# Basic multiplication | Multiplication and division | Arithmetic | Khan Academy

Let’s learn to multiply. M U L T I P L Y. And the best way I think to do

anything is just to actually do some examples, and then talk

through the examples, and try to figure out what they mean. In my first example

I have 2 times 3. By now you probably

know what 2 plus 3 is. That’s equal to 5. And if you need a bit of a

review you could think of if I had 2– I don’t

know– 2 magenta– this color– cherries. And I wanted to add

to it 3 blueberries. How many total pieces of

fruit do I now have? And you’d say, oh,

1, 2, 3, 4, 5. Or likewise, if I had our

number line, and you probably don’t need this review,

but it never hurts. Never hurts to

reinforce the concept. And it this is 0,

1, 2, 3, 4, 5. If you’re sitting 2 to the

right of 0 and in general, when we go positive

we go to the right. And if you were to add 3

to it, you would move 3 spaces to the right. So if I said, if I just

moved over 3 to the right, where do I end up? 1, 2, 3. I end up at 5. So either way, you understand

that 2 plus 3 is equal to 5. So what is 2 times 3? An easy way to think about

multiplication or timesing something is it’s just a

simple way of doing addition over and over again. So that you means is, and

it’s a little tricky. You’re not going to add 2 to 3. You’re going to add– and

there’s actually two ways to think about it. You’re going to add 2

to itself three times. Now what does that mean? Well, it means you’re going

to say 2 plus 2 plus 2. Now where did the 3 go? Well, how many 2’s

do we have here? Let’s see, I have– this

is one 2, I have two 2’s, I have three 2’s. I’m counting the numbers here

the same way that I counted blueberries up here. I had 1, 2, 3 blueberries. I have one, two, three 2’s. So this three tells me how

many 2’s I’m going to have. So what’s 2 times 3? Well, I took 2 and I added

to itself three times. So 2 plus 2 is 4. 4 plus 2 is equal to 6. Now that’s only one way

to think about it. The other way we could have

thought about this is we could’ve said, instead of

having 2 added to itself three times, we could’ve added

3 to itself two times. And I know it’s maybe becoming

a little bit confusing, but the more practice you do it’ll

make a little sense. So this statement up

here, let me rewrite it. 2 times 3. It could also be rewritten

as 3 two times. So 3 plus 3. And once again, you’re

like, where did this 2 go? You know, I had 2 times 3 and

whenever you do addition you see I have 2– oh, I don’t

know these– well, I said cherries, but they could be

raspberries or anything. And then I had two things, I

have three things and the 2 and the 3 never disappear. And I add them

together, I get 5. But here I’m saying that

2 times 3 is the same thing as 3 plus 3. Where did the 2 go? 2 in this case, in this

scenario, is telling me how many times I’m going

to add 3 to itself. But what’s interesting is,

regardless of which way I interpret 2 times 3, I can

interpret it as 2 plus 2 plus 2 or adding 2 to

itself three times. I can interpret it that way or

I can interpret it as adding 3 to itself two times. But notice, I get

the same answer. What’s 3 plus 3? That is also equal to 6. And this is probably the first

time in mathematics you’ll encounter something very neat. Sometimes, regardless of the

path you take, as long as you take a correct path you

get the same answer. So two people can kind of

visualize it– as long as they’re visualizing it

correctly, two different problems, but they come up

with the name solution. And so you’re probably

saying, Sal, when is this multiplication

thing even useful? And this is where it’s useful. Sometimes it

simplifies counting. So let’s say I have a–

well, let’s stick with our fruit analogy. An analogy is just when

you kind of use something as– well, I won’t

go too much into it. But our fruit example. Let’s say I had lemons. Let me draw a bunch of lemons. I’ll draw them in rows of 3. So I have 1, 2, 3– well, I’m

not going to count them because that’ll give our answer away. I’m just drawing a

bunch of lemons. Now, if I said, you tell me how

many lemons there are here. And if I did that you would

proceed to just count all of the lemons. And it wouldn’t take you too

long to say, that oh, there’s 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

11, 12 lemons I actually already gave you the answer. We know that there

are 12 lemons there. But there’s an easier way

and a faster way to count the number of lemons. Notice: how many lemons

are in each row? And a row is kind of the

side to side lemons. I think you know what a row is. I don’t want to

talk down to you. So how many lemons

are there in a row? Well, there are 3

lemons in a row. And now let me ask you

another question, how many rows are there? Well, this was one row, and

this is the second row, this is the third row, and

this is the fourth row. So an easy way to count it

is say, I have 3 lemons per row and I have 4 of them. So let’s say I have

3 lemons per row. I hope I’m not confusing you,

but I think you’ll enjoy this. And then I have 4 rows. So I have 4 times 3 lemons. And that should be equal to the

number of lemons I have– 12. And just to make that gel

with what I just did with the addition,

let’s think about this. 4 times 3– literally, when you

actually say out the word 4 times 3, I visualize this. I visualize 4 times 3. So 3 four times. 3 plus 3 plus 3. And if we did that we

get 3 plus 3 is 6. 6 plus 3 is 9. 9 plus 3 is 12. And we learned up here, this

part of the video, we learned that this same multiplication

could also be interpreted as 3 times 4. You can switch the order and

this is one of the useful and interesting actually, kind of

properties of multiplication. But this could also be

written as 4 three times. 4 plus 4 plus 4. You add 4 to itself

three times. 4 plus 4 is 8. 8 plus 4 is 12. And in the U.S. we always say 4

times 3, but you know, I’ve met people and a lot of people in

my family they kind of learned in the– I guess, you could

call it the English system. And they’ll often call this

four 3’s or three 4’s. And that in some ways is

a lot more intuitive. It’s not intuitive the first

time you hear it, but they’ll write this multiplication

problem or they’ll say this multiplication problem and

they’ll say, what are four 3’s? And when they say four 3’s,

they’re literally saying, what are four 3’s? So this is one 3, two 3’s,

three 3’s, four 3’s. So what are four 3’s

when you add them up? It’s 12. And you could also say,

what are three 4’s? So let me write this down. Let me do it in a

different color. That is four 3’s. I mean literally,

that’s four 3’s. If I told you to say, write

down for four 3’s and add them up, that’s what that is. And that is 4 times

3 or 3 four times. And this is– let me do

that in a different color. That is three 4’s. And it could also be

written as 3 times 4. And they all equal 12. And now you’re probably

saying, OK, this is nice. It’s a cute little trick,

Sal, that you’ve taught me. But it took you less time

to count these lemons than to do this problem. And well first of all, that’s

only right now because you’re new to multiplication. But what you’ll find is there

are times and there are actually many times– and I

don’t want to use the word times too much in a video on

multiplication– where each row of lemons, instead of having 3

maybe they have 100 lemons. Maybe there’s 100 rows. And then it would take you

forever to count all the lemons and that’s where multiplication

comes really useful. Although, we’re not going

to learn right now how to multiply 100 times 100. Now, the one thing that I

want to get you and this is kind of a trick. I remember my sister just to

try to show how much smarter she was than me when I was in

kindergarten and she was in third grade, she would say

Sal, what is 3 times 1? And I would say, because

my brain would say, oh, that’s like 3 plus 1. And I would say 3 plus

1 is equal to 4. And so I’d say, 3 times 1? That must be 4 as well. And she would say, no, silly. It’s 3. And I was like,

how can that be? How can the 3 times some

other number still be the same number? And think about

what this means. You could view this

as three 1’s. What are three 1’s? That’s one 1 plus another

one 1 plus another 1. And that’s equal to 3. Or you could view

this as 3 one time. So what’s 3 one time? It’s almost silly

how easy it is. It’s just 3. That’s one 3. You could write this as one 3. And that’s why anything

times 1 or 1 times anything is that anything. So then 3 times 1 is 3. 1 times 3 is 3. And you know, I could say 100

times 1 is equal to 100. I could say that 1 times

39 is equal to 39. And I think you’re familiar

with numbers this large by now. So that’s interesting. Now there’s one other

really interesting thing about multiplication. And that’s when you

multiply by 0. And I’ll start with the analogy

or the example when you add. 3 plus 0 you’ve

hopefully learned is 3. Because I’m adding

nothing to the 3. If I have 3 apples and I

give you 0 more apples, you still have 3 apples. But what is 3 and maybe I’m

just fixated on the number 3 a little bit too much. Let me switch. What is 4 times 0? Well this is saying,

0 four times. So what’s 0 plus

0 plus 0 plus 0? Well, that’s 0. I have nothing plus nothing

plus nothing plus nothing, so I get nothing. Another way to think of it,

I could say 4 zero times. So how do I write 4 zero times? Well, I just don’t

write anything, right? Because if I write anything, if

I write 1/4 and I don’t have no 4’s– let me write this. This is four 0’s, but I

could also write zero 4’s. And what is zero 4’s? I’ll just write a

big blank here. There, I wrote it. There are no 4’s here. So there’s just a big blank. And that’s another fun thing. So anything times 0 is 0. I could write a huge number,

you know, 5,493,692 times 0. What does that equal? That equals 0. And by the way, what’s

this number times 1? Well, it’s that number again. And what’s 0 times 17? Once again, that is 0. Anyway, I think I’ve

talked for long enough. See you in the next video.

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Booooo

bunch of idiots in the comments

Hi not to be rude but I know this

thank you boring

you really helped me

I don't remember number lines as a kid with addition.

You get more views on the more complex ones and once you got 1 view.

That view was me

"Let's learn to multiply" uhhh no thanks sal…

100*100=10,000! I did it!

very good

2 times 3 is 3+3 not 2+2+2

Basically 2 times 3 means 2 groups of 3

would you please add subtitles to your videos? to be able to understand u more &more.thanks 4 ur efforts

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omg, I'm glad I'm a student… (COMMENTING AT HOME)

Thanks i needed some help ๐

How to divide a decimal till the time we get zero as remainder. This is my request. My name is krishiv and i study in grade five. I like the concepts you tech in. Thanks. Please upload the video for thia

This is a helful video Thank you~๐โจ

๐๐๐๐๐๐๐๐๐๐๐๐ best

it is quite easy but it would help like, 7 or under

This helped me a lot thx ๐

A little babyish though blueberries ๐ realy lol

You should be a teacher!๐

Wow. It's was that easy?

Thank You so much. Iโm totally gonna ace the history test tomorrow

Iโm here because I have not been in school for years and now Iโm going back so some of these things I forgot

Go to 9:30 for good times =D

Boring

1:48 sal is the worlds most humble

he posted this when I was 2 yrs old

How to win a reading competition in grade one class

Thx for helping me for 4th grade

I just needed to review

Equal 6

thank you for making these videos… math is not my strongest subject but your videos really helped me understand basic concepts working my way up.

VladTv doing math now ๐๐๐

tis helps me a hole lot with school thank you ๐

so its basically groups

Good

Math is to hard ๐ฃ๐ข๐ ๐ญ๐๐

I just finished the One World Schoolhouse and want to applaud you for all you have done for advancing education.

Thank you my sun learned so much

That's not the definition of multiplication.

6:45 to 7:12 is all wrong. 4×3 is 4+4+4.

there is no audio in this video please fix

i do it at school

12

I donโt know why Iโm watching this because I know this

Iโm watching this after watching videos on fundamental theorem of calculus

you thing it easy

Name altaf

Thank you ๐

6

anyone 2018 sep

good video

ํ๊ตญ์ธ ์ฐพ์์~~~~~

This really helps me

0:03 MULTIPLY!

i need the name of thise application please

2×3=6

4×3=12

100×100=1000. 100×10=1,000

4×0=0

hi sir,

100 -100= 2

solve that

I no evrything now and if i don't no then I watch it again and again thank you for making this video my kids love this video and they learn more and get a+ in there reportcard

Hi

๐

Real

This is. easy

Thx for helping me I am a 2nd grade ๐๐๐๐คฉ

it helped me practicing my 3's thx. next time can you teach us DIVISion

wish i discovered this channel during my middle school or primary school . I totally sucked at Maths and still sucks.

Needed the review for my Real Analysis course

thank you for helping my kids homework

First thing my son will watch on YouTube is this video.

very good

Deer Khan I need help with math if I don't get better I'll be be held back with division i,m only

11

I have a calc final today, what am I doing with my life

This is a good video cuz I need to Learn more๐๐๐๐nice video sir๐

please explain 2 x 0.5 with the addition equation

Thanks.

india.

I searched up "khan academy arrays" in hoping to learn how arrays in coding C work for computer science 1. I thought it would show examples of how to multiply arrays in a code or something.. but instead got to learn how to multiply.. lmao

I watch this to go to sleep

Hi

since everyone's talking about calculus

d/dx 3x^2+2x-3 = ?

Answer: 6x+2

Bruh I'm 15 and watching this.

90% sure this teacher is karl from llamad with hats

I'm in 6th grade now. This is awesome but I don't think a kid in 4th grade would understand words like " reinforce " and "concept" ;3

i looooovvveeeee khan academy

Yea. Now I know. How. To. Multiply 3 grade. Here. I come

My school told me to watch this so I did ๐๐๐๐๐

good job ๐๐ป. Khan. Academyโค๏ธ๐ฎ

Whyyyyyy do they have math videos my mom says I have to do this if I want to keep my tablet

i dont know 3 plus 2 XD

thanks

I like maths

2×3=6

and multiply

My mom put this on when I asked what is a multiplecation story…