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At this point I think you know a little bit about

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what multiplication is.

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What we're going to do in this video is to give you just a ton

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of more practice and start you on your memorization of the

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multiplication tables.

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And if you watch enough Khan Academy videos, and hopefully

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you will in the future, you'll realize that I'm normally not

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a big fan of memorization.

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But the one thing about multiplication is if you

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memorize your multiplication tables that we'll start to do

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in this video, 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, and the

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rest of your life everything will be-- well, I don't want to

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make false promises to you, but they'll be better than if you

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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 2 times 1?

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That is equal to 2 plus itself one time.

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So this is equal to just 2.

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That's 2 plus itself one time.

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I don't have to say plus anything because there's

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only one 2 there.

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I could also write this as 1 plus itself two times.

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So that's also 1 plus 1.

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Well that also equals 2.

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Fair enough.

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So 2 times 1 is 2.

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And if you watched the last video, what's 2 times 0?

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Well that's 0.

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So you don't have to memorize your 0 multiplication tables

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because everything times 0 is 0, or 0 times anything is 0.

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So let's see.

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What's 2 times 2?

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Well, this is equal to-- we're going to add 2

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to itself two times.

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So that's 2 plus 2.

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And there's only a way to do that.

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I could say take this 2 and add it to itself two times,

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but it's the same thing.

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And what's 2 plus 2?

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That's equal to 4.

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What's 2 times 3?

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2 times 3 is equal to 2 plus 2 plus 2.

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It can also be equal to 3 plus 3.

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We learned in a previous video this statement can be written

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either of these ways.

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And in either case, what's it equal to?

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Well, 3 plus 3 is the same thing as 2 plus 2 plus 2,

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and that's equal to 6.

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All right.

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Now what is 2 times 4?

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Well that's equal to 2 plus 2 plus 2 plus 2.

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And notice, it's exactly what 2 times 3 was.

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2 times 3 was that.

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I have that here, but now I'm just adding another 2 to it.

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So if we're too lazy to sit here and add 2 plus 2 is 4.

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4 plus 2 is 6.

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Instead of doing that, we could say, hey look, we already know

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that this thing over here, this was 6.

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We figured it out in the previous line right there.

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We figured out this is 6, so we could just say, oh, 2 times 4

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is going to be 2 more than that, which is equal to 8.

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And you should hopefully see that pattern.

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As we go from 2 times 1, to 2 times 2, to 2 times

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3, what's happening?

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How much are we going up by?

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From 2 to 4 we're going plus 2.

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From 4 to 6 we're going plus 2.

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And then from 6 to 8 we're going plus 2.

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So you could figure out what 2 times 5 is, even without

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doing the addition.

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2 times 5 is equal to 2 plus 2 plus 2 plus 2 plus 2.

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It could also be written as 5 plus 5.

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2 times 4 could've been written as 4 plus 4 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 2 times 4.

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So it's going to be 10.

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I'll finish the 2 times tables.

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And I think you see all of the patterns that emerge from it.

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So 2 times 6.

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That's going to be 2 plus itself six times.

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Let's see.

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1, 2, 3, 4, 5, 6, which should also be equal to

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6 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 12.

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Once again, two more than 2 times 5 because we're adding

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2 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 2 times 7.

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2 times 7 is equal to-- well, I could write 2 plus 2 plus 2

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plus 2-- this is getting tiring-- plus 2 plus 2.

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Is that 7?

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1, 2, 3, 4, 5, 6, 7.

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And that's the same thing as 7 plus 7, which you may or may

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not know is equal to 14.

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You could just say hey, that's going to be two more than 12.

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So 12 plus 1 plus 2 is-- 12 plus 1 is 13.

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12 plus 2 is 14.

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All right, let's just keep going.

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2 times 8.

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I could do all of this business here where I add the 2's or I

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could say look, it's just going to be two more than 2 times 7.

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So I could say it's going to be 14 plus 2.

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I'm just adding two to that one.

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So I could say it's 16.

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Or I could also say that's 8 plus 8.

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That's also 16.

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I could have done all the 2's out, but if you like you

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could do that for your own benefit and learning.

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We're almost-- well, we could go forever because there

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is no largest number.

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I can keep going.

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2 times 9 times 10 times 100 times 1,000 times 1,000,000.

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But I'm going to stop at 12 because that tends to be what

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people need to memorize.

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But if you really want to be a mathlete you

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want to go up to 20.

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But let's go to 2 times 9.

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That's going to be two more than 2 times 8.

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It's going to be 18.

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Or that's 9 plus 9.

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Also 18.

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What's 2 times 10?

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And 10 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 2 times 10?

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Two more than 2 times 9.

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It's 20.

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Or we could also say that's 10 plus 10.

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10 plus itself two times.

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Now what's interesting about this?

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This looks just like a 2 with a 0 added.

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And you're going to see that anything times 10.

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You just put a 0 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 10's is 20.

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That's what 20 is.

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We're almost done.

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Let's do 2 times 11.

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2 times 11 is going to be 2 more than this right here.

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It's going to be 22.

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Another interesting pattern.

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I have the number repeated twice-- a 2 and a 2.

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Interesting.

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Something to watch out for as we look at other

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multiplication tables.

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And then finally-- it's not finally, we could keep going.

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2 times-- that's too dark of a color.

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2 times 12.

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2 times 12 is going to be two more than 2 times 11.

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That's 24.

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We could have also written that as 12 plus 12.

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Or we could've said 2 plus 2 plus 2 plus 2 plus

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2 twelve times.

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It all gets you to 24.

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So that's the 2 times tables and I think

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you see the pattern.

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Every time you multiply it by one higher number you just

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add 2 to that number.

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So now that we see that pattern, let's see

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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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1, 2, 3, 4, 5, 6, 7, 8, 9.

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Actually, I'll just do it till 9.

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I'll just keep going.

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9.

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Actually I won't have space to do that because I want you

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to see the entire table.

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So I'm just going up till 9 here, but I encourage

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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 1, 2, 3, 4,

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5, 6, 7, 8, and 9.

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Actually I should have written this 1 under-

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well, what's 1 times 1?

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So this is the way I'm going to view it.

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Whatever is 1 times 1 I'm going to write here.

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Well that's 1.

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What's 1 times 2?

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That's 2.

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What's 1 times 3?

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That's 3.

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1 times anything is that number, so I can just

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write 4, 5, 6, 7, 8, 9.

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1 times 9 is 9.

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Fair enough.

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Now let's do the 2 times tables.

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I'll do that in a blue.

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Actually, let me do 1 in that color and now in maybe a

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darker blue I'll do the 2 times tables.

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What's 2 times 1?

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That's 2.

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It's the same thing as 1 times 2.

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Notice, these two numbers are the same thing.

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What's 2 times 2?

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That's 4.

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2 times 3 is 6.

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We just did this.

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Every time you increment or you multiply by a higher

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number, you just add by 2.

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2 times 4 is 8.

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Same thing as 4 times 2.

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2 times 5 is 10.

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2 times 6 is 12.

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I'm just adding 2 every time.

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Up here I added 1 from every step, here I'm adding 2.

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2 times 7, 14.

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2 times 8, 16.

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2 two times 9, 18.

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All right, let's do our 3 times tables.

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I'll do it in yellow.

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3 times 1 is 3.

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Notice, 3 times 1 is 3.

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1 times 3 is 3.

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These are the same values.

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3 times 2 is the same thing as 2 times 3.

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3 times 2 should be the same thing as 2 times 3.

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So it's 6.

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And that makes sense.

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3 plus 3 is 6 or 2 plus 2 plus 2 is 6.

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So every time here we're going to increase by 3.

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You see the pattern.

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3 times 3 is 9.

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3 plus 3 plus 3.

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So we went from 3 to 6 to 9.

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So 3 times 4 is going to be 12.

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I'm just adding 3 every time.

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12 plus 3 is 15.

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15 plus 3 is 18.

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18 plus 3 is 21.

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21 plus 3 is 24.

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24 plus 3 is 27.

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So 3 times 9 is 27.

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3 times 8 is 24.

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So if you were to say 8 plus 8 plus 8, it would be 24.

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So now I'm going to speed it up a little bit now that

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we see the pattern.

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And you should do this on your own and you really should

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memorize everything we're doing.

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You should actually go all the way up to 12

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in both directions.

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So let's see.

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4 times 1 is 4.

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I'm just going to go up by increments of 4.

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So 4 plus 4 is 8.

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8 plus 4 is 12.

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12 plus 4 is 16.

264
00:10:43,929 --> 00:10:46,459
16 plus 4 is 20.

265
00:10:46,460 --> 00:10:48,460
20 plus 4 is 24.

266
00:10:48,460 --> 00:10:51,470
4 times 6 is 24.

267
00:10:51,470 --> 00:10:52,980
4 times 7, 28.

268
00:10:52,980 --> 00:10:54,259
I'm just going up by 4.

269
00:10:54,259 --> 00:10:58,750
32 and 365.

270
00:10:58,750 --> 00:11:01,490
All right, 5 times 1.

271
00:11:01,490 --> 00:11:06,680
5 times 1 is going to be 5.

272
00:11:06,679 --> 00:11:08,789
Actually, we know that anything-- well, I want to keep

273
00:11:08,789 --> 00:11:11,419
changing colors, so I'll just do it in rows like this.

274
00:11:11,419 --> 00:11:12,579
5 times 1 is 5.

275
00:11:12,580 --> 00:11:15,790
5 times 2 is 10.

276
00:11:15,789 --> 00:11:17,269
5 times 3 is 15.

277
00:11:17,269 --> 00:11:18,439
I'm just going to increase by 5.

278
00:11:18,440 --> 00:11:21,210
5 times tables are very fun as well because every number

279
00:11:21,210 --> 00:11:24,129
you're going to add-- if we multiply 5 times-- well, we'll

280
00:11:24,129 --> 00:11:25,889
learn about even and odd in the future.

281
00:11:25,889 --> 00:11:29,620
But every other number in its times tables is going to end

282
00:11:29,620 --> 00:11:32,250
with a 5, and then every other one's going to end with a 0.

283
00:11:32,250 --> 00:11:34,799
Because if you add 5 to 15 you get 20.

284
00:11:34,799 --> 00:11:41,449
You get 25, 30, 35, 40, 45.

285
00:11:41,450 --> 00:11:43,390
Fair enough.

286
00:11:43,389 --> 00:11:47,129
6 times tables, let me do it in green.

287
00:11:47,129 --> 00:11:48,220
6 times 1 is 6.

288
00:11:48,220 --> 00:11:49,080
That's easy.

289
00:11:49,080 --> 00:11:50,810
You add 6 to that, you get 12.

290
00:11:50,809 --> 00:11:52,500
You add 6 to that, you get 18.

291
00:11:52,500 --> 00:11:54,250
You add 6 to that, you get 24.

292
00:11:54,250 --> 00:11:56,220
You add 6 to that, you get 30.

293
00:11:56,220 --> 00:12:01,220
Then you go 6 more, 36, 42, 48.

294
00:12:01,220 --> 00:12:04,629
48 plus 6 is 54.

295
00:12:04,629 --> 00:12:07,629
So 6 times 9 is 54.

296
00:12:07,629 --> 00:12:09,009
All right, we're almost there.

297
00:12:09,009 --> 00:12:11,620
7 times 1, that's 7.

298
00:12:11,620 --> 00:12:13,529
7 times 1 is 7.

299
00:12:13,529 --> 00:12:15,620
7 times 2 is 14.

300
00:12:15,620 --> 00:12:17,740
7 times 3, 21.

301
00:12:17,740 --> 00:12:20,049
7 times 4, 28.

302
00:12:20,049 --> 00:12:23,669
7 times 5, what's 28 plus 7?

303
00:12:23,669 --> 00:12:23,819
Let's see.

304
00:12:23,820 --> 00:12:25,140
If you add 2 you get to 30.

305
00:12:25,139 --> 00:12:27,710
Then you have 5, 35.

306
00:12:27,710 --> 00:12:29,490
7 times 6, 42.

307
00:12:29,490 --> 00:12:32,649
7 times 7, 49.

308
00:12:32,649 --> 00:12:34,990
7 times 8.

309
00:12:34,990 --> 00:12:37,830
Seven times is going to be 7 plus this, so it's 56.

310
00:12:37,830 --> 00:12:41,590
I always used to get confused between 7 times 8 being 56

311
00:12:41,590 --> 00:12:43,620
and 6 times 9 being 54.

312
00:12:43,620 --> 00:12:45,690
So now that I pointed out to you that I always got confused

313
00:12:45,690 --> 00:12:48,230
between those two, it's your job not to be confused

314
00:12:48,230 --> 00:12:49,399
by those two.

315
00:12:49,399 --> 00:12:52,620
7 times 8 you could say has the 6 in it.

316
00:12:52,620 --> 00:12:54,850
6 times 9 doesn't have the 6 in it.

317
00:12:54,850 --> 00:12:56,080
That's the way I think of it.

318
00:12:56,080 --> 00:12:57,580
Anyway, 7 times 9.

319
00:12:57,580 --> 00:12:59,320
We're going to add another 7 here.

320
00:12:59,320 --> 00:13:00,665
It's going to be 63.

321
00:13:00,664 --> 00:13:04,839
I'll do it in the same color.

322
00:13:04,840 --> 00:13:08,360
All right, we're at our 8 times tables.

323
00:13:08,360 --> 00:13:10,669
8 times 1 is 8.

324
00:13:10,669 --> 00:13:12,529
8 times 2 is 16.

325
00:13:12,529 --> 00:13:14,100
24.

326
00:13:14,100 --> 00:13:15,690
8 times 3 is 24.

327
00:13:15,690 --> 00:13:18,310
And if we go to 3 times 8 we should also see the 24.

328
00:13:18,309 --> 00:13:19,509
Yep, it's there.

329
00:13:19,509 --> 00:13:21,120
These values are the same.

330
00:13:21,120 --> 00:13:22,810
So we're actually doing things twice.

331
00:13:22,809 --> 00:13:25,149
We're doing it when you do 8 times 3 and we're doing

332
00:13:25,149 --> 00:13:27,480
it when we did 3 times 8.

333
00:13:27,480 --> 00:13:27,789
Let's see.

334
00:13:27,789 --> 00:13:31,219
8 times 4, you're going to add 8 to it-- 32.

335
00:13:31,220 --> 00:13:32,490
40.

336
00:13:32,490 --> 00:13:34,690
Add another 8, 48.

337
00:13:34,690 --> 00:13:37,280
Notice, 8 times 6, 48.

338
00:13:37,279 --> 00:13:40,240
6 times 8, 48.

339
00:13:40,240 --> 00:13:42,450
All right, 8 times 7.

340
00:13:42,450 --> 00:13:45,870
Well, we already pointed that one out, that was 56.

341
00:13:45,870 --> 00:13:48,200
8 times 8, 64.

342
00:13:48,200 --> 00:13:52,020
8 times 9, add 8 to this, is 72.

343
00:13:52,019 --> 00:13:54,659
Now we're at the 9 times tables.

344
00:13:54,659 --> 00:13:57,269
I'm running out of colors.

345
00:13:57,269 --> 00:13:59,539
Maybe I'll reuse a color or two.

346
00:13:59,539 --> 00:14:01,110
I'll use the blue again.

347
00:14:01,110 --> 00:14:03,289
9 times 1 is 9.

348
00:14:03,289 --> 00:14:06,709
9 times 2, 18 9 times 3-- we actually know all of these.

349
00:14:06,710 --> 00:14:09,425
We could look it up in the rest of the table because 9 times 3

350
00:14:09,424 --> 00:14:11,299
is the same thing as 3 times 9.

351
00:14:11,299 --> 00:14:13,289
It's 27.

352
00:14:13,289 --> 00:14:14,509
Add 9 to that.

353
00:14:14,509 --> 00:14:18,399
27 plus 9 is 36.

354
00:14:18,399 --> 00:14:21,539
36 plus 9 is 45.

355
00:14:21,539 --> 00:14:24,909
Notice, every time you add 9, you go almost up by

356
00:14:24,909 --> 00:14:26,250
10, but 1 less than that.

357
00:14:26,250 --> 00:14:29,970
So up by 10 would be 46, and then one less than that is 45.

358
00:14:29,970 --> 00:14:33,379
But anyway, notice, the 1's-- well, I'll talk more

359
00:14:33,379 --> 00:14:33,899
about it in the future.

360
00:14:33,899 --> 00:14:37,529
But we go from a 9, 8, 7, 6, 5 on this digit,

361
00:14:37,529 --> 00:14:39,250
on the second digit.

362
00:14:39,250 --> 00:14:42,519
And on this digit here you go 1, 2, 3, 4.

363
00:14:42,519 --> 00:14:44,029
So it's an interesting pattern.

364
00:14:44,029 --> 00:14:47,250
Another interesting pattern is the digits will add up to 9.

365
00:14:47,250 --> 00:14:49,279
3 plus 6 is 9, 2 plus 7 is 9.

366
00:14:49,279 --> 00:14:51,009
We'll talk more about that in the future and maybe

367
00:14:51,009 --> 00:14:52,639
prove that to you.

368
00:14:52,639 --> 00:14:56,350
9 times 6, 54.

369
00:14:56,350 --> 00:14:58,159
That was this one as well.

370
00:14:58,159 --> 00:15:01,730
9 times 7, 63.

371
00:15:01,730 --> 00:15:03,860
9 times 8, 72.

372
00:15:03,860 --> 00:15:05,919
9 times 9 is 81.

373
00:15:05,919 --> 00:15:07,049
I don't know if you can see that.

374
00:15:07,049 --> 00:15:08,370
81.

375
00:15:08,370 --> 00:15:09,480
There you go.

376
00:15:09,480 --> 00:15:11,080
Now, I could keep going.

377
00:15:11,080 --> 00:15:13,790
Actually, I should keep going.

378
00:15:13,789 --> 00:15:17,549
Well, I realize this video is already pretty long.

379
00:15:17,549 --> 00:15:19,679
I want you to memorize this right now because this is

380
00:15:19,679 --> 00:15:21,209
going to get you pretty far.

381
00:15:21,210 --> 00:15:25,052
In the next video I'm going to do the times tables past 9.

382
00:15:25,052 --> 00:15:26,970
See you soon.