## Multiplication 2: The Multiplication Tables

• 0:01 - 0:03
At this point I think you
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what multiplication is.
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5
00:00:08,74 --> 00:00:11,9
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
• 0:17 - 0:18
multiplication tables.
• 0:18 - 0:20
And if you watch enough Khan
• 0:20 - 0:23
you will in the future, you'll
realize that I'm normally not
• 0:23 - 0:25
a big fan of memorization.
• 0:25 - 0:27
multiplication is if you
• 0:27 - 0:30
tables that we'll start to do
• 0:30 - 0:34
in this video, it'll pay huge
benefits the rest of your life.
• 0:34 - 0:38
So I promise you, do it now,
you'll never forget it, and the
• 0:38 - 0:40
will be-- well, I don't want to
• 0:40 - 0:43
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
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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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40
00:01:35,75 --> 00:01:37,91
Well, this is equal to--
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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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All right.
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Now what is 2 times 4?
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59
00:02:20,67 --> 00:02:26,06
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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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
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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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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
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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
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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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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
• 7:05 - 7:07
• 7:07 - 7:09
So now that we see that
pattern, let's see
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if we can complete a
multiplication table.
• 7:12 - 7:16
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
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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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189
00:08:00,95 --> 00:08:03,28
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
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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.
• 9:18 - 9:22

228
00:09:21,7 --> 00:09:23,82
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.
• 9:29 - 9:33
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.
• 9:40 - 9:40
And that makes sense.
• 9:40 - 9:46
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.
• 9:49 - 9:51
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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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.
• 10:20 - 10:22
So now I'm going to speed it
up a little bit now that
• 10:22 - 10:23
we see the pattern.
• 10:23 - 10:25
And you should do this on your
own and you really should
• 10:25 - 10:27
memorize everything
we're doing.
• 10:31 - 10:31
So let's see.
• 10:31 - 10:35
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.
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16 plus 4 is 20.
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20 plus 4 is 24.
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4 times 6 is 24.
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4 times 7, 28.
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I'm just going up by 4.
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32 and 365.
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All right, 5 times 1.
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5 times 1 is going to be 5.
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Actually, we know that
anything-- well, I want to keep
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changing colors, so I'll just
do it in rows like this.
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5 times 1 is 5.
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5 times 2 is 10.
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5 times 3 is 15.
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I'm just going to
increase by 5.
• 11:18 - 11:21
5 times tables are very fun as
well because every number
• 11:21 - 11:24
you're going to add-- if we
multiply 5 times-- well, we'll
• 11:24 - 11:26
odd in the future.
• 11:26 - 11:30
But every other number in its
times tables is going to end
• 11:30 - 11:32
with a 5, and then every other
one's going to end with a 0.
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to 15 you get 20.
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You get 25, 30, 35, 40, 45.
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Fair enough.
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6 times tables, let
me do it in green.
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6 times 1 is 6.
• 11:48 - 11:49
That's easy.
• 11:49 - 11:51
You add 6 to that, you get 12.
• 11:51 - 11:52
You add 6 to that, you get 18.
• 11:52 - 11:54
You add 6 to that, you get 24.
• 11:54 - 11:56
You add 6 to that, you get 30.
• 11:56 - 12:01
Then you go 6 more, 36, 42, 48.
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48 plus 6 is 54.
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So 6 times 9 is 54.
• 12:08 - 12:09
All right, we're almost there.
• 12:09 - 12:12
7 times 1, that's 7.
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7 times 1 is 7.
• 12:14 - 12:16
7 times 2 is 14.
• 12:16 - 12:18
7 times 3, 21.
• 12:18 - 12:20
7 times 4, 28.
• 12:20 - 12:24
7 times 5, what's 28 plus 7?
• 12:24 - 12:24
Let's see.
• 12:24 - 12:25
If you add 2 you get to 30.
• 12:25 - 12:28
Then you have 5, 35.
• 12:28 - 12:29
7 times 6, 42.
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7 times 7, 49.
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7 times 8.
• 12:35 - 12:38
Seven times is going to be
7 plus this, so it's 56.
• 12:38 - 12:42
I always used to get confused
between 7 times 8 being 56
• 12:42 - 12:44
and 6 times 9 being 54.
• 12:44 - 12:46
So now that I pointed out to
you that I always got confused
• 12:46 - 12:48
between those two, it's your
job not to be confused
• 12:48 - 12:49
by those two.
• 12:49 - 12:53
7 times 8 you could
say has the 6 in it.
• 12:53 - 12:55
6 times 9 doesn't
have the 6 in it.
• 12:55 - 12:56
That's the way I think of it.
• 12:56 - 12:58
Anyway, 7 times 9.
• 12:58 - 12:59
another 7 here.
• 12:59 - 13:01
It's going to be 63.
• 13:01 - 13:05
I'll do it in the same color.
• 13:05 - 13:08
All right, we're at
our 8 times tables.
• 13:08 - 13:11
8 times 1 is 8.
• 13:11 - 13:13
8 times 2 is 16.
• 13:13 - 13:14
24.
• 13:14 - 13:16
8 times 3 is 24.
• 13:16 - 13:18
And if we go to 3 times 8
we should also see the 24.
• 13:18 - 13:20
Yep, it's there.
• 13:20 - 13:21
These values are the same.
• 13:21 - 13:23
So we're actually
doing things twice.
• 13:23 - 13:25
We're doing it when you do
8 times 3 and we're doing
• 13:25 - 13:27
it when we did 3 times 8.
• 13:27 - 13:28
Let's see.
• 13:28 - 13:31
8 times 4, you're going
to add 8 to it-- 32.
• 13:31 - 13:32
40.
• 13:32 - 13:35
• 13:35 - 13:37
Notice, 8 times 6, 48.
• 13:37 - 13:40
6 times 8, 48.
• 13:40 - 13:42
All right, 8 times 7.
• 13:42 - 13:46
that one out, that was 56.
• 13:46 - 13:48
8 times 8, 64.
• 13:48 - 13:52
to this, is 72.
• 13:52 - 13:55
Now we're at the
9 times tables.
• 13:55 - 13:57
I'm running out of colors.
• 13:57 - 14:00
Maybe I'll reuse
a color or two.
• 14:00 - 14:01
I'll use the blue again.
• 14:01 - 14:03
9 times 1 is 9.
• 14:03 - 14:07
9 times 2, 18 9 times 3-- we
actually know all of these.
• 14:07 - 14:09
We could look it up in the rest
of the table because 9 times 3
• 14:09 - 14:11
is the same thing as 3 times 9.
• 14:11 - 14:13
It's 27.
• 14:13 - 14:15
• 14:15 - 14:18
27 plus 9 is 36.
• 14:18 - 14:22
36 plus 9 is 45.
• 14:22 - 14:25
9, you go almost up by
• 14:25 - 14:26
10, but 1 less than that.
• 14:26 - 14:30
So up by 10 would be 46, and
then one less than that is 45.
• 14:30 - 14:33
But anyway, notice, the
1's-- well, I'll talk more
• 14:33 - 14:34
• 14:34 - 14:38
But we go from a 9, 8,
7, 6, 5 on this digit,
• 14:38 - 14:39
on the second digit.
• 14:39 - 14:43
And on this digit here
you go 1, 2, 3, 4.
• 14:43 - 14:44
So it's an interesting pattern.
• 14:44 - 14:47
Another interesting pattern is
the digits will add up to 9.
• 14:47 - 14:49
3 plus 6 is 9, 2 plus 7 is 9.
• 14:49 - 14:51
in the future and maybe
• 14:51 - 14:53
prove that to you.
• 14:53 - 14:56
9 times 6, 54.
• 14:56 - 14:58
• 14:58 - 15:02
9 times 7, 63.
• 15:02 - 15:04
9 times 8, 72.
• 15:04 - 15:06
9 times 9 is 81.
• 15:06 - 15:07
I don't know if
you can see that.
• 15:07 - 15:08
81.
• 15:08 - 15:09
There you go.
• 15:09 - 15:11
Now, I could keep going.
• 15:11 - 15:14
Actually, I should keep going.
• 15:14 - 15:18
Well, I realize this video
• 15:18 - 15:20
I want you to memorize this
right now because this is
• 15:20 - 15:21
going to get you pretty far.
• 15:21 - 15:25
In the next video I'm going to
do the times tables past 9.
• 15:25 - 15:27
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
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