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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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    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.
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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

English subtitles

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