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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 get--
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    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 to 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,
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    that 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,
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    you 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 third, 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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    This is the third third, but that's not filled in.
    So 10/15 is the same thing as 2/3.
Title:
Adding and subtracting fractions
Description:

How to add and subtract fractions.

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Video Language:
English
Duration:
03:18

English subtitles

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