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Multiplication 2: The Multiplication Tables

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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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    5
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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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    40
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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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    All right.
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    Now what is 2 times 4?
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    59
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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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    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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    189
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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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    228
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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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    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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    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.
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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.
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    5 times tables are very fun as
    well because every number
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    you're going to add-- if we
    multiply 5 times-- well, we'll
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    learn about even and
    odd in the future.
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    But every other number in its
    times tables is going to end
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    with a 5, and then every other
    one's going to end with a 0.
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    Because if you add 5
    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.
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    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.
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    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.
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    All right, we're almost there.
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    7 times 1, that's 7.
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    7 times 1 is 7.
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    7 times 2 is 14.
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    7 times 3, 21.
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    7 times 4, 28.
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    7 times 5, what's 28 plus 7?
  • 12:24 - 12:24
    Let's see.
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    If you add 2 you get to 30.
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    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.
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    Seven times is going to be
    7 plus this, so it's 56.
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    I always used to get confused
    between 7 times 8 being 56
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    and 6 times 9 being 54.
  • 12:44 - 12:46
    So now that I pointed out to
    you that I always got confused
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    between those two, it's your
    job not to be confused
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    by those two.
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    7 times 8 you could
    say has the 6 in it.
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    6 times 9 doesn't
    have the 6 in it.
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    That's the way I think of it.
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    Anyway, 7 times 9.
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    We're going to add
    another 7 here.
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    It's going to be 63.
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    I'll do it in the same color.
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    All right, we're at
    our 8 times tables.
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    8 times 1 is 8.
  • 13:11 - 13:13
    8 times 2 is 16.
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    24.
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    8 times 3 is 24.
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    And if we go to 3 times 8
    we should also see the 24.
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    Yep, it's there.
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    These values are the same.
  • 13:21 - 13:23
    So we're actually
    doing things twice.
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    We're doing it when you do
    8 times 3 and we're doing
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    it when we did 3 times 8.
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    Let's see.
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    8 times 4, you're going
    to add 8 to it-- 32.
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    40.
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    Add another 8, 48.
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    Notice, 8 times 6, 48.
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    6 times 8, 48.
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    All right, 8 times 7.
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    Well, we already pointed
    that one out, that was 56.
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    8 times 8, 64.
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    8 times 9, add 8
    to this, is 72.
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    Now we're at the
    9 times tables.
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    I'm running out of colors.
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    Maybe I'll reuse
    a color or two.
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    I'll use the blue again.
  • 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
    Add 9 to that.
  • 14:15 - 14:18
    27 plus 9 is 36.
  • 14:18 - 14:22
    36 plus 9 is 45.
  • 14:22 - 14:25
    Notice, every time you add
    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
    about it in the future.
  • 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
    We'll talk more about that
    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
    That was this one as well.
  • 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
    is already pretty long.
  • 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.

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Video Language:
English
Duration:
15:27

English subtitles

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