[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.60,0:00:05.57,Default,,0000,0000,0000,,So we're asked to add 3/15 plus 7/15, 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 add fractions is if they
Dialogue: 0,0:00:09.81,0:00:12.00,Default,,0000,0000,0000,,already-- well, first of all, if they're not mixed numbers,
Dialogue: 0,0:00:12.00,0:00:14.65,Default,,0000,0000,0000,,and neither of these are, and if 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 denominators
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 fractions, your sum is going
Dialogue: 0,0:00:24.59,0:00:28.86,Default,,0000,0000,0000,,to have the same denominator, 15, 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 numerator, 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 to 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 this, we'd look for the
Dialogue: 0,0:00:39.34,0:00:43.08,Default,,0000,0000,0000,,greatest common factor in both the 10 and the 15, and as far\N
Dialogue: 0,0:00:43.08,0:00:45.68,Default,,0000,0000,0000,,as I can tell, 5 is the largest number 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 divide the 15 by 5, \Nand you get--
Dialogue: 0,0:00:53.64,0:00:59.02,Default,,0000,0000,0000,,10 divided by 5 is 2 and 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 works, let's draw it out.
Dialogue: 0,0:01:04.10,0:01:08.86,Default,,0000,0000,0000,,Let's split something up to 15 sections.
Dialogue: 0,0:01:08.86,0:01:11.46,Default,,0000,0000,0000,,So let me split it up into 15 sections.
Dialogue: 0,0:01:11.48,0:01:13.67,Default,,0000,0000,0000,,Let me see how well I can do this.
Dialogue: 0,0:01:13.67,0:01:16.30,Default,,0000,0000,0000,,Well, actually, even a better way, 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: 0,0:01:20.07,0:01:21.78,Default,,0000,0000,0000,,So let me draw.
Dialogue: 0,0:01:22.26,0:01:25.69,Default,,0000,0000,0000,,So that is one section right over there
Dialogue: 0,0:01:25.80,0:01:30.14,Default,,0000,0000,0000,,That is one section and then if I copy and paste it,
Dialogue: 0,0:01:33.17,0:01:39.71,Default,,0000,0000,0000,,that is a second section, and then a third section, fourth
Dialogue: 0,0:01:39.71,0:01:44.76,Default,,0000,0000,0000,,section, and then we have a fifth section.
Dialogue: 0,0:01:44.76,0:01:46.96,Default,,0000,0000,0000,,Let me copy and paste this whole thing.
Dialogue: 0,0:01:46.96,0:01:49.92,Default,,0000,0000,0000,,So that's five sections right there.
Dialogue: 0,0:01:49.92,0:01:53.30,Default,,0000,0000,0000,,Let me copy and then paste that.
Dialogue: 0,0:01:53.30,0:01:56.20,Default,,0000,0000,0000,,So that is 10 sections, and 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 thing 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 it 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 3 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, two, three: 3/15.
Dialogue: 0,0:02:17.57,0:02:20.88,Default,,0000,0000,0000,,Now, to that, were adding 7 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 of those to it.
Dialogue: 0,0:02:26.26,0:02:35.24,Default,,0000,0000,0000,,So that's one, two, three, four, 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 orange and the blue,
Dialogue: 0,0:02:37.94,0:02:41.31,Default,,0000,0000,0000,,you get one, two, three, four, five, six, seven, eight, nine,
Dialogue: 0,0:02:41.31,0:02:45.80,Default,,0000,0000,0000,,ten of the sections, or 10 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 same thing as 2/3, you can\N
Dialogue: 0,0:02:49.23,0:02:53.22,Default,,0000,0000,0000,,just split this candy bar into third, 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, so that is 1/3 right there.
Dialogue: 0,0:02:59.30,0:03:01.59,Default,,0000,0000,0000,,One, two, three, four, five, 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 this, we have filled out
Dialogue: 0,0:03:06.81,0:03:11.19,Default,,0000,0000,0000,,exactly two-- one, two-- of the thirds.
Dialogue: 0,0:03:11.19,0:03:13.78,Default,,0000,0000,0000,,This is the third third, but that's not filled in.\N
Dialogue: 0,0:03:13.78,0:03:16.21,Default,,0000,0000,0000,,This is the third third, but that's not filled in.\NSo 10/15 is the same thing as 2/3.\N