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  • 00:00:00,970 --> 00:00:02,890 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.

  • 00:00:27,300 --> 00:00:28,470 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.

  • 00:06:46,210 --> 00:06:50,600 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.

00:00:00,970 --> 00:00:02,890 Let's learn to multiply.

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