you were going in the positive direction. you changed to the negative direction(because of the start number being negative 2), and then, when you multiplied it by 2, you changed directions again. you can think of it as multiplying a number by negative one, means change directions.
So anyway, you now multiply by 2, change directions, and get 4. so the answer to 2 * 2 = 4. thanks! hope this helps!
now, if you multiplied by 2 (so now the new problem is 2 * 2), you would change directions, again. first you were going in the positive direction. you changed to the negative direction(because of the start number being negative 2), and then, when you multiplied it by 2, you changed directions again. you can think of it as multiplying a number by negative one, means change directions.
So anyway, you now multiply by 2, change directions, and get 4. so the answer to 2 * 2 = 4. thanks! hope this helps!
I don't get this video? It doesn't make since to me i don't know why but I don't get it
The way I remember how to multiply negatives and positives is this:
Think of positive numbers as good guys and negative numbers as bad guys.
A good thing happening to a good guy is a good thing
Positive x Positive = Positive
A good thing happening to a bad guy is a bad thing.
Positive x Negative = Negative
A bad thing happening to a good guy is bad.
Negative x Positive = Negative
A bad thing happening to a bad guy is good.
Negative x Negative = Negative
I hope this helps. :)
Think of positive numbers as good guys and negative numbers as bad guys.
A good thing happening to a good guy is a good thing
Positive x Positive = Positive
A good thing happening to a bad guy is a bad thing.
Positive x Negative = Negative
A bad thing happening to a good guy is bad.
Negative x Positive = Negative
A bad thing happening to a bad guy is good.
Negative x Negative = Negative
I hope this helps. :)
I wish I could help but this video doesn't help me either
what if the question is pos+pos+neg
if you are adding, it depends on the numbers. for multiplying, the answer would be a negative.
How will this help me
This will help you when measuring lengths.
do you have avidei of a mi x o negitive and positive numbers their called comlacaited number (i read it in a book)?
I have a question about subtracting negative numbers... how do you know how to subtract a problem like this: (2)  10 I will do it the way I know how...
(2  10 = 8,
but this ends up being wrong and it's actually the answer you would get if you were to add. I am a little confused. Could someone help me answer this question? Thanks! ^_^
(2  10 = 8,
but this ends up being wrong and it's actually the answer you would get if you were to add. I am a little confused. Could someone help me answer this question? Thanks! ^_^
( 2 )  10 = ?
2 + 10 = 12
The answer to your problem is 12
You forget 2 is negative, if it wasn't, this is what it would look like:
2  10 = ?
2  10 = 8
2 + 10 = 12
The answer to your problem is 12
You forget 2 is negative, if it wasn't, this is what it would look like:
2  10 = ?
2  10 = 8
could a negative cancel out a positive
only if it's the same or higher number
If you multiply a positive times a positive times a negative...is is positive or negative?
you would use associotive property so multiply 4 and 2 first then by negative
negative, think if you multiply 4 x 2x (5), its the same thing as 8 x (5), and since positive times negative equals a negative it would equal 40
the videos should include more difficult problems and not use things like 6+(3), just a suggestion
Multiplying and dividing negative numbers have always confused me. I'm sure that the answer is really obvious but how do you know if the answer is a positive or a negative?
Well, here are the four general rules to know:
```Positive x Positive = Positive
Positive x Negative = Negative
Negative x Positive = Negative
Negative x Negative = Positive
```
```Positive x Positive = Positive
Positive x Negative = Negative
Negative x Positive = Negative
Negative x Negative = Positive
```
Why is that when a negative plus a negative would be a positive I do not get that concept and when a positive pluse a positive is a negative
😳😕😧😦😜😝😎
😳😕😧😦😜😝😎
decimals are like fraictons so its bellow 1.
exzample: 40.86 86 is on the right and the decilmals are pernosed tenths or hundredths so you need a  in your fraiction
exzample: 40.86 86 is on the right and the decilmals are pernosed tenths or hundredths so you need a  in your fraiction
@ 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 if a positive times a positive, it is still positive right?
Right. Its Positive x Positive is just like basic multiplication. :) positive answer every time
If I'm calculating (2)2 meaning negative 2 squared, is my answer to the problem of 1 x 4 a negative 4 or positive 4?
The answer is negative four because you first distribute the negative sign in front of the (2) into (2). A negative times a negative equals a positive, so the question is now (2)2.
2 • 2 = 4.
2 • 2 = 4.
What would happen if you multiplied negative times negative times positive?
The commutative property of addition states order does not matter in multiplication so you can say:
1.negative times negative is a positive. positive times positive is positive.
2. negative times positive is negative. Negative times negative is positive.
So you would get a positive.
1.negative times negative is a positive. positive times positive is positive.
2. negative times positive is negative. Negative times negative is positive.
So you would get a positive.
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
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.
its kinda confusing when we do a negative times a negative and get a positive how is that
Look at this video: https://www.khanacademy.org/math/arithmetic/absolutevalue/mult_div_negatives/v/whyanegativetimesanegativeisapositive
Also, they cancel each other out.
Also, they cancel each other out.
Is there a 0?
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.
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.
I just thought that two lines like in 2 x3 and their are two lines in a positive sign like in +6 so that is my way of looking at it.
Yeah that's what the answer is just look at 1:14