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Multiplying and dividing negative numbers

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    Welcome to the presentation
    on multiplying and
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    dividing negative numbers.
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    Let's get started.
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    I think you're going to find
    that multiplying and dividing
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    negative numbers are a lot
    easier than it might
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    look initially. You just have to
    remember a couple of rules.
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    And I am going to teach probably
    in the future like I'm actually going
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    to give you more intuition on
    why there rules work.
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    So the basic rules are when you
    multiply two negative numbers,
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    so let's say I had negative
    2 times negative 2.
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    First you just look at each
    of the numbers as if there
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    was no negative sign.
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    Well you say well, 2
    times 2 that equals 4.
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    And it turns out that if you
    have a negative times a
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    negative, that that
    equals a positive.
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    So let's write that
    first rule down.
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    A negative times a negative
    equals a positive.
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    What if it was negative
    2 times positive 2?
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    Well in this case, let's
    first of all look at the
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    two numbers without signs.
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    We know that 2 times 2 is 4.
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    But here we have a negative
    times a positive 2, and it
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    turns out that when you
    multiply a negative times a
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    positive you get a negative.
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    So that's another rule.
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    Negative times positive
    is equal to negative.
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    What happens if you have a
    positive 2 times a negative 2?
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    I think you'll probably guess
    this one right, as you can tell
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    that these two are pretty much
    the same thing by, I believe
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    it's the transitive property --
    no, no I think it's the
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    communicative property.
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    I have to remember that.
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    But 2 times negative 2, this
    also equals negative 4.
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    So we have the final rule that
    a positive times a negative
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    also equals the negative.
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    And actually these second
    two rules, they're kind
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    of the same thing.
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    A negative times a positive
    is a negative, or a positive
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    times a negative is negative.
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    You could also say that as when
    the signs are different and
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    you multiply the two numbers,
    you get a negative number.
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    And of course, you already know
    what happens when you have a
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    positive times a positive.
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    Well that's just a positive.
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    So let's review.
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    Negative times a
    negative is a positive.
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    A negative times a
    positive is a negative.
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    A positive times a
    negative is a negative.
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    And positive times each
    other equals positive.
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    I think that last little bit
    completely confused you.
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    Maybe I can simplify
    it for you.
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    What if I just told you if when
    you're multiplying and they're
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    the same signs that gets
    you a positive result.
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    And different signs gets
    you a negative result.
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    So that would be either, let's
    say a 1 times 1 is equal to 1,
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    or if I said negative 1 times
    negative 1 is equal to
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    positive 1 as well.
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    Or if I said 1 times negative
    1 is equal to negative 1, or
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    negative 1 times 1 is
    equal to negative 1.
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    You see how on the bottom two
    problems I had two different
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    signs, positive 1
    and negative 1?
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    And the top two problems,
    this one right here
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    both 1s are positive.
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    And this one right here
    both 1s are negative.
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    So let's do a bunch of problems
    now, and hopefully it'll hit
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    the point home, and you also
    could try to do along the
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    practice problems and also give
    the hints and give you what rules to you so that should help you as well
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    So if I said negative 4 times
    positive 3, well 4 times
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    3 is 12, and we have a
    negative and a positive.
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    So different signs
    mean negative.
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    So negative 4 times
    3 is a negative 12.
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    That makes sense because we're
    essentially saying what's
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    negative 4 times itself three
    times, so it's like negative 4
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    plus negative 4 plus negative
    4, which is negative 12.
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    If you've seen the video on
    adding and subtracting negative
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    numbers, you probably
    should watch first.
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    Let's do another one.
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    What if I said minus
    2 times minus 7.
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    And you might want to pause the
    video at any time to see if you
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    know how to do it and
    then restart it to see
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    what the answer is.
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    Well, 2 times 7 is 14, and we
    have the same sign here, so
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    it's a positive 14 -- normally
    you wouldn't have to write the
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    positive but that makes it a
    little bit more explicit.
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    And what if I had -- let me
    think -- 9 times negative 5.
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    Well, 9 times 5 is 45.
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    And once again, the signs are
    different so it's a negative.
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    And then finally what if it I
    had -- let me think of some
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    good numbers -- minus
    6 times minus 11.
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    Well, 6 times 11 is 66 and
    then it's a negative and
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    negative, it's a positive.
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    Let me give you a
    trick problem.
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    What is 0 times negative 12?
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    Well, you might say that the
    signs are different, but
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    0 is actually neither
    positive nor negative.
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    And 0 times anything
    is still 0.
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    It doesn't matter if the thing
    you multiply it by is a
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    negative number or
    a positive number.
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    0 times anything is still 0.
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    So let's see if we can apply
    these same rules to division.
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    It actually turns out that
    the same rules apply.
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    If I have 9 divided
    by negative 3.
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    Well, first we say
    what's 9 divided by 3?
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    Well that's 3.
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    And they have different signs,
    positive 9, negative 3.
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    So different signs
    means a negative.
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    9 divided by negative 3
    is equal to negative 3.
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    What is minus 16 divided by 8?
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    Well, once again, 16
    divided by 8 is 2, but
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    the signs are different.
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    Negative 16 divided by positive
    8, that equals negative 2.
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    Remember, different signs will
    get you a negative result.
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    What is minus 54
    divided by minus 6?
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    Well, 54 divided by 6 is 9.
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    And since both terms, the
    divisor and the dividend, are
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    both negative -- negative 54
    and negative 6 -- it turns out
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    that the answer is positive.
    Remember, same signs
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    result in a positive sign.
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    Let's do one more.
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    Obviously, 0 divided by
    anything is still 0.
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    That's pretty straightforward.
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    And of course, you can't
    divide anything by 0
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    -- that's undefined.
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    Let's do one more.
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    What is -- I'm just going to
    think of random numbers --
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    4 divided by negative 1?
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    Well, 4 divided by 1 is 4,
    but the signs are different.
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    So it's negative 4.
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    I hope that helps.
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    Now what I want you to do is
    actually try
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    as many of these multiplying and dividing
    negative numbers as you can.
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    And you click on hints
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    and it'll remind you of which rule to use.
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    In your own time you might want
    to actually think about
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    why these rules apply and what it
    means
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    to multiply a negative number times a positive number.
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    And even more interesting, what
    it means
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    to multiply a negative number times a negative number.
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    But I think at this point,
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    hopefully, you are ready to start doing some problems.
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    Good luck.
Title:
Multiplying and dividing negative numbers
Description:

Multiplying and dividing negative numbers

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Video Language:
English
Duration:
08:28

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