## Multiplication 4: 2-digit times 1-digit number

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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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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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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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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.
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Thirty-two.
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And then you have nine times seven.
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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.
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You write the six here,
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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.
Title:
Multiplication 4: 2-digit times 1-digit number
Description:

Multiplying a 2-digit times a 1-digit number

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Video Language:
English
Duration:
12:08
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