## 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,
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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
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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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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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Well three plus three
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is the same thing as two plus two plus two,
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and that's equal to six.
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All right.
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Now what is two times four?
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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,
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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. 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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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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And then finally--
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and it's not finally, we could keep going--
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Two times-- that's too dark of a color.
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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
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plus 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
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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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What I'm going to do is, I'm going to--
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So first of all--
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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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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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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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So three times four is going to be twelve.
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I'm just adding three every time.
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Twelve plus three is fifteen.
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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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Let's see if I can--
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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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You should actually go all the way up to twelve in both directions.
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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 thirty-six.
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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 that-- well, I want us 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, if you add two you get to thirty.
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Then you add five, it's 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, eight times four, you're going to add eight to it-- thirty-two.
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Forty.
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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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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.
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We'll talk more about that in the future
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and maybe prove that to you.
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Nine times six, fifty-four.
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Nine times seven, sixty-three.
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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.
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Actually, I should keep going.
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Well, I realize this video is already pretty long.
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I want you to memorize this right now
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because this is going to get you pretty far.
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In the next video I'm going to do the times tables past nine.
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See you soon!
Title:
Multiplication 2: The Multiplication Tables
Description:

Introduction to the multiplication tables from 2-9.

more » « less
Video Language:
English
Duration:
15:27
 booksforlife commented on English subtitles for Multiplication 2: The Multiplication Tables booksforlife edited English subtitles for Multiplication 2: The Multiplication Tables booksforlife edited English subtitles for Multiplication 2: The Multiplication Tables booksforlife commented on English subtitles for Multiplication 2: The Multiplication Tables booksforlife edited English subtitles for Multiplication 2: The Multiplication Tables brettle edited English subtitles for Multiplication 2: The Multiplication Tables brettle edited English subtitles for Multiplication 2: The Multiplication Tables brettle edited English subtitles for Multiplication 2: The Multiplication Tables

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