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If you've practiced

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and hopefully, memorized your multiplication tables,

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you'll now find out that you're prepared to do most any multiplication problem.

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You just have to understand,

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I guess for lack of a 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,

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we're going to show you why it works.

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So let's start with a multiplication problem

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

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Let's do sixteen times nine.

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Sixteen times nine.

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And you immediately might say,

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Sal, I haven't memorized my sixteen times tables,

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there's no way I'm going to be able to do that problem.

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

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because we can break it down into problems

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that you do know the answer to.

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The way you do this one

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is first multiply nine times the ones place here.

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So you multiply nine times six.

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And I think you know what nine times six is.

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I'll write it down here.

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So nine times six is fifty-four.

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You know that from your multiplication tables.

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And so what you do is you write fifty-four,

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but you only write the four down here in the ones place,

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and you carry the five.

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That's exactly what you're doing.

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We also use word carry when you add

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and you kind of have an extra five to deal with,

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but let's just call that carrying.

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For lack of better words.

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Now, we then multiply nine times one.

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Nine times one.

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Well, that's straightforward.

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Nine times one is equal to nine.

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Anything times one is equal to itself.

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But we have this five sitting up here, so nine times one,

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we have to add that five.

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So we have to add that plus five.

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And so what do we get?

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So nine times one plus five

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is nine plus five, which is fourteen.

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Let me write it right there.

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Fourteen.

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And there you have it.

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Sixteen times nine is one hundred forty-four.

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And if you remembered your times tables up to twelve

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you also realize that's twelve times twelve.

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But just knowing only these two pieces of information,

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we were able to solve a harder problem.

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Now you might say, Okay Sal, that's a neat little trick you just did,

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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--

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you shouldn't just memorize 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 sixteen as ten-- let me do it right here.

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Ten plus six.

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This is sixteen.

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And I can rewrite nine,

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well, I'm just going to write nine as nine. Right there.

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And now let me do the multiplication problem.

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I'll put a little multiplication sign out there.

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So first I want to multiply the nine times the six.

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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 ones place from the tens place.

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This one here that's in the second column,

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it isn't a one, it's a ten.

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It's a ten plus a six,

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so that's why I wanted 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 nine times six--

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let me write that down.

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Nine times six is equal to fifty-four.

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But instead of writing fifty-four,

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I'm going to write that's equal to fifty plus four.

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Nine times six is equal to fifty plus four.

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Well, this is my ones column right here.

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Let me make a little dotted line.

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This is my ones column.

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So I can only put a four down here,

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but I need something to do with the fifty.

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I have to put it some place

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and just the convention or at least the way that I've learned it,

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you put the fifty up here.

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I could've put the fifty down here too,

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as long as we remember that this fifty now goes into this column.

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So you can stick the fifty over here.

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That's what we did in the first video.

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I just wrote a five.

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In that first video, I just put a five here

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because that was in the tens place.

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A five here really means fifty.

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A one here really means ten.

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But now I'm writing it out,

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so you can see that they really mean fifty and ten.

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And then you say, what's nine times ten?

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Nine times ten.

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Well, you've memorized this.

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And anything times ten is just that anything with a zero.

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So it's ninety.

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So it's nine times ten is ninety,

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and then we want to add fifty to it.

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So we want to add fifty to it.

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What's ninety plus fifty?

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It is one hundred forty.

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So nine times ten is ninety,

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plus fifty is one hundred forty.

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And we could rewrite one hundred forty

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as one hundred plus forty just to be consistent.

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So what we'll do is we'll put the forty down here,

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and then we carry the one hundred,

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but the one hundred really doesn't go anywhere.

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I mean we could write it up here.

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We could put it--

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Well, we could write the one hundred 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 one hundred,

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but the important thing is that it sticks out into this next column

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that I haven't drawn yet.

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So then you'll put one hundred here.

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So our answer is one hundred plus forty plus four,

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which is one hundred forty-four.

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Hopefully you found that reasonably explanatory.

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Let's try a couple of other problems,

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because I think it's all about seeing examples.

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So let's try fifty-five times eight.

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Fifty-five times eight.

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Same exercise.

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First, you start with the eight.

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Eight times five.

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Let me write it down.

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Eight times five we know is forty.

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So eight times five, you write the zero down here.

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It's zero plus forty.

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And then you say eight times five again.

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That's forty.

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But then you add the four to here, so you get forty-four.

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So it's four hundred forty.

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

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where I broke it out into fifty plus five and then an eight.

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But I think with more examples,

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you'll see this will all become a bit of second nature to you.

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So let me do another one in this--

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let me do it in this salmon. This light red, salmon color.

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So let's say I had seventy-eight times-- let's do it times seven.

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Eight times seven.

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Eight times seven is fifty-six.

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

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So eight times seven is equal to fifty-six.

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We write the six down here, put the five up there.

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Seven times seven is forty-nine.

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Seven times seven is equal to forty-nine.

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

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What's forty-nine plus five?

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Well, that's fifty-four.

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So seven times seven is forty-nine.

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Plus five is fifty-four.

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Five hundred forty-six.

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Ten minutes ago,

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you probably never thought that you could figure out the seventy-eight multiplication tables,

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but 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 eighty-nine times-- let's do it times three.

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What's three times nine?

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Three times nine is equal to twenty-seven.

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Put the seven in the ones place.

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Put the two up here in the tens place,

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because it's twenty plus seven.

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Two tens is twenty.

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Plus seven is twenty-seven.

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And then three times eight is twenty-four.

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Three times eight is equal to twenty-four.

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But I have this two sitting up here

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so I'm going to have to add a two.

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So I get twenty-six.

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Three times eight is twenty-four.

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Plus two is twenty-six.

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Two hundred sixty-seven.

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Now I'm going to do another one,

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but I'm going to up the stakes a little bit.

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Just when you thought you were getting comfortable with this,

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I'm going to make you uncomfortable!

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Let's do two hundred thirty-nine times six.

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I thought this was a video about two-digit multiplication times one-digit.

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Well, it is, but I just want to show you

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that you can really do any number of digits times this one digit,

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and it's 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 six times nine?

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Let me write it here.

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Six times nine.

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We saw this show before.

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This is fifty-four.

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So we put the four down here, we put the five in the tens place

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because the fifty in fifty-four is really five tens.

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Fair enough.

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Now we're going to do six times three.

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So six times three,

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that's equal to eighteen.

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We still have that five hanging out there,

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so we have to add that five up there and we get--

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what's eighteen plus five?

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So six times three is eighteen, plus five is twenty-three.

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Just to be clear,

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we didn't multiply six times three and add five.

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We actually,

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if you looked at where we are in our place on the problem,

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this is actually a thirty.

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I just happened to do a three here.

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But this is six times thirty plus fifty.

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Because thirty-nine is three tens or thirty.

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So this number, actually, even though we said six times three is eighteen.

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Plus five is twenty-three.

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This number is really two hundred thirty.

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So we put the three in the tens place.

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Actually, let me do it in a different color

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than what I did up here.

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This is equal to twenty-three.

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We can put the three in the tens place

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and then put this two up here.

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Now we're almost done, one multiplication left.

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This is the six times the two.

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That's an easy one.

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That's twelve.

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But I have this other two hanging out up here,

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so I have to add this other two.

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So plus two.

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And what is that equal to?

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That is equal to

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twelve plus two is equal to fourteen.

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So I write the four.

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So six times two is twelve.

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Plus two is fourteen.

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I write the four down here.

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

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but there aren't any more digits.

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So I write the one over here.

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So two hundred thirty-nine times six is one thousand four hundred thirty-four.

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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,

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let's go to four-digits.

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Let's do seven thousand three hundred sixty-two times--

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let's do a hard one.

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Times nine.

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So what's nine times two?

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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 nine times two?

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Nine times two is eighteen.

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Eighteen.

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Then we do nine times six.

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Nine times six is fifty-four.

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And fifty-four plus one is fifty-five.

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Fifty-five.

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What's nine times three?

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Nine times three is twenty-seven-- if we have that memorized.

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And then twenty-seven plus five is thirty-two.

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Let me switch colors.

266
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Thirty-two.

267
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And then you have nine times seven.

268
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That's sixty-three, but we have this three hanging out there.

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So that's nine times seven is sixty-three,

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plus three is sixty-six.

271
00:11:50,460 --> 00:11:52,032
You write the six here,

272
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and then you have no where to put the sixty in the sixty-six,

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so you write that down here as well.

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And so seven thousand three hundred sixty-two times nine

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is sixty-six thousand two hundred fifty-eight.

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Hopefully you found that useful.