[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.60,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.60,0:00:05.57,Default,,0000,0000,0000,,So we're asked to add 3/15 plus\N7/15, and then simplify
Dialogue: 0,0:00:05.57,0:00:06.59,Default,,0000,0000,0000,,the answer.
Dialogue: 0,0:00:06.59,0:00:09.81,Default,,0000,0000,0000,,So just the process when you\Nadd fractions is if they
Dialogue: 0,0:00:09.81,0:00:12.00,Default,,0000,0000,0000,,already-- well, first of all, if\Nthey're not mixed numbers,
Dialogue: 0,0:00:12.00,0:00:14.65,Default,,0000,0000,0000,,and neither of these are, and\Nif they have the same
Dialogue: 0,0:00:14.65,0:00:15.28,Default,,0000,0000,0000,,denominator.
Dialogue: 0,0:00:15.28,0:00:17.19,Default,,0000,0000,0000,,In this example, the\Ndenominators
Dialogue: 0,0:00:17.19,0:00:18.37,Default,,0000,0000,0000,,are already the same.
Dialogue: 0,0:00:18.37,0:00:20.46,Default,,0000,0000,0000,,The denominator is 15.
Dialogue: 0,0:00:20.46,0:00:24.59,Default,,0000,0000,0000,,So if you add these two\Nfractions, your sum is going
Dialogue: 0,0:00:24.59,0:00:28.86,Default,,0000,0000,0000,,to have the same denominator,\N15, and your numerator is just
Dialogue: 0,0:00:28.86,0:00:30.91,Default,,0000,0000,0000,,going to be the sum of the\Nnumerator, so it's going to be
Dialogue: 0,0:00:30.91,0:00:37.49,Default,,0000,0000,0000,,3 plus 7, or it's going\Nto be equal to 10/15.
Dialogue: 0,0:00:37.49,0:00:39.34,Default,,0000,0000,0000,,Now, if we wanted to simplify\Nthis, we'd look for the
Dialogue: 0,0:00:39.34,0:00:43.08,Default,,0000,0000,0000,,greatest common factor in both\Nthe 10 and the 15, and as far
Dialogue: 0,0:00:43.08,0:00:45.68,Default,,0000,0000,0000,,as I can tell, 5 is the largest\Nnumber that goes into
Dialogue: 0,0:00:45.68,0:00:46.48,Default,,0000,0000,0000,,both of them.
Dialogue: 0,0:00:46.48,0:00:53.64,Default,,0000,0000,0000,,So divide the 10 by 5 and you\Ndivide the 15 by 5, and you
Dialogue: 0,0:00:53.64,0:00:59.02,Default,,0000,0000,0000,,get-- 10 divided by 5 is 2\Nand 15 divided by 5 is 3.
Dialogue: 0,0:00:59.02,0:01:00.90,Default,,0000,0000,0000,,You get 2/3.
Dialogue: 0,0:01:00.90,0:01:04.10,Default,,0000,0000,0000,,Now, to understand why this\Nworks, let's draw it out.
Dialogue: 0,0:01:04.10,0:01:08.86,Default,,0000,0000,0000,,Let's split something\Nup into 15 sections.
Dialogue: 0,0:01:08.86,0:01:11.47,Default,,0000,0000,0000,,So let me split it up\Ninto 15 sections.
Dialogue: 0,0:01:11.47,0:01:13.67,Default,,0000,0000,0000,,Let me see how well\NI can do this.
Dialogue: 0,0:01:13.67,0:01:16.30,Default,,0000,0000,0000,,Well, actually, even a better\Nway, an easier way might be to
Dialogue: 0,0:01:16.30,0:01:17.74,Default,,0000,0000,0000,,draw circles.
Dialogue: 0,0:01:17.74,0:01:20.07,Default,,0000,0000,0000,,So let me do the 15 sections.
Dialogue: 0,0:01:20.07,0:01:22.26,Default,,0000,0000,0000,,So let me draw.
Dialogue: 0,0:01:22.26,0:01:25.80,Default,,0000,0000,0000,,So that is one section\Nright over there.
Dialogue: 0,0:01:25.80,0:01:33.34,Default,,0000,0000,0000,,That is one section and then if\NI copy and paste it, that
Dialogue: 0,0:01:33.34,0:01:39.71,Default,,0000,0000,0000,,is a second section, and then\Na third section, fourth
Dialogue: 0,0:01:39.71,0:01:44.76,Default,,0000,0000,0000,,section, and then we have\Na fifth section.
Dialogue: 0,0:01:44.76,0:01:46.96,Default,,0000,0000,0000,,Let me copy and paste\Nthis whole thing.
Dialogue: 0,0:01:46.96,0:01:49.92,Default,,0000,0000,0000,,So that's five sections\Nright there.
Dialogue: 0,0:01:49.92,0:01:53.30,Default,,0000,0000,0000,,Let me copy and then\Npaste that.
Dialogue: 0,0:01:53.30,0:01:56.20,Default,,0000,0000,0000,,So that is 10 sections,\Nand then let me
Dialogue: 0,0:01:56.20,0:01:57.08,Default,,0000,0000,0000,,do it one more time.
Dialogue: 0,0:01:57.08,0:01:58.57,Default,,0000,0000,0000,,So that is 15 sections.
Dialogue: 0,0:01:58.57,0:02:01.01,Default,,0000,0000,0000,,So you can imagine this whole\Nthing is like a candy bar or
Dialogue: 0,0:02:01.01,0:02:04.95,Default,,0000,0000,0000,,something, and we have now split\Nit up into 15 sections.
Dialogue: 0,0:02:04.95,0:02:07.87,Default,,0000,0000,0000,,Now, what is 3/15?
Dialogue: 0,0:02:07.87,0:02:10.42,Default,,0000,0000,0000,,Well, it's going to be\N3 of the 15 sections.
Dialogue: 0,0:02:10.42,0:02:17.57,Default,,0000,0000,0000,,So 3/15 is going to be one,\Ntwo, three: 3/15.
Dialogue: 0,0:02:17.57,0:02:20.88,Default,,0000,0000,0000,,Now, to that, were adding\N7 of the 1/15
Dialogue: 0,0:02:20.88,0:02:23.49,Default,,0000,0000,0000,,sections, or 7 of the sections.
Dialogue: 0,0:02:23.49,0:02:26.26,Default,,0000,0000,0000,,So we're adding 7\Nof those to it.
Dialogue: 0,0:02:26.26,0:02:35.24,Default,,0000,0000,0000,,So that's one, two, three,\Nfour, five, six, seven.
Dialogue: 0,0:02:35.24,0:02:37.94,Default,,0000,0000,0000,,And you see now, if you take the\Norange and the blue, you
Dialogue: 0,0:02:37.94,0:02:41.31,Default,,0000,0000,0000,,get one, two, three, four, five,\Nsix, seven, eight, nine,
Dialogue: 0,0:02:41.31,0:02:45.80,Default,,0000,0000,0000,,ten of the sections, or\N10 of the 15 sections.
Dialogue: 0,0:02:45.80,0:02:49.23,Default,,0000,0000,0000,,And then to see why this is the\Nsame thing as 2/3, you can
Dialogue: 0,0:02:49.23,0:02:53.22,Default,,0000,0000,0000,,just split this candy bar into\Nthirds, so each third would
Dialogue: 0,0:02:53.22,0:02:54.76,Default,,0000,0000,0000,,have five sections in it.
Dialogue: 0,0:02:54.76,0:02:55.46,Default,,0000,0000,0000,,So let's do that.
Dialogue: 0,0:02:55.46,0:02:59.30,Default,,0000,0000,0000,,One, two, three, four, five,\Nso that is 1/3 right there.
Dialogue: 0,0:02:59.30,0:03:01.59,Default,,0000,0000,0000,,One, two, three, four,\Nfive, that is
Dialogue: 0,0:03:01.59,0:03:03.36,Default,,0000,0000,0000,,another third right there.
Dialogue: 0,0:03:03.36,0:03:06.81,Default,,0000,0000,0000,,And notice, when you do it like\Nthis, we have filled out
Dialogue: 0,0:03:06.81,0:03:11.19,Default,,0000,0000,0000,,exactly two-- one, two--\Nof the thirds.
Dialogue: 0,0:03:11.19,0:03:13.78,Default,,0000,0000,0000,,This is the third third, but\Nthat's not filled in.
Dialogue: 0,0:03:13.78,0:03:16.21,Default,,0000,0000,0000,,So 10/15 is the same\Nthing as 2/3.
Dialogue: 0,0:03:16.21,0:03:17.46,Default,,0000,0000,0000,,