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If you've practiced and hopefully, memorized your

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multiplication tables, you'll now find out that you're

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prepared to do most any multiplication problem.

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You just have to understand, I guess for lack of better word,

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the system of how to do it.

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But we're not just going to teach you the system, we're

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going to show you why it works.

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So let's start with a multiplication problem that

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you probably think that you don't know how to do.

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Let's do 16 times 9.

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And you immediately might say, sal, I haven't memorized my 16

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times tables, there's no way I'm going to be able

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to do that problem.

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And my answer to you is, you can absolutely do it because we

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can break it down into problems that you do know the answer to.

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The way you do this one is first multiply 9 times

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the 1's place here.

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So you multiply 9 times 6.

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And I think you know what 9 times 6 is.

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I'll write it down here.

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So 9 times 6 is 54.

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You know that from your multiplication tables.

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And so what you do is you write 54, but you only write the 4

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down here in the 1's place, and you carry the 5.

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That's exactly what you're doing.

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We also use word carry when you add and you kind of have an

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extra 5 to deal with, but let's just call that carrying

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for lack of better words.

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Now, then we multiply 9 times 1.

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Well, that's straightforward.

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9 times 1 is equal to 9.

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Anything times 1 is equal to 1.

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But we have this 5 sitting up here, so 9 times 1,

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we have to add that 5.

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So we have to add that plus 5.

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And so what do we get?

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So 9 times 1 plus 5 is 9 plus 5, which is 14.

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Let me write it right there.

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And there you have it.

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16 times 9 is 144.

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And if you remembered your times tables up to 12 you also

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realize that's 12 times 12.

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But just knowing only these two pieces of information, we were

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able to solve a harder problem.

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Now you might say, OK Sal, that's a neat little trick you

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just did, but how does it work?

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And you should always ask that.

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You shouldn't just take it-- you shouldn't just memorize

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the system and assume that it works.

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And to explain that I'm just going to rewrite these numbers.

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I can rewrite 16 as 10-- let me do it right here.

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10 plus 6.

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This is 16.

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And I can rewrite 9, well, I'm just going to write

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9 as 9 right there.

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And now let me do the multiplication problem.

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Put a little multiplication sign out there.

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So first I want to multiply the 9 times the 6.

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And you might say, hey Sal, why did you divide it this way?

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Well, I wanted to separate the 1's place from the 10's place.

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This 1 here that's in the second column, it

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isn't a 1, it's a 10.

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It's a 10 plus a 6, so that's why I wanted

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to write it that way.

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But anyway, let's do this problem.

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So we do it the exact same way we did it before.

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We say 9 times 6-- let me write that down.

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9 times 6 is equal to 54.

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But instead of writing 54 I'm going to write that's

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equal to 50 plus 4.

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9 times 6 is equal to 50 plus 4.

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Well, this is my 1's column right here.

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Let me make a little dotted line.

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This is my 1's column.

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So I can only put a 4 down here, but I need something

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to do with the 50.

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I have to put it some place and just the convention or at least

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the way that I've learned it, you put the 50 up here.

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I could've put the 50 down here too, as long as we remember

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that this 50 now goes into this column.

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So you can stick the 50 over here.

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That's what we did in the first video.

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I just wrote a 5.

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In that first video, I just put a 5 here because that

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was in the 10's place.

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A 5 here really means 50.

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A 1 here really means 10.

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But now I'm writing it out, so you can see that they

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really mean 50 and 10.

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And then you say, what's 9 times 10?

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Well, you've memorized this.

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And anything times 10 is just that anything with a 0.

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So it's 90.

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So it's 9 times 10 is 90, and then we want to add 50 to it.

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So we want to add 50 to it.

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What's 90 plus 50?

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It is 140.

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So 9 times 10 is 90.

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Plus 50 is 140.

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And we could rewrite a 140 as 100 plus 40

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just to be consistent.

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So what we'll do is we'll put the 40 down here and then we

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carry the 100, but the 100 really doesn't go anywhere.

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I mean we could write it up here.

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Well, we could write the 100 over here.

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We could put it over here.

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There's a bunch of different places we could put the 100,

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but the important thing is that it sticks out into this

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next column that I haven't drawn yet.

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So then you'll put 100 here.

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So our answer is 100 plus 40 plus 4, which is 144.

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Hopefully you found that reasonably explanatory.

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Let's try a couple of other problems because I think it's

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all about seeing examples.

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So let's try 55 times 8.

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Same exercise.

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First, you start with the 8.

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8 times 5.

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Let me write it down.

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8 times 5 we know is 40.

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So 8 times 5, you write the 0 down here.

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It's 0 plus 40.

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And then you say 8 times 5 again.

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That's 40.

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But then you add the 4 to here, so you get 44.

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So it's 440.

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And you can try to do it the same why I did that last one

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where I broke it out into 500 plus 5 and then an 8.

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But I think the more examples you'll see, this all become a

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bit of second nature to you.

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So let me do another one in this-- let me do it in this

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salmon, this light red, salmon color.

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So let's say I had 78 times-- let's do it times 7.

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8 times 7.

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8 times 7 is 56.

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Let me write it-- this is a different problem now.

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So 8 times 7 is equal to 56.

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We write the 6 down here, put the 5 up there.

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7 times 7 is 49.

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7 times 7 is equal to 49.

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But we have to add this 5 up here, so you add this 5.

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What's 49 plus 5?

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Well, that's 54.

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So 7 times 7 is 49.

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Plus 5 is 54.

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546.

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10 minutes ago you probably never thought that you

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could figure out the 78 multiplication tables, but

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you see it's a pretty straightforward process.

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Let's do a bunch more.

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I'm just going to do these until we all just collapse.

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Collapse from multiplication fatigue.

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Let's do an 89 times-- let's do it times 3.

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What's 3 times 9?

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3 times 9 is equal to 27.

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Put the 7 in the 1's place.

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Put the 2 up here in the 10's place because it's 20 plus 7.

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Two 10's is 20.

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Plus 7 is 27.

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And then 3 times 8 is 24.

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3 times 8 is equal to 24.

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But I have this 2 sitting up here so I'm going

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to have to add a 2.

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So I get 26.

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3 times 8 is 24.

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Plus 2 is 26.

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267.

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Now I'm going to do another one, but I'm going to up

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the stakes a little bit.

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Just when you were thought you were getting comfortable with

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this, I'm going to make you uncomfortable.

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Let's do 239 times 6.

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I thought this was a video about two-digit multiplication

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times one-digit.

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Well, it is, but I just want to show you that you can really do

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any number of digits times this one digit, and it's

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really the same process.

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You could probably guess how we're going to do it.

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So what's 6 times 9?

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Let me write it here.

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6 times 9.

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We saw this show before.

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This is 54.

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So we put the 4 down here, we put the 5 in the 10's place

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because the 50 in 54 is really five 10's.

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Fair enough.

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Now we're going to do 6 times 3.

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That's equal to 18.

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We still have that 5 hanging out there, so we have to add

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that 5 up there and we get-- what's eighteen plus 5?

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So 6 times 3 is 18, plus five is 23.

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Just to be clear, we didn't multiply 6 times 3 and add 5.

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We actually, if you looked at where we are in our place on

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the problem, this is actually a 30.

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I just happened to do a 3 here.

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But this is 6 times 30 plus 50.

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Because 39 is three 10's or 30.

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So this number, actually, even though we said 6 times 3 is 18.

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Plus 5 is 23.

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This number's really 230.

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So we put the 2 in the 10's place.

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Actually, let me do it in a different color than

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what I did up here.

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This is equal to 23.

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We can put the 3 in the 10's place and then

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put this 2 up here.

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Now we're almost done, one multiplication left.

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This is the 6 times the 2.

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That's an easy one.

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That's 12.

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But I have this other 2 hanging out up here, so I have

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to add this other 2.

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So plus 2.

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And what is that equal to?

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12 plus 2 is equal to 14.

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So I write the 4.

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So 6 times 2 is 23 .

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Plus 2 is 14.

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I write the 4 down here.

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If there was any more digits I would write the 1 up there, but

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there aren't any more digits.

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So I write the 1 over here.

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So 239 times 6 is 1,434.

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Let's do another one.

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I need to get some space cleaned out.

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And hey, while we're escalating the situation, let's

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go to four-digits.

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Let's do 7,362 times-- let's do a hard one.

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Times 9.

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So what's 9 times 2?

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And I won't do this side math over here.

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I think you're getting the pattern.

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What's 9 times 2?

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9 times 2 is 18.

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Then we do 9 times 6.

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9 times 6 is 54.

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And 54 plus 1 is 55.

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What's 9 times 3?

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9 times 3 is 27-- if we have that memorized.

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And then 27 plus 5 is 32.

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Let me switch colors.

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And then you have 9 times 7.

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That's 63, but we have this 3 hanging out there.

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9 times 7 is 63.

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Plus 3 is 66.

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You write the 6 here, but then you have no where to put the 60

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in the 66, so you write that down here as well.

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And so 7,362 times 9 is 66,258.

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Hopefully you found that useful.

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