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## Arithmetic (all content)

### Unit 3: Lesson 2

Multiplication facts# Multiplication tables for 2-9

Introduction to the multiplication 'times tables' from 2-9. Created by Sal Khan.

## Video transcript

At this point I think you
know a little bit about what multiplication is. What we're going to do in this
video is to give you just a ton of more practice and start you
on your memorization of the multiplication tables. And if you watch enough Khan
Academy videos, and hopefully you will in the future, you'll
realize that I'm normally not a big fan of memorization. But the one thing about
multiplication is if you memorize your multiplication
tables that we'll start to do in this video, it'll pay huge
benefits the rest of your life. So I promise you, do it now,
you'll never forget it, and the rest of your life everything
will be-- well, I don't want to make false promises to you, but
they'll be better than if you didn't memorize your
multiplication tables. So what are the
multiplication tables? Well that's all of the
different numbers times each other. So let's actually do a
little bit of review. So if I say what is 2 times 1? That is equal to 2
plus itself one time. So this is equal to just 2. That's 2 plus itself one time. I don't have to say plus
anything because there's only one 2 there. I could also write this as
1 plus itself two times. So that's also 1 plus 1. Well that also equals 2. Fair enough. So 2 times 1 is 2. And if you watched the last
video, what's 2 times 0? Well that's 0. So you don't have to memorize
your 0 multiplication tables because everything times 0 is
0, or 0 times anything is 0. So let's see. What's 2 times 2? Well, this is equal to--
we're going to add 2 to itself two times. So that's 2 plus 2. And there's only a
way to do that. I could say take this 2 and
add it to itself two times, but it's the same thing. And what's 2 plus 2? That's equal to 4. What's 2 times 3? 2 times 3 is equal
to 2 plus 2 plus 2. It can also be
equal to 3 plus 3. We learned in a previous video
this statement can be written either of these ways. And in either case,
what's it equal to? Well, 3 plus 3 is the same
thing as 2 plus 2 plus 2, and that's equal to 6. All right. Now what is 2 times 4? Well that's equal to 2
plus 2 plus 2 plus 2. And notice, it's exactly
what 2 times 3 was. 2 times 3 was that. I have that here, but now I'm
just adding another 2 to it. So if we're too lazy to sit
here and add 2 plus 2 is 4. 4 plus 2 is 6. Instead of doing that, we could
say, hey look, we already know that this thing over
here, this was 6. We figured it out in the
previous line right there. We figured out this is 6, so we
could just say, oh, 2 times 4 is going to be 2 more than
that, which is equal to 8. And you should hopefully
see that pattern. As we go from 2 times 1,
to 2 times 2, to 2 times 3, what's happening? How much are we going up by? From 2 to 4 we're going plus 2. From 4 to 6 we're going plus 2. And then from 6 to 8
we're going plus 2. So you could figure out what
2 times 5 is, even without doing the addition. 2 times 5 is equal to 2 plus
2 plus 2 plus 2 plus 2. It could also be
written as 5 plus 5. 2 times 4 could've been
written as 4 plus 4 as well. And what's that equal to? We could add all of these up
or we could add these two up. Or we could just say it's going
to be two more than 2 times 4. So it's going to be 10. I'll finish the 2 times tables. And I think you see all of the
patterns that emerge from it. So 2 times 6. That's going to be 2
plus itself six times. Let's see. 1, 2, 3, 4, 5, 6, which
should also be equal to 6 plus itself two times. This could be
interpreted either way. And that's going to
be equal to 12. Once again, two more than 2
times 5 because we're adding 2 to itself one more time. So it's going to be two more. Let's keep going. So 2 times 7. 2 times 7 is equal to-- well, I
could write 2 plus 2 plus 2 plus 2-- this is getting
tiring-- plus 2 plus 2. Is that 7? 1, 2, 3, 4, 5, 6, 7. And that's the same thing as 7
plus 7, which you may or may not know is equal to 14. You could just say hey, that's
going to be two more than 12. So 12 plus 1 plus 2
is-- 12 plus 1 is 13. 12 plus 2 is 14. All right, let's
just keep going. 2 times 8. I could do all of this business
here where I add the 2's or I could say look, it's just going
to be two more than 2 times 7. So I could say it's
going to be 14 plus 2. I'm just adding
two to that one. So I could say it's 16. Or I could also say
that's 8 plus 8. That's also 16. I could have done all the 2's
out, but if you like you could do that for your
own benefit and learning. We're almost-- well, we could
go forever because there is no largest number. I can keep going. 2 times 9 times 10 times 100
times 1,000 times 1,000,000. But I'm going to stop at 12
because that tends to be what people need to memorize. But if you really want
to be a mathlete you want to go up to 20. But let's go to 2 times 9. That's going to be two
more than 2 times 8. It's going to be 18. Or that's 9 plus 9. Also 18. What's 2 times 10? And 10 times tables
are interesting. And we're going to see a
pattern there in a second when we try to complete
an entire times tables. So 2 times 10? Two more than 2 times 9. It's 20. Or we could also say
that's 10 plus 10. 10 plus itself two times. Now what's interesting
about this? This looks just like
a 2 with a 0 added. And you're going to see
that anything times 10. You just put a 0 on the right. And you can think
about why that is. You can view this
as two 10's is 20. That's what 20 is. We're almost done. Let's do 2 times 11. 2 times 11 is going to be 2
more than this right here. It's going to be 22. Another interesting pattern. I have the number repeated
twice-- a 2 and a 2. Interesting. Something to watch out
for as we look at other multiplication tables. And then finally-- it's not
finally, we could keep going. 2 times-- that's too
dark of a color. 2 times 12. 2 times 12 is going to be
two more than 2 times 11. That's 24. We could have also written
that as 12 plus 12. Or we could've said 2 plus
2 plus 2 plus 2 plus 2 twelve times. It all gets you to 24. So that's the 2 times
tables and I think you see the pattern. Every time you multiply it by
one higher number you just add 2 to that number. So now that we see that
pattern, let's see if we can complete a
multiplication table. So what I want to do, I'm going
to write all the numbers. Let's see. I hope I have space for this. 1, 2, 3, 4, 5, 6, 7, 8, 9. Actually, I'll just
do it till 9. I'll just keep going. 9. Actually I won't have space to
do that because I want you to see the entire table. So I'm just going up till
9 here, but I encourage you after this video to
complete it on your own. Maybe if we have time I'll
complete it here as well. So these are the first numbers
that I'm going to multiply. And I'm going to multiply
it times 1, 2, 3, 4, 5, 6, 7, 8, and 9. Actually I should have
written this 1 under- well, what's 1 times 1? So this is the way I'm
going to view it. Whatever is 1 times 1 I'm
going to write here. Well that's 1. What's 1 times 2? That's 2. What's 1 times 3? That's 3. 1 times anything is that
number, so I can just write 4, 5, 6, 7, 8, 9. 1 times 9 is 9. Fair enough. Now let's do the
2 times tables. I'll do that in a blue. Actually, let me do 1 in that
color and now in maybe a darker blue I'll do
the 2 times tables. What's 2 times 1? That's 2. It's the same thing
as 1 times 2. Notice, these two numbers
are the same thing. What's 2 times 2? That's 4. 2 times 3 is 6. We just did this. Every time you increment or
you multiply by a higher number, you just add by 2. 2 times 4 is 8. Same thing as 4 times 2. 2 times 5 is 10. 2 times 6 is 12. I'm just adding 2 every time. Up here I added 1 from every
step, here I'm adding 2. 2 times 7, 14. 2 times 8, 16. 2 two times 9, 18. All right, let's do
our 3 times tables. I'll do it in yellow. 3 times 1 is 3. Notice, 3 times 1 is 3. 1 times 3 is 3. These are the same values. 3 times 2 is the same
thing as 2 times 3. 3 times 2 should be the
same thing as 2 times 3. So it's 6. And that makes sense. 3 plus 3 is 6 or 2
plus 2 plus 2 is 6. So every time here we're
going to increase by 3. You see the pattern. 3 times 3 is 9. 3 plus 3 plus 3. So we went from 3 to 6 to 9. So 3 times 4 is going to be 12. I'm just adding 3 every time. 12 plus 3 is 15. 15 plus 3 is 18. 18 plus 3 is 21. 21 plus 3 is 24. 24 plus 3 is 27. So 3 times 9 is 27. 3 times 8 is 24. So if you were to say 8 plus
8 plus 8, it would be 24. So now I'm going to speed it
up a little bit now that we see the pattern. And you should do this on your
own and you really should memorize everything
we're doing. You should actually go
all the way up to 12 in both directions. So let's see. 4 times 1 is 4. I'm just going to go up
by increments of 4. So 4 plus 4 is 8. 8 plus 4 is 12. 12 plus 4 is 16. 16 plus 4 is 20. 20 plus 4 is 24. 4 times 6 is 24. 4 times 7, 28. I'm just going up by 4. 32 and 365. All right, 5 times 1. 5 times 1 is going to be 5. Actually, we know that
anything-- well, I want to keep changing colors, so I'll just
do it in rows like this. 5 times 1 is 5. 5 times 2 is 10. 5 times 3 is 15. I'm just going to
increase by 5. 5 times tables are very fun as
well because every number you're going to add-- if we
multiply 5 times-- well, we'll learn about even and
odd in the future. But every other number in its
times tables is going to end with a 5, and then every other
one's going to end with a 0. Because if you add 5
to 15 you get 20. You get 25, 30, 35, 40, 45. Fair enough. 6 times tables, let
me do it in green. 6 times 1 is 6. That's easy. You add 6 to that, you get 12. You add 6 to that, you get 18. You add 6 to that, you get 24. You add 6 to that, you get 30. Then you go 6 more, 36, 42, 48. 48 plus 6 is 54. So 6 times 9 is 54. All right, we're almost there. 7 times 1, that's 7. 7 times 1 is 7. 7 times 2 is 14. 7 times 3, 21. 7 times 4, 28. 7 times 5, what's 28 plus 7? Let's see. If you add 2 you get to 30. Then you have 5, 35. 7 times 6, 42. 7 times 7, 49. 7 times 8. Seven times is going to be
7 plus this, so it's 56. I always used to get confused
between 7 times 8 being 56 and 6 times 9 being 54. So now that I pointed out to
you that I always got confused between those two, it's your
job not to be confused by those two. 7 times 8 you could
say has the 6 in it. 6 times 9 doesn't
have the 6 in it. That's the way I think of it. Anyway, 7 times 9. We're going to add
another 7 here. It's going to be 63. I'll do it in the same color. All right, we're at
our 8 times tables. 8 times 1 is 8. 8 times 2 is 16. 24. 8 times 3 is 24. And if we go to 3 times 8
we should also see the 24. Yep, it's there. These values are the same. So we're actually
doing things twice. We're doing it when you do
8 times 3 and we're doing it when we did 3 times 8. Let's see. 8 times 4, you're going
to add 8 to it-- 32. 40. Add another 8, 48. Notice, 8 times 6, 48. 6 times 8, 48. All right, 8 times 7. Well, we already pointed
that one out, that was 56. 8 times 8, 64. 8 times 9, add 8
to this, is 72. Now we're at the
9 times tables. I'm running out of colors. Maybe I'll reuse
a color or two. I'll use the blue again. 9 times 1 is 9. 9 times 2, 18 9 times 3-- we
actually know all of these. We could look it up in the rest
of the table because 9 times 3 is the same thing as 3 times 9. It's 27. Add 9 to that. 27 plus 9 is 36. 36 plus 9 is 45. Notice, every time you add
9, you go almost up by 10, but 1 less than that. So up by 10 would be 46, and
then one less than that is 45. But anyway, notice, the
1's-- well, I'll talk more about it in the future. But we go from a 9, 8,
7, 6, 5 on this digit, on the second digit. And on this digit here
you go 1, 2, 3, 4. So it's an interesting pattern. Another interesting pattern is
the digits will add up to 9. 3 plus 6 is 9, 2 plus 7 is 9. We'll talk more about that
in the future and maybe prove that to you. 9 times 6, 54. That was this one as well. 9 times 7, 63. 9 times 8, 72. 9 times 9 is 81. I don't know if
you can see that. 81. There you go. Now, I could keep going. Actually, I should keep going. Well, I realize this video
is already pretty long. I want you to memorize this
right now because this is going to get you pretty far. In the next video I'm going to
do the times tables past 9. See you soon.