WEBVTT
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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.