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Adding and subtracting fractions

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    So we're asked to add 3/15 plus
    7/15, and then simplify
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    the answer.
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    So just the process when you
    add fractions is if they
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    already-- well, first of all, if
    they're not mixed numbers,
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    and neither of these are, and
    if they have the same
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    denominator.
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    In this example, the
    denominators
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    are already the same.
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    The denominator is 15.
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    So if you add these two
    fractions, your sum is going
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    to have the same denominator,
    15, and your numerator is just
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    going to be the sum of the
    numerator, so it's going to be
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    3 plus 7, or it's going
    to be equal to 10/15.
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    Now, if we wanted to simplify
    this, we'd look for the
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    greatest common factor in both
    the 10 and the 15, and as far
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    as I can tell, 5 is the largest
    number that goes into
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    both of them.
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    So divide the 10 by 5 and you
    divide the 15 by 5, and you
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    get-- 10 divided by 5 is 2
    and 15 divided by 5 is 3.
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    You get 2/3.
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    Now, to understand why this
    works, let's draw it out.
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    Let's split something
    up into 15 sections.
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    So let me split it up
    into 15 sections.
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    Let me see how well
    I can do this.
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    Well, actually, even a better
    way, an easier way might be to
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    draw circles.
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    So let me do the 15 sections.
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    So let me draw.
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    So that is one section
    right over there.
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    That is one section and then if
    I copy and paste it, that
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    is a second section, and then
    a third section, fourth
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    section, and then we have
    a fifth section.
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    Let me copy and paste
    this whole thing.
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    So that's five sections
    right there.
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    Let me copy and then
    paste that.
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    So that is 10 sections,
    and then let me
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    do it one more time.
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    So that is 15 sections.
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    So you can imagine this whole
    thing is like a candy bar or
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    something, and we have now split
    it up into 15 sections.
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    Now, what is 3/15?
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    Well, it's going to be
    3 of the 15 sections.
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    So 3/15 is going to be one,
    two, three: 3/15.
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    Now, to that, were adding
    7 of the 1/15
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    sections, or 7 of the sections.
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    So we're adding 7
    of those to it.
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    So that's one, two, three,
    four, five, six, seven.
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    And you see now, if you take the
    orange and the blue, you
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    get one, two, three, four, five,
    six, seven, eight, nine,
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    ten of the sections, or
    10 of the 15 sections.
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    And then to see why this is the
    same thing as 2/3, you can
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    just split this candy bar into
    thirds, so each third would
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    have five sections in it.
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    So let's do that.
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    One, two, three, four, five,
    so that is 1/3 right there.
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    One, two, three, four,
    five, that is
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    another third right there.
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    And notice, when you do it like
    this, we have filled out
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    exactly two-- one, two--
    of the thirds.
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    This is the third third, but
    that's not filled in.
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    So 10/15 is the same
    thing as 2/3.
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Title:
Adding and subtracting fractions
Description:

U02_L3_T1_we1 Adding Fractions with Like Denominators

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Video Language:
English
Duration:
03:18

English subtitles

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