0:00:00.880,0:00:05.805
At this point I think you know a little bit about what multiplication is.
0:00:05.805,0:00:09.025
Or "multi"-plication.
0:00:09.025,0:00:13.315
What we're going to do in this video is to give you just a ton of more practice,
0:00:13.315,0:00:17.706
and start you on your memorization of the multiplication tables.
0:00:17.706,0:00:20.009
And if you watch enough Khan Academy videos,
0:00:20.009,0:00:21.279
and hopefully you will in the future,
0:00:21.279,0:00:24.540
you'll realize that I'm normally not a big fan of memorization.
0:00:24.550,0:00:26.385
But the one thing about multiplication
0:00:26.385,0:00:31.220
is if you memorize your multiplication tables that we'll start to do in this video,
0:00:31.220,0:00:33.850
it'll pay huge benefits the rest of your life.
0:00:33.850,0:00:36.724
So I promise you, do it now, you'll never forget it,
0:00:36.724,0:00:39.547
and the rest of your life everything will be--
0:00:39.547,0:00:41.517
well, I don't want to make false promises to you,
0:00:41.517,0:00:45.790
but they'll be better than if you didn't memorize your multiplication tables.
0:00:45.790,0:00:47.290
So what are the multiplication tables?
0:00:47.290,0:00:49.745
Well that's all of the different numbers
0:00:49.745,0:00:50.850
times each other.
0:00:50.850,0:00:53.590
So let's actually do a little bit of review.
0:00:53.600,0:00:58.900
So if I say, what is two times one?
0:00:58.900,0:01:02.270
That is equal to two plus itself one time.
0:01:02.280,0:01:05.010
So this is equal to just two.
0:01:05.010,0:01:07.060
That's two plus itself one time.
0:01:07.060,0:01:08.059
I don't have to say plus anything
0:01:08.059,0:01:09.430
because there's only one two there.
0:01:09.430,0:01:13.460
I could also write this as one plus itself two times.
0:01:13.460,0:01:15.390
So that's also one plus one.
0:01:15.400,0:01:17.580
Well that also equals two.
0:01:17.590,0:01:18.210
Fair enough.
0:01:18.210,0:01:19.901
So two times one is two.
0:01:19.901,0:01:22.722
And if you watched the last video, what's two times zero?
0:01:22.722,0:01:23.516
Well that's zero.
0:01:23.516,0:01:26.660
So you don't have to memorize your zero multiplication tables
0:01:26.670,0:01:30.560
because everything times zero is zero, or zero times anything is zero.
0:01:30.560,0:01:31.090
So let's see.
0:01:31.090,0:01:33.682
What's two times two?
0:01:33.682,0:01:35.988
Two times two.
0:01:35.988,0:01:37.254
Well, this is equal to--
0:01:37.254,0:01:39.460
we're going to add two to itself two times.
0:01:39.460,0:01:41.830
So that's two plus two.
0:01:41.840,0:01:42.770
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.
0:01:46.680,0:01:47.610
And what's two plus two?
0:01:47.620,0:01:49.450
That's equal to four.
0:01:49.450,0:01:51.400
What's two times three?
0:01:51.400,0:01:57.900
Two times three is equal to two plus two plus two.
0:01:57.900,0:02:03.355
It can also be equal to three plus three.
0:02:03.355,0:02:04.905
We learned in a previous video
0:02:04.920,0:02:07.498
this statement can be written either of these ways.
0:02:07.498,0:02:09.380
And in either case, what's it equal to?
0:02:09.397,0:02:10.282
Well three plus three
0:02:10.282,0:02:12.028
is the same thing as two plus two plus two,
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and that's equal to six.
0:02:14.774,0:02:15.812
All right.
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Now what is two times four?
0:02:18.153,0:02:20.686
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.
0:02:29.870,0:02:32.610
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,
0:02:41.802,0:02:45.680
hey look, we already know that this thing over here, this was six.
0:02:45.680,0:02:48.300
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
0:02:51.560,0:02:55.610
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,
0:03:01.907,0:03:03.760
to two times three, what's happening?
0:03:03.770,0:03:05.500
How much are we going up by?
0:03:05.500,0:03:08.120
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.
0:03:13.340,0:03:15.685
So you could figure out what two times five is,
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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.
0:03:26.080,0:03:29.110
Two times four could've been written as four plus four as well.
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And what's that equal to?
0:03:30.500,0:03:33.090
We could add all of these up or we could add these two up.
0:03:33.090,0:03:36.285
Or we could just say it's going to be two more than two times four.
0:03:36.285,0:03:38.564
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.
0:03:51.595,0:03:55.369
Let's see. One, two, three, four, five, six,
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which should also be equal to six plus itself two times.
0:03:58.690,0:04:00.620
This could be interpreted either way.
0:04:00.620,0:04:02.980
And that's going to be equal to twelve.
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Once again, two more than two times five
0:04:06.898,0:04:09.710
because we're adding two to itself one more time.
0:04:09.710,0:04:12.290
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--
0:04:24.104,0:04:27.230
this is getting tiring-- plus two plus two.
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Is that seven?
0:04:27.810,0:04:31.200
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.
0:04:47.580,0:04:50.740
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.
0:04:56.670,0:04:59.528
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.
0:05:01.822,0:05:05.610
Or I could also say that's eight plus eight.
0:05:05.620,0:05:06.800
That's also sixteen.
0:05:06.810,0:05:08.174
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
0:05:17.848,0:05:19.360
because there is no largest number.
0:05:19.370,0:05:21.510
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.
0:05:42.690,0:05:44.060
Also eighteen.
0:05:44.060,0:05:45.930
What's two times ten?
0:05:45.940,0:05:47.940
And ten times tables are interesting.
0:05:47.940,0:05:49.550
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?
0:05:54.640,0:05:56.800
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?
0:06:05.060,0:06:09.115
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
0:06:35.818,0:06:38.690
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
0:07:00.961,0:07:01.970
and I think you see the pattern.
0:07:01.980,0:07:04.755
Every time you multiply it by one higher number
0:07:04.755,0:07:06.670
you just add two to that number.
0:07:06.680,0:07:08.748
So now that we see that pattern,
0:07:08.748,0:07:11.950
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.
0:07:32.970,0:07:34.106
Actually I won't have space to do that
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because I want you to see the entire table.
0:07:35.680,0:07:37.045
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,
0:07:52.060,0:07:57.650
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--
0:08:01.298,0:08:03.321
Actually I should have written this one under--
0:08:03.321,0:08:04.710
well, what's one times one?
0:08:04.720,0:08:06.110
So this is the way I'm going to view it.
0:08:06.120,0:08:08.730
Whatever is one times one I'm going to write here.
0:08:08.730,0:08:09.970
Well that's one.
0:08:09.970,0:08:11.510
What's one times two?
0:08:11.510,0:08:12.400
That's two.
0:08:12.410,0:08:13.730
What's one times three?
0:08:13.740,0:08:14.360
That's three.
0:08:14.360,0:08:15.866
One times anything is that number,
0:08:15.866,0:08:21.360
so I can just write four, five, six, seven, eight, nine.
0:08:21.370,0:08:23.540
One times nine is nine.
0:08:23.540,0:08:24.540
Fair enough.
0:08:24.540,0:08:26.300
Now let's do the two times tables.
0:08:26.310,0:08:27.570
I'll do that in a blue.
0:08:27.570,0:08:30.270
Actually, let me do one in that color
0:08:30.285,0:08:33.980
and now in maybe a darker blue I'll do the two times tables.
0:08:33.990,0:08:35.250
What's two times one?
0:08:35.250,0:08:36.430
That's two.
0:08:36.440,0:08:37.690
It's the same thing as one times two.
0:08:37.700,0:08:40.000
Notice, these two numbers are the same thing.
0:08:40.000,0:08:41.700
What's two times two?
0:08:41.710,0:08:43.000
That's four.
0:08:43.000,0:08:44.610
Two times three is six.
0:08:44.620,0:08:45.840
We just did this.
0:08:45.840,0:08:49.821
Every time you increment or you multiply by a higher number,
0:08:49.821,0:08:51.190
you just add by two.
0:08:51.190,0:08:52.840
Two times four is eight.
0:08:52.850,0:08:55.110
Same thing as four times two.
0:08:55.120,0:08:57.260
Two times five is ten.
0:08:57.260,0:08:59.010
Two times six is twelve.
0:08:59.010,0:09:00.660
I'm just adding two every time.
0:09:00.670,0:09:03.970
Up here I added one from every step, here I'm adding two.
0:09:03.980,0:09:06.830
Two times seven, fourteen.
0:09:06.830,0:09:09.813
Two times eight, sixteen.
0:09:09.813,0:09:12.970
Two times nine, eighteen.
0:09:12.980,0:09:17.789
All right, let's do our three times tables.
0:09:17.789,0:09:20.508
I'll do it in yellow.
0:09:20.508,0:09:21.783
Yellow.
0:09:21.783,0:09:23.828
Three times one is three.
0:09:23.828,0:09:25.350
Notice, three times one is three.
0:09:25.360,0:09:26.910
One times three is three.
0:09:26.910,0:09:28.740
These are the same values.
0:09:28.750,0:09:32.158
Three times two is the same thing as two times three.
0:09:32.158,0:09:37.640
Three times two should be the same thing as two times three.
0:09:37.640,0:09:39.680
So it's six.
0:09:39.690,0:09:40.485
And that makes sense.
0:09:40.485,0:09:45.690
Three plus three is six or two plus two plus two is six.
0:09:45.690,0:09:47.780
So every time here we're going to increase by three.
0:09:47.780,0:09:48.880
You see the pattern.
0:09:48.880,0:09:51.000
Three times three is nine.
0:09:51.010,0:09:52.852
Three plus three plus three.
0:09:52.852,0:09:54.725
So we went from three to six to nine.
0:09:54.736,0:09:57.001
So three times four is going to be twelve.
0:09:57.001,0:09:58.850
I'm just adding three every time.
0:09:58.850,0:10:00.642
Twelve plus three is fifteen.
0:10:00.642,0:10:03.404
Fifteen plus three is eighteen.
0:10:03.404,0:10:05.580
Eighteen plus three is twenty-one.
0:10:05.580,0:10:08.080
Twenty-one plus three is twenty-four.
0:10:08.090,0:10:10.500
Twenty-four plus three is twenty-seven.
0:10:10.500,0:10:13.110
So three times nine is twenty-seven.
0:10:13.120,0:10:14.840
Three times eight is twenty-four.
0:10:14.840,0:10:19.094
So if you were to say eight plus eight plus eight, it would be twenty-four.
0:10:19.094,0:10:20.180
Let's see if I can--
0:10:20.180,0:10:21.544
So now I'm going to speed it up a little bit,
0:10:21.544,0:10:22.830
now that we see the pattern.
0:10:22.840,0:10:24.088
And you should do this on your own
0:10:24.088,0:10:26.970
and you really should memorize everything we're doing.
0:10:26.980,0:10:30.495
You should actually go all the way up to twelve in both directions.
0:10:30.495,0:10:31.057
So let's see.
0:10:31.057,0:10:35.330
Four times one is four.
0:10:35.330,0:10:37.640
I'm just going to go up by increments of four.
0:10:37.640,0:10:40.080
So four plus four is eight.
0:10:40.090,0:10:41.960
Eight plus four is twelve.
0:10:41.970,0:10:43.920
Twelve plus four is sixteen.
0:10:43.920,0:10:46.450
Sixteen plus four is twenty.
0:10:46.460,0:10:48.460
Twenty plus four is twenty-four.
0:10:48.460,0:10:51.460
Four times six is twenty-four.
0:10:51.470,0:10:52.970
Four times seven, twenty-eight.
0:10:52.980,0:10:54.250
I'm just going up by four.
0:10:54.250,0:10:58.740
Thirty-two and thirty-six.
0:10:58.750,0:11:01.490
All right, five times one.
0:11:01.490,0:11:06.670
Five times one is going to be five.
0:11:06.670,0:11:09.565
Actually, we know that anything that-- well, I want us to keep changing colors,
0:11:09.565,0:11:11.400
so I'll just do it in rows like this.
0:11:11.410,0:11:12.570
Five times one is five.
0:11:12.580,0:11:15.780
Five times two is ten.
0:11:15.780,0:11:17.260
Five times three is fifteen.
0:11:17.260,0:11:18.430
I'm just going to increase by five.
0:11:18.440,0:11:20.687
Five times tables are very fun as well
0:11:20.687,0:11:24.120
because every number you're going to add-- if we multiply five times--
0:11:24.120,0:11:25.870
well, we'll learn about even and odd in the future.
0:11:25.880,0:11:30.241
But every other number in its times tables is going to end with a five,
0:11:30.241,0:11:32.240
and then every other one's going to end with a zero.
0:11:32.250,0:11:34.790
Because if you add five to fifteen you get twenty.
0:11:34.790,0:11:41.871
You get twenty-five, thirty, thirty-five, forty, forty-five.
0:11:41.871,0:11:43.380
Fair enough.
0:11:43.380,0:11:47.120
Six times tables, let me do it in green.
0:11:47.120,0:11:48.210
Six times one is six.
0:11:48.220,0:11:49.080
That's easy.
0:11:49.080,0:11:50.800
You add six to that, you get twelve.
0:11:50.800,0:11:52.490
You add six to that, you get eighteen.
0:11:52.500,0:11:54.250
You add six to that, you get twenty-four.
0:11:54.250,0:11:56.220
You add six to that, you get thirty.
0:11:56.220,0:12:01.220
Then you go six more, thirty-six, forty-two, forty-eight.
0:12:01.220,0:12:04.620
Forty-eight plus six is fifty-four.
0:12:04.620,0:12:07.620
So six times nine is fifty-four.
0:12:07.620,0:12:08.990
All right, we're almost there.
0:12:09.000,0:12:11.610
Seven times one, that's seven.
0:12:11.620,0:12:13.520
Seven times one is seven.
0:12:13.520,0:12:15.610
Seven times two is fourteen.
0:12:15.620,0:12:17.740
Seven times three, twenty-one.
0:12:17.740,0:12:20.040
Seven times four, twenty-eight.
0:12:20.040,0:12:23.512
Seven times five, what's twenty-eight plus seven?
0:12:23.512,0:12:25.130
Let's see, if you add two you get to thirty.
0:12:25.130,0:12:27.700
Then you add five, it's thirty-five.
0:12:27.710,0:12:29.480
Seven times six, forty-two.
0:12:29.490,0:12:32.640
Seven times seven, forty-nine.
0:12:32.640,0:12:34.775
Seven times eight--
0:12:34.775,0:12:37.830
seven times is going to be seven plus this, so it's fifty-six.
0:12:37.830,0:12:41.580
I always used to get confused between seven times eight being fifty-six
0:12:41.590,0:12:43.610
and six times nine being fifty-four.
0:12:43.620,0:12:46.705
So now that I pointed out to you that I always got confused between those two,
0:12:46.705,0:12:49.389
it's your job not to be confused by those two.
0:12:49.390,0:12:52.610
Seven times eight you could say has the six in it.
0:12:52.620,0:12:54.850
Six times nine doesn't have the six in it.
0:12:54.850,0:12:56.080
That's the way I think of it.
0:12:56.080,0:12:57.580
Anyway, seven times nine.
0:12:57.580,0:12:59.320
We're going to add another seven here.
0:12:59.320,0:13:01.152
It's going to be sixty-three.
0:13:01.152,0:13:04.830
I'll do it in the same color.
0:13:04.840,0:13:08.350
All right, we're at our eight times tables.
0:13:08.360,0:13:10.660
Eight times one is eight.
0:13:10.660,0:13:12.520
Eight times two is sixteen.
0:13:12.520,0:13:14.090
Twenty-four.
0:13:14.100,0:13:15.690
Eight times three is twenty-four.
0:13:15.690,0:13:18.300
And if we go to three times eight we should also see the twenty-four.
0:13:18.300,0:13:19.500
Yep, it's there.
0:13:19.500,0:13:21.110
These values are the same.
0:13:21.120,0:13:22.800
So we're actually doing things twice.
0:13:22.800,0:13:24.848
We're doing it when you do eight times three
0:13:24.848,0:13:27.470
and we're doing it when we did three times eight.
0:13:27.472,0:13:31.210
Let's see, eight times four, you're going to add eight to it-- thirty-two.
0:13:31.220,0:13:32.480
Forty.
0:13:32.490,0:13:34.690
Add another eight, forty-eight.
0:13:34.690,0:13:37.270
Notice, eight times six, forty-eight.
0:13:37.270,0:13:40.230
Six times eight, forty-eight.
0:13:40.240,0:13:42.450
All right, eight times seven.
0:13:42.450,0:13:45.860
Well, we already pointed that one out, that was fifty-six.
0:13:45.870,0:13:48.200
Eight times eight, sixty-four.
0:13:48.200,0:13:52.010
Eight times nine, add eight to this, is seventy-two.
0:13:52.010,0:13:54.640
Now we're at the nine times tables.
0:13:54.650,0:13:57.260
I'm running out of colors.
0:13:57.260,0:13:59.520
Maybe I'll reuse a color or two.
0:13:59.530,0:14:01.100
I'll use the blue again.
0:14:01.110,0:14:03.280
Nine times one is nine.
0:14:03.280,0:14:06.700
Nine times two, eighteen nine times three-- we actually know all of these.
0:14:06.710,0:14:08.097
We could look it up in the rest of the table
0:14:08.097,0:14:11.290
because nine times three is the same thing as three times nine.
0:14:11.290,0:14:13.280
It's twenty-seven.
0:14:13.280,0:14:14.500
Add nine to that.
0:14:14.500,0:14:18.380
Twenty-seven plus nine is thirty-six.
0:14:18.390,0:14:21.520
Thirty-six plus nine is forty-five.
0:14:21.530,0:14:25.331
Notice, every time you add nine, you go almost up by ten,
0:14:25.331,0:14:26.219
but one less than that.
0:14:26.219,0:14:29.970
So up by ten would be forty-six, and then one less than that is forty-five.
0:14:29.970,0:14:32.647
But anyway, notice, the ones--
0:14:32.647,0:14:33.880
well, I'll talk more about it in the future.
0:14:33.890,0:14:37.510
But we go from a nine, eight, seven, six, five on this digit,
0:14:37.520,0:14:38.835
on the second digit.
0:14:38.835,0:14:42.510
And on this digit here you go one, two, three, four.
0:14:42.510,0:14:44.010
So it's an interesting pattern.
0:14:44.020,0:14:47.240
Another interesting pattern is the digits will add up to nine.
0:14:47.250,0:14:49.270
Three plus six is nine, two plus seven is nine.
0:14:49.270,0:14:50.831
We'll talk more about that in the future
0:14:50.831,0:14:52.620
and maybe prove that to you.
0:14:52.630,0:14:56.340
Nine times six, fifty-four.
0:14:56.350,0:14:58.150
That was this one as well.
0:14:58.150,0:15:01.720
Nine times seven, sixty-three.
0:15:01.730,0:15:03.850
Nine times eight, seventy-two.
0:15:03.860,0:15:05.910
Nine times nine is eighty-one.
0:15:05.910,0:15:07.030
I don't know if you can see that.
0:15:07.040,0:15:08.360
Eighty-one.
0:15:08.370,0:15:09.480
There you go.
0:15:09.480,0:15:11.080
Now, I could keep going.
0:15:11.080,0:15:13.780
Actually, I should keep going.
0:15:13.780,0:15:17.525
Well, I realize this video is already pretty long.
0:15:17.525,0:15:19.316
I want you to memorize this right now
0:15:19.316,0:15:21.200
because this is going to get you pretty far.
0:15:21.210,0:15:25.542
In the next video I'm going to do the times tables past nine.
0:15:25.542,0:15:26.960
See you soon!