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Adding Mixed Numbers Word Problem

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    Regina rode her bike 2 and 1/4
    miles from her house to school
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    and then 1 and 5/8 miles
    to her friend's house.
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    How many miles did Regina
    ride in total?
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    So she first rode 2 and 1/4
    miles, and then she
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    rode 1 and 5/8 miles.
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    then she rode 1 and 5/8 miles
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    So the sum is the total number
    of miles she rode.
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    So to take this sum, we've seen
    that we can add the whole
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    number parts, because this is
    really the same thing as 2
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    plus 1/4 plus 1 plus 5/8, so we
    can just switch the order,
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    if you want to view
    it that way.
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    So we can add the 2 plus the 1
    first, and then we get-- let
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    me do that here.
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    So 2 plus the 1, you get 3, and
    then we need to add the
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    1/4 plus 5/8.
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    And to add these two fractions,
    we have to find the
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    least common multiple
    of 4 and 8.
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    That'll be our new
    denominator.
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    8 is divisible by both 8 and 4,
    so that is the least common
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    multiple of 4 and 8, so our
    common denominator will be 8.
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    Obviously, 5/8 will
    still be 5/8.
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    Now to go from a denominator
    of 4 to 8, you have to
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    multiply the denominator by 2,
    so we also need to multiply
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    the numerator by 2,
    so 1 times 2 is 2.
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    And, of course, we still
    have this 3 out there.
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    So 2 and 1/4 plus 1 and 5/8 is
    the same thing as this right
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    here, and this is equal to-- we
    have our 3 plus, and then
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    over 8 we add the 2 plus 5.
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    We have 7/8.
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    So this is going to be equal
    to 3 and 7/8 miles.
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    She rode a total of
    3 and 7/8 miles.
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    Now, I want to make one
    thing very clear.
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    So far when we've been adding
    these mixed numbers, the
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    fraction part always ended
    up as a proper fraction.
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    The numerator was smaller
    than the denominator.
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    But I want to do a quick example
    to show you what you
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    do when the numerator is not
    smaller than the denominator.
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    So let's say we had 1 and
    5/8 plus 2 and 4/8.
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    So if you add just the
    whole number parts, 1
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    plus 2, you get 3.
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    Plus 5/8 plus 4/8, 5/8
    plus 4/8 is 9/8, so
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    you get 3 plus 9/8.
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    Now it would be really strange
    to just say, OK, that's the
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    same thing as 3 and 9/8, because
    you have a mixed
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    number with a whole number
    and an improper fraction.
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    If you're going through the
    trouble of making it a mixed
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    number, the fraction better
    be a proper fraction.
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    So what you need to do is
    rewrite 9/8, and you know that
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    9/8 is the same thing
    as 1 and 1/8, right?
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    8 goes into 9 one time with 1
    left over, so it's 1 and 1/8.
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    So this is the same thing
    as 3 plus 1 and 1/8.
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    So now we can add the
    whole number parts.
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    3 plus 1 is equal to 4, and then
    you have your 1/8 over
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    there: 4 and 1/8.
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    I just wanted to give you that
    special circumstance when your
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    fraction part ends
    up improper.
Title:
Adding Mixed Numbers Word Problem
Description:

U02_L3_T1_we5 Adding Mixed Numbers Word Problem

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Video Language:
English
Duration:
03:22

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