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 multiply–I’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 more–all 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 eighty-three, that is also going to be zero. Now what about two–let me do some interesting ones. What about–I’m looking a new color. Twelve times negative four. Well, once again, twelve times positive four would be fourty-eight. 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 fourty-eight. 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 twenty-one. 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.

lol he goes from vector fields to multiplying positive and negative numbers. the contrast!

Monetary*

Stokes' theorem is easy but I don't have a clue what this is about.

I just watch because it is pure pleasure, of course I know this stuff.

stfu

You're so helpful. I love you.

boreing

yhe school makes you watch it

So helpful!

very smart

THANK YOUUUUUUUUUUUUUUU OMG FINALLY I REMEMBER GOD BLESS YOU MY NIGGA

Hi.. Am.. I was just wondering that what, application b or program do you use to write with a black background

Hey thank you so much for this video great work. I had some thought on this and this is what i came up with:

Multiplication is the Mathematical Operation of repeated Addition or Subtraction of numbers to provide an equivalent single value.

The numbers being multiplied are called the 'Factors' and the result is called the 'Product'.

Factor x Factor = Product

Example 1: What is the product of 5 x 2 = ?

The example above uses a 'Positive Integer' for the first 'Factor' and it tells us what Mathematical Operation Symbol to use and how many grouped brackets we will need.

If the first factor is a 'Positive Integer' write the Addition Symbol and then the 5 Grouped brackets:

+ ( ) ( ) ( ) ( ) ( )

The second 'Factor' tells us what number to place in the grouped brackets.

write the number inside the grouped brackets: + (2) (2) (2) (2) (2)

Once this information has been completed, add up all the values to give the result for the 'Product'. which is 10.

Example 2: What is the product of -4 x 3 = ?

The example above uses a 'Negative Integer' for the first 'Factor' and it tells us what Mathematical Operation Symbol to use and how many grouped brackets we will need.

If the first factor is a 'Negative Integer' write the Subtraction Symbol and then the 4 Grouped brackets:

– ( ) ( ) ( ) ( ) ( )

The second 'Factor' tells us what number to place in the grouped brackets.

write the number inside the grouped brackets: – (3) (3) (3) (3)

Following the Rule for Subtraction turn the Mathematical operation into addition and substitue the Subtrahends the groups of numbers in this case to their opposites:

Write it out: + (-3) (-3) (-3) (-3)

Once this information has been completed, add up all the values to give the result for the 'Product'. which is -12.

Hope this helps as it tries to incorporate the rules of addition and sbtraction

What if there was pos neg pos

thank you!

nice good job with this site guys

I don't believe two negatives cancel each other out and make a positive any more than I believe two positives cancel each other out and make a negative. Can you help me? I think maths would be neater if -1 multiplied by -2= -1/2 not -1/-2 nor 2. As mathematical negativity is positivist omission not positively expansive, I believe multiplication and division should be 'reversed' for double negative equations. -1/-2= -2 not -1/-2 nor -1/2. The reason not to leave -1/-2 equalling itself is in order to perform the function of the equation instead of not performing a mathematical act. Moreover as the negative numbers are omissive the larger number becomes the denominator in negative multiplication and a numerator in negative division. Until negative numbers are treated as opposite to the whole values of positive numbers, maths may not become efficient enough to construct quantum computing. This is because the bits in the computer will not be applied sensibly to their non-predictability. Perhaps you could organise a computer calculator along this rule? I am not a mathematician but as a Political Scientist that two negatives can generate a number on the positive side of the number line smacks of delusional nihilism. Can you help me?

(0:44)

I lol'd pretty hard right here.

Thank you for your work Sal! Caught up in 4 months cause of your site! Keep on do'n you!

l=D

thank you!!

YEAH NOW I CAN DO MY WORK CORRECTLY AND NOT GET A F- LIKE LAST TIME!!!!

thank you so much

fuckin' math class..

Thanks Khan Academy! I no longer have to pay attention in class, because this is much easier!!

This was really helpful!

So what do you do if you have more than 3 multiplying?

your the best maths teacher i will subscibe to learn more

2 x X2 + 2 x -5

a=2

b=2

c=-5

__________x= -b + or – √b2 – 4ac

__________2a

Thanks a LOT!!!!!!!!!!!!!!!! You are the BEST in teaching math 😉

what is a=9, b=-24 i got this in math class.

Twenty one yeah

Math is awesome

THANK U

When I say "Eat!" I am encouraging you to eat (positive)

But when 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).

OML finally i found a vid that can help me in math class!!!

who is watching this in 2016?

this helped a lot

Thx i had this for homework and i got confused

FINALLY I UNDERSTAND!

Thank you!!!!! This video helped me soooooo much preparing my test!!!!!

Dis stoof Is ez

Thank you. I liked and subscribed

I am watching this in 2016. I am creating a maths club that only some people are invited to. And it's secret. I'm the smartest at maths apart from my teacher or teachers in practically all of grade 4 at my school.

thanks bro

very well explained – tysm <3

oh wow i have always had trouble with negatives even though i'm almost in highschool and this really helped so thanks !

I had this problem while studying for my half yearly. You earned a sub

what if (-10) x (-100) x (-99) x 103 x (-105)?

you are literally the best at this ever… every video you've made has helped me beyond belief. I got a years worth of work done in 3 days because of you.. thank you so much!!

Thanks so much! you helped me figure out how to do it

how come u guys explain better than the real teachers

Y u make it good but still so less watch?

He said-2 into -6 that is funny

thanks this helped

Jokes aside, this actually helped me. thxxxx

He helps me so much I’ve gone to this channel b4 and he’s great at explaining cuz my math teacher isn’t so I go to him

This is what I needed. I learn best through example, not by pictures or words.

Gee thanks man!!!

shukran

thank you so much! you just saved me from failing my negative numbers exam lol.

I have a login in khan academy my name is Diana112233 it was kinda hard to find a good name lol

Thanks so much

coo

on ixl it says this is wrong :/

thank you

they made us watch this in school and i already knew dis :')

i dont get this to old style

Thank u

Is there a possibility of a negative five having its own square root?

I get it now

What about (-3) (-3) (-3)?

My math teacher sucks when it comes to her teaching us… BUT THIS VID… HELPS SO MUCH. THANK U! 🤗

get off ms pait

Go watch the video ur gonna fail the test u have tomorrow lmao

this helped a lot thanks

math sux

OH MY GOD THE DISLIKE BUTTON WORKS THE DISLIKE BUTTON RELLEY WORKS!!!!! :))))_

Thx youre voice is chill

Thanks for this

who else came here from seneca learning

What I do is I Just Imagine The Odd And Even In Addition (I’m That 22Jtran Dude U Gave The Coding award to)

U r so good at explaining……. Thankx a lot

i came here from khan acadamy.org

Thank you so much

I’m not not tired

I’m tired

You are jesus

hi

Thanks a lot

what about multiple positive and negatives? such as: (-5) x 6 x (7) how do you know what sign to use? please help!

I really like khan Academy because they explain so clearly then the teachers in my school!

Lol my last name is khan and everyone in class was looking at me when the teacher was showing them

Thanks

i supposed to open youtube 7 years ago

True