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Multiplication 2: The Multiplication Tables

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    At this point I think you know a little bit about what multiplication is.
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    Or multi-plication.
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    What we're going to do in this video is to give you just a ton of more practice,
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    and start you on your memorization of the multiplication tables.
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    And if you watch enough Khan Academy videos,
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    and hopefully you will in the future, you'll realize that I'm normally not
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    you'll realize that I'm normally not a big fan of memorization.
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    But the one thing about multiplication is if you
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    is if you memorize your multiplication tables that we'll start to do in this video,
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    it'll pay huge benefits the rest of your life.
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    So I promise you, do it now, you'll never forget it,
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    and the rest of your life everything will be--
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    well, I don't want to make false promises to you,
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    but they'll be better than if you didn't memorize your multiplication tables.
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    So what are the multiplication tables?
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    Well that's all of the different numbers
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    times each other.
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    So let's actually do a little bit of review.
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    So if I say, what is two times one?
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    That is equal to two plus itself one time.
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    So this is equal to just two.
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    That's two plus itself one time.
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    I don't have to say plus anything
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    because there's only one two there.
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    I could also write this as one plus itself two times.
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    So that's also one plus one.
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    Well that also equals two.
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    Fair enough.
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    So two times one is two.
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    And if you watched the last video, what's two times zero?
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    Well that's zero.
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    So you don't have to memorize your zero multiplication tables
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    because everything times zero is zero, or zero times anything is zero.
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    So let's see.
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    What's two times two?
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    Well, this is equal to--
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    we're going to add two to itself two times.
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    So that's two plus two.
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    And there's only a way to do that.
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    I could say take this two and add it to itself two times,
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    but it's the same thing.
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    And what's two plus two?
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    That's equal to four.
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    What's two times three?
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    Two times three is equal to two plus two plus two.
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    It can also be equal to three plus three.
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    We learned in a previous video
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    this statement can be written either of these ways.
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    And in either case, what's it equal to?
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    All right.
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    Now what is two times four?
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    Well that's equal to two plus two plus two plus two.
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    And notice, it's exactly what two times three was.
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    Two times three was that.
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    I have that here, but now I'm just adding another two to it.
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    So if we're too lazy to sit here and add two plus two is four.
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    Four plus two is six.
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    Instead of doing that, we could say,
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    hey look, we already know that this thing over here, this was six.
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    We figured it out in the previous line right there.
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    We figured out this is six, so we could just say, oh, two times four
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    is going to be two more than that, which is equal to eight.
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    And you should hopefully see that pattern.
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    As we go from two times one, to two times two,
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    to two times three, what's happening?
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    How much are we going up by?
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    From two to four we're going plus two.
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    From four to six we're going plus two.
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    And then from six to eight we're going plus two.
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    So you could figure out what two times five is, even without
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    even without doing the addition.
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    Two times five is equal to two plus two plus two plus two plus two.
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    It could also be written as five plus five.
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    Two times four could've been written as four plus four as well.
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    And what's that equal to?
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    We could add all of these up or we could add these two up.
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    Or we could just say it's going to be two more than two times four.
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    So it's going to be ten.
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    I'll finish the two times tables.
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    And I think you see all of the patterns that emerge from it.
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    So two times six.
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    That's going to be two plus itself six times.
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    Let's see.
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    One, two, three, four, five, six,
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    which should also be equal to six plus itself two times.
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    This could be interpreted either way.
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    And that's going to be equal to twelve.
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    Once again, two more than two times five
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    because we're adding two to itself one more time.
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    So it's going to be two more.
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    Let's keep going.
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    So two times seven.
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    Two times seven is equal to--
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    well, I could write two plus two plus two plus two--
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    this is getting tiring-- plus two plus two.
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    Is that seven?
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    One, two, three, four, five, six, seven.
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    And that's the same thing as seven plus seven,
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    which you may or may not know is equal to fourteen.
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    You could just say hey, that's going to be two more than twelve.
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    So twelve plus one plus two is-- twelve plus one is thirteen.
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    Twelve plus two is fourteen.
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    All right, let's just keep going.
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    Two times eight.
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    I could do all of this business here where I add the twos
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    or I could say, look, it's just going to be two more than two times seven.
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    So I could say it's going to be fourteen plus two.
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    I'm just adding two to that one.
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    So I could say it's sixteen.
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    Or I could also say that's eight plus eight.
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    That's also sixteen.
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    I could have done all the twos out,
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    but if you like you could do that for your own benefit and learning.
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    We're almost-- well, we could go forever
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    because there is no largest number.
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    I can keep going.
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    Two times nine times ten times one hundred times one thousand times one million.
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    But I'm going to stop at twelve
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    because that tends to be what people need to memorize.
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    But if you really want to be a "mathelete"
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    you want to go up to twenty.
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    But let's go to two times nine.
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    That's going to be two more than two times eight.
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    It's going to be eighteen.
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    Or that's nine plus nine.
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    Also eighteen.
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    What's two times ten?
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    And ten times tables are interesting.
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    And we're going to see a pattern there in a second
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    when we try to complete an entire times tables.
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    So two times ten?
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    Two more than two times nine.
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    It's twenty.
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    Or we could also say that's ten plus ten.
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    Ten plus itself two times.
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    Now what's interesting about this?
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    This looks just like a two with a zero added.
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    And you're going to see that with anything times ten,
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    you just put a zero on the right.
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    And you can think about why that is.
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    You can view this as two tens is twenty.
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    That's what twenty is.
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    We're almost done.
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    Let's do two times eleven.
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    Two times eleven is going to be two more than this right here.
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    It's going to be twenty-two.
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    Another interesting pattern.
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    I have the number repeated twice-- a two and a two.
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    Interesting.
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    Something to watch out for
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    as we look at other multiplication tables.
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    Two times twelve.
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    Two times twelve is going to be two more than two times eleven.
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    That's twenty-four.
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    We could have also written that as twelve plus twelve.
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    Or we could've said two plus two plus two plus two plus
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    two... twelve times.
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    It all gets you to twenty-four.
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    So that's the two times tables and I think
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    and I think you see the pattern.
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    Every time you multiply it by one higher number
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    you just add two to that number.
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    So now that we see that pattern,
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    let's see if we can complete a multiplication table.
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    So what I want to do, I'm going to write all the numbers.
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    Let's see.
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    I hope I have space for this.
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    One, two, three, four, five, six, seven, eight, nine.
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    Actually, I'll just do it till nine.
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    I'll just keep going.
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    Nine.
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    Actually I won't have space to do that
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    because I want you to see the entire table.
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    So I'm just going up till nine here,
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    but I encourage you after this video to complete it on your own.
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    Maybe if we have time I'll complete it here as well.
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    So these are the first numbers that I'm going to multiply.
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    And I'm going to multiply it times one, two, three, four,
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    five, six, seven, eight, and nine.
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    Actually I should have written this one under--
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    well, what's one times one?
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    So this is the way I'm going to view it.
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    Whatever is one times one I'm going to write here.
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    Well that's one.
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    What's one times two?
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    That's two.
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    What's one times three?
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    That's three.
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    One times anything is that number,
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    so I can just write four, five, six, seven, eight, nine.
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    One times nine is nine.
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    Fair enough.
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    Now let's do the two times tables.
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    I'll do that in a blue.
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    Actually, let me do one in that color
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    and now in maybe a darker blue I'll do the two times tables.
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    What's two times one?
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    That's two.
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    It's the same thing as one times two.
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    Notice, these two numbers are the same thing.
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    What's two times two?
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    That's four.
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    Two times three is six.
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    We just did this.
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    Every time you increment or you multiply by a higher number,
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    you just add by two.
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    Two times four is eight.
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    Same thing as four times two.
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    Two times five is ten.
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    Two times six is twelve.
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    I'm just adding two every time.
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    Up here I added one from every step, here I'm adding two.
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    Two times seven, fourteen.
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    Two times eight, sixteen.
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    Two times nine, eighteen.
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    All right, let's do our three times tables.
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    I'll do it in yellow.
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    Three times one is three.
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    Notice, three times one is three.
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    One times three is three.
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    These are the same values.
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    Three times two is the same thing as two times three.
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    Three times two should be the same thing as two times three.
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    So it's six.
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    And that makes sense.
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    Three plus three is six or two plus two plus two is six.
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    So every time here we're going to increase by three.
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    You see the pattern.
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    Three times three is nine.
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    Three plus three plus three.
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    So we went from three to six to nine.
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    Fifteen plus three is eighteen.
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    Eighteen plus three is twenty-one.
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    Twenty-one plus three is twenty-four.
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    Twenty-four plus three is twenty-seven.
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    So three times nine is twenty-seven.
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    Three times eight is twenty-four.
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    So if you were to say eight plus eight plus eight, it would be twenty-four.
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    So now I'm going to speed it up a little bit,
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    now that we see the pattern.
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    And you should do this on your own
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    and you really should memorize everything we're doing.
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    So let's see.
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    Four times one is four.
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    I'm just going to go up by increments of four.
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    So four plus four is eight.
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    Eight plus four is twelve.
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    Twelve plus four is sixteen.
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    Sixteen plus four is twenty.
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    Twenty plus four is twenty-four.
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    Four times six is twenty-four.
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    Four times seven, twenty-eight.
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    I'm just going up by four.
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    Thirty-two and three hundred and sixty-five.
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    All right, five times one.
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    Five times one is going to be five.
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    Actually, we know that anything-- well, I want to keep changing colors,
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    so I'll just do it in rows like this.
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    Five times one is five.
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    Five times two is ten.
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    Five times three is fifteen.
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    I'm just going to increase by five.
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    Five times tables are very fun as well
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    because every number you're going to add-- if we multiply five times--
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    well, we'll learn about even and odd in the future.
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    But every other number in its times tables is going to end with a five,
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    and then every other one's going to end with a zero.
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    Because if you add five to fifteen you get twenty.
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    You get twenty-five, thirty, thirty-five, forty, forty-five.
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    Fair enough.
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    Six times tables, let me do it in green.
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    Six times one is six.
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    That's easy.
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    You add six to that, you get twelve.
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    You add six to that, you get eighteen.
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    You add six to that, you get twenty-four.
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    You add six to that, you get thirty.
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    Then you go six more, thirty-six, forty-two, forty-eight.
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    Forty-eight plus six is fifty-four.
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    So six times nine is fifty-four.
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    All right, we're almost there.
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    Seven times one, that's seven.
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    Seven times one is seven.
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    Seven times two is fourteen.
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    Seven times three, twenty-one.
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    Seven times four, twenty-eight.
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    Seven times five, what's twenty-eight plus seven?
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    Let's see.
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    If you add two you get to thirty.
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    Then you have five, thirty-five.
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    Seven times six, forty-two.
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    Seven times seven, forty-nine.
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    Seven times eight--
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    seven times is going to be seven plus this, so it's fifty-six.
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    I always used to get confused between seven times eight being fifty-six
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    and six times nine being fifty-four.
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    So now that I pointed out to you that I always got confused between those two,
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    it's your job not to be confused by those two.
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    Seven times eight you could say has the six in it.
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    Six times nine doesn't have the six in it.
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    That's the way I think of it.
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    Anyway, seven times nine.
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    We're going to add another seven here.
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    It's going to be sixty-three.
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    I'll do it in the same color.
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    All right, we're at our eight times tables.
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    Eight times one is eight.
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    Eight times two is sixteen.
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    Twenty-four.
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    Eight times three is twenty-four.
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    And if we go to three times eight we should also see the twenty-four.
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    Yep, it's there.
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    These values are the same.
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    So we're actually doing things twice.
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    We're doing it when you do eight times three
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    and we're doing it when we did three times eight.
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    Let's see.
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    Eight times four, you're going to add eight to it-- thirty-two.
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    Forty.
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    Add another eight, forty-eight.
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    Notice, eight times six, forty-eight.
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    Six times eight, forty-eight.
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    All right, eight times seven.
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    Well, we already pointed that one out, that was fifty-six.
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    Eight times eight, sixty-four.
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    Eight times nine, add eight to this, is seventy-two.
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    Now we're at the nine times tables.
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    I'm running out of colors.
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    Maybe I'll reuse a color or two.
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    I'll use the blue again.
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    Nine times one is nine.
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    Nine times two, eighteen nine times three-- we actually know all of these.
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    We could look it up in the rest of the table
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    because nine times three is the same thing as three times nine.
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    It's twenty-seven.
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    Add nine to that.
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    Twenty-seven plus nine is thirty-six.
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    Thirty-six plus nine is forty-five.
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    Notice, every time you add nine, you go almost up by ten,
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    but one less than that.
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    So up by ten would be forty-six, and then one less than that is forty-five.
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    But anyway, notice, the ones--
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    well, I'll talk more about it in the future.
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    But we go from a nine, eight, seven, six, five on this digit,
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    on the second digit.
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    And on this digit here you go one, two, three, four.
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    So it's an interesting pattern.
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    Another interesting pattern is the digits will add up to nine.
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    Three plus six is nine, two plus seven is nine.
  • 14:49 - 14:51
    We'll talk more about that in the future
  • 14:51 - 14:53
    and maybe prove that to you.
  • 14:53 - 14:56
    Nine times six, fifty-four.
  • 14:56 - 14:58
    That was this one as well.
  • 14:58 - 15:02
    Nine times seven, sixty-three.
  • 15:02 - 15:04
    Nine times eight, seventy-two.
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    Nine times nine is eighty-one.
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    I don't know if you can see that.
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    Eighty-one.
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    There you go.
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    Now, I could keep going.
  • 15:11 - 15:14
    Actually, I should keep going.
  • 15:14 - 15:18
    Well, I realize this video is already pretty long.
  • 15:18 - 15:20
    I want you to memorize this right now
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    because this is going to get you pretty far.
  • 15:21 - 15:25
    In the next video I'm going to do the times tables past nine.
  • 15:25 - 15:27
    See you soon.
Title:
Multiplication 2: The Multiplication Tables
Description:

Introduction to the multiplication tables from 2-9.

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Video Language:
English
Duration:
15:27

English subtitles

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