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Dividing fractions

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    Welcome to the presentation
    on dividing fractions.
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    Let's get started.
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    So before I give you the
    intuition-- actually, I might
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    do that in a different module--
    I'm just going to show you the
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    mechanics of how you
    divide a fraction.
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    And it turns out that
    it's actually not much
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    more difficult than
    multiplying fractions.
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    If I were to ask you, 1/2
    divided by 1/2, whenever you
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    divide by a fraction, or
    actually, when you divide by
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    any number, it's the same thing
    as multiplying by its inverse.
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    So 1/2 divided by 1/2 is
    equal to 1/2 times 2/1.
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    We just inverted--
    inverse-- the second 1/2.
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    And we know from the
    multiplication module, 1/2
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    times 2/1, well, that's
    just equal to 2/2,
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    or it's equal to 1.
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    And that makes sense because,
    actually, any number divided
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    by itself is equal to 1.
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    1/2 divided by 1/2 is 1, just
    like 5 divided by 5 is 1, just
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    like 100 divided by 100 is 1.
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    And this isn't a new principal.
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    Actually, you were
    always doing it.
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    But isn't this also the
    same thing as 2 times the
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    inverse of 2, which is 1?
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    I'll show it to you.
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    Actually, let me give you a
    couple more examples to show
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    that dividing fractions really
    isn't a new concept, this whole
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    notion of multiplying
    by the inverse.
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    If I were to tell you
    what is 12 divided by 4?
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    Well, we know the answer to
    this, but I'm going to show
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    you that this is the same
    thing as 12 times 1/4.
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    12/1 times 1/4 4 is
    12/4, which is 3.
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    And 12/4 is really just another
    way of writing 12 divided by 4,
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    so it's kind of a long way of
    getting to the same point.
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    But I just wanted to show you
    that what we're doing in this
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    module is nothing new than
    what we've always been doing
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    when we divide by a number.
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    Division is the same thing.
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    Dividing by a number is the
    same thing as multiplying by
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    the inverse of that number.
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    And just as a review, an
    inverse, if I have a number
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    A, the inverse-- inv, short
    for inverse-- is 1 over A.
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    So the inverse of 2/3 is 3/2,
    or the inverse of 5, because 5
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    is the same thing as 5/1,
    so the inverse is 1/5.
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    So let's do some fraction
    division problems.
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    What is 2/3 divided by 5/6?
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    Well, we know that this is the
    same thing as 2/3 times 6/5,
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    and that's equal to 12/15.
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    We can divide the numerator and
    denominator by 3, that's 4/5.
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    What is 7/8 divided by 1/4?
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    Well, that's the same
    thing as 7/8 times 4/1.
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    Remember, I just
    flipped this 1/4.
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    Divide by 1/4 is the same
    thing as multiplying by 4/1.
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    That's all you've got to do.
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    And then we could use a little
    shortcut we learned in the
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    multiplication module.
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    8 divided by 4 is 2.
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    4 divided by 4 is 1.
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    So that equals 7/2.
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    Or if you wanted to write that
    as a mixed number, this is, of
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    course, an improper fraction.
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    Improper fractions have
    a numerator larger
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    than the denominator.
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    If you wanted to write that as
    a mixed number, 2 goes into 7
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    three times with a remainder
    of 1, so that's 3 and a half.
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    You can write it either way.
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    I tend to keep it this
    way because it's
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    easier to deal with.
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    Let's do a ton of more
    problems, or at least as many
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    more as we can do in the
    next four or five minutes.
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    What's negative 2/3
    divided by 5/2?
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    Once again, that's the same
    thing as minus 2/3-- whoops--
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    as minus 2/3 times what?
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    It's times the inverse of
    5/2, which is 2/5, and
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    that equals minus 4/15.
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    What is 3/2 divided by 1/6?
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    Well, that's just the same
    thing as 3/2 times 6/1,
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    I think you might
    be getting it now.
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    Let's see, let's
    do a couple more.
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    And, of course, you can always
    pause, and look at this whole
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    presentation again, so you can
    get confused all over again.
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    Let's see, let's do minus
    5/7 divided by 10/3.
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    Well, this is the same thing
    as minus 5/7 times 3/10.
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    I just multiplied
    by the inverse.
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    That's all I keep doing
    over and over again.
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    Minus 5 times 3.
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    Minus 15.
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    7 times 10 is 70.
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    If we divide the numerator
    and the denominator by
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    5, we get minus 3/14.
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    We could have also
    just done it here.
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    We could have done 5, 2,
    and we would have gotten
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    minus 3/14 as well.
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    Let's do one or two
    more problems.
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    I think you kind of
    get it, though.
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    Let's say 1/2
    divided by minus 3.
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    Ah-ha!
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    So what happens when you take a
    fraction and you divide it by
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    a whole number or an integer?
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    Well, we know any whole number
    can be written as a fraction.
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    This is the same thing as
    1/2 divided by minus 3/1.
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    And dividing by a fraction is
    the same thing as multiplying
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    by it's inverse.
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    So the inverse of negative 3/1
    is negative 1/3, and this
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    equals negative 1/6.
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    Let's do it the other way.
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    What if I had negative
    3 divided by 1/2?
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    Same thing.
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    Negative 3 is the same thing as
    minus 3/1 divided by 1/2, which
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    is the same thing as minus 3/1
    times 2/1, which is equal to
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    minus 6/1, which
    equals minus 6.
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    Now, let me give you a
    little bit of intuition
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    of why this works.
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    Let's say I said 2
    divided by 1/3.
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    Well, we know that this
    is equal to 2/1 times
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    3/1, which equals 6.
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    So how does 2, 1/3,
    and 6 relate?
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    Well, let's look
    at it this way.
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    If I had two pieces of pizza.
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    I have two pieces of pizza.
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    Here's my two pieces
    of pizza right.
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    Two right here.
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    So I have two pieces of pizza,
    and I'm going to divide
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    them into thirds.
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    So I'm going to divide
    each pizza into a third.
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    I'll draw the little
    Mercedes sign.
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    So I'm dividing each pizza
    into a third, right?
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    How many pieces do I have?
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    Let's see, 1, 2, 3, 4, 5, 6.
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    I have 6 pieces.
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    So you might want to sit and
    ponder that for a little bit,
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    but I think it might make a
    little bit of sense to you.
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    Let's do one more just
    to tire your brain.
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    If I had negative 7/2 divided
    by 4/9-- let's pick a negative
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    4/9-- well, that's the same
    thing as minus 7/2 times
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    minus 9/4, right?
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    I just multiplied by the
    inverse of negative 4/9.
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    9 times 7 is equal to--
    negative 7 times negative
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    9 is positive 63,
    and 2 times 4 is 8.
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    Hopefully, I think you have a
    good idea of how to divide by
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    a fraction now, and you can
    try out the dividing
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    fractions modules.
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    Have fun!
Title:
Dividing fractions
Description:

Dividing fractions

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Video Language:
English
Duration:
08:58

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