[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.73,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.73,0:00:01.25,Default,,0000,0000,0000,,Add.
Dialogue: 0,0:00:01.25,0:00:03.57,Default,,0000,0000,0000,,Simplify the answer and write\Nas a mixed number.
Dialogue: 0,0:00:03.57,0:00:06.74,Default,,0000,0000,0000,,And we have three mixed numbers\Nhere: 3 and 1/2 plus
Dialogue: 0,0:00:06.74,0:00:10.13,Default,,0000,0000,0000,,11 and 2/5 plus 4 and 3/15.
Dialogue: 0,0:00:10.13,0:00:13.87,Default,,0000,0000,0000,,So we've already seen that we\Ncould view this as 3 plus 1/12
Dialogue: 0,0:00:13.87,0:00:16.22,Default,,0000,0000,0000,,plus 11 plus 2/5-- let\Nme write that down.
Dialogue: 0,0:00:16.22,0:00:23.18,Default,,0000,0000,0000,,This is the same thing as 3\Nplus 1/12 plus 11 plus 2/5
Dialogue: 0,0:00:23.18,0:00:27.33,Default,,0000,0000,0000,,plus 4 plus 3/15.
Dialogue: 0,0:00:27.33,0:00:30.17,Default,,0000,0000,0000,,The mixed number 3 and 1/12\Njust literally means 3 and
Dialogue: 0,0:00:30.17,0:00:32.84,Default,,0000,0000,0000,,1/12 or 3 plus 1/12.
Dialogue: 0,0:00:32.84,0:00:35.93,Default,,0000,0000,0000,,And since we're just adding\Na bunch of numbers, order
Dialogue: 0,0:00:35.93,0:00:37.69,Default,,0000,0000,0000,,doesn't matter, so we\Ncould add all the
Dialogue: 0,0:00:37.69,0:00:39.50,Default,,0000,0000,0000,,whole numbers at once.
Dialogue: 0,0:00:39.50,0:00:46.50,Default,,0000,0000,0000,,So we have 3 plus 11 plus 4,\Nand then we can add the
Dialogue: 0,0:00:46.50,0:00:57.08,Default,,0000,0000,0000,,fractions: the 1/12 plus\N2/5 plus 3/15.
Dialogue: 0,0:00:57.08,0:00:58.65,Default,,0000,0000,0000,,Now, the blue part's pretty\Nstraightforward.
Dialogue: 0,0:00:58.65,0:00:59.54,Default,,0000,0000,0000,,We're just adding numbers.
Dialogue: 0,0:00:59.54,0:01:05.36,Default,,0000,0000,0000,,3 plus 11 is 14 plus 4 is\N18, so that part right
Dialogue: 0,0:01:05.36,0:01:06.74,Default,,0000,0000,0000,,there is just 18.
Dialogue: 0,0:01:06.74,0:01:09.08,Default,,0000,0000,0000,,This will be a little bit\Ntrickier, because we know that
Dialogue: 0,0:01:09.08,0:01:12.12,Default,,0000,0000,0000,,when we add fractions, we have\Nto have the same denominator.
Dialogue: 0,0:01:12.12,0:01:14.59,Default,,0000,0000,0000,,And now we have to make all\Nthree of these characters have
Dialogue: 0,0:01:14.59,0:01:17.03,Default,,0000,0000,0000,,the same denominator and that\Ndenominator has to be the
Dialogue: 0,0:01:17.03,0:01:21.91,Default,,0000,0000,0000,,least common multiple\Nof 12 and 5 and 15.
Dialogue: 0,0:01:21.91,0:01:24.21,Default,,0000,0000,0000,,Now, we could just do it kind\Nof the brute force way.
Dialogue: 0,0:01:24.21,0:01:25.53,Default,,0000,0000,0000,,We could just look\Nat the multiples.
Dialogue: 0,0:01:25.53,0:01:28.31,Default,,0000,0000,0000,,We could pick one of these guys\Nand keep taking their
Dialogue: 0,0:01:28.31,0:01:31.02,Default,,0000,0000,0000,,multiples, and then figuring\Nout whether those multiples
Dialogue: 0,0:01:31.02,0:01:34.08,Default,,0000,0000,0000,,are both divisible\Nby 5 and 15.
Dialogue: 0,0:01:34.08,0:01:36.33,Default,,0000,0000,0000,,Or the other way we can do\Nit is take the prime
Dialogue: 0,0:01:36.33,0:01:39.59,Default,,0000,0000,0000,,factorization of each of these\Nnumbers, and just say that the
Dialogue: 0,0:01:39.59,0:01:42.67,Default,,0000,0000,0000,,least common multiple has\Nto contain the prime
Dialogue: 0,0:01:42.67,0:01:45.96,Default,,0000,0000,0000,,factorization each of these\Nguys, which means it contains
Dialogue: 0,0:01:45.96,0:01:47.20,Default,,0000,0000,0000,,each of those numbers.
Dialogue: 0,0:01:47.20,0:01:48.91,Default,,0000,0000,0000,,So let me show you what\NI'm talking about.
Dialogue: 0,0:01:48.91,0:01:54.64,Default,,0000,0000,0000,,If we take the prime\Nfactorization of 12, 12 is 2
Dialogue: 0,0:01:54.64,0:02:03.02,Default,,0000,0000,0000,,times 6, 6 is 2 times 3, so 12\Nis equal to 2 times 2 times 3.
Dialogue: 0,0:02:03.02,0:02:05.31,Default,,0000,0000,0000,,That's the prime factorization\Nof 12.
Dialogue: 0,0:02:05.31,0:02:08.94,Default,,0000,0000,0000,,Now, if we do 5, prime\Nfactorization of 5, well, 5 is
Dialogue: 0,0:02:08.94,0:02:12.90,Default,,0000,0000,0000,,just 1 and 5, so 5 is\Na prime number.
Dialogue: 0,0:02:12.90,0:02:14.67,Default,,0000,0000,0000,,It is the prime factorization\Nof 5.
Dialogue: 0,0:02:14.67,0:02:16.21,Default,,0000,0000,0000,,There's just a 5 there.
Dialogue: 0,0:02:16.21,0:02:17.66,Default,,0000,0000,0000,,This 1 is kind of useless.
Dialogue: 0,0:02:17.66,0:02:19.88,Default,,0000,0000,0000,,So 5 is just 5.
Dialogue: 0,0:02:19.88,0:02:23.34,Default,,0000,0000,0000,,And then 15, let's do 15.
Dialogue: 0,0:02:23.34,0:02:25.62,Default,,0000,0000,0000,,Actually, when I did the prime\Nfactorization of 5, I should
Dialogue: 0,0:02:25.62,0:02:27.62,Default,,0000,0000,0000,,have said, look, 5 is prime.
Dialogue: 0,0:02:27.62,0:02:30.88,Default,,0000,0000,0000,,There's no number larger than\N1 that divides into it, so
Dialogue: 0,0:02:30.88,0:02:33.07,Default,,0000,0000,0000,,it's actually silly to even\Nmake a tree there.
Dialogue: 0,0:02:33.07,0:02:38.23,Default,,0000,0000,0000,,And now let's do 15, 15's\Nprime factorization.
Dialogue: 0,0:02:38.23,0:02:43.45,Default,,0000,0000,0000,,15 is 3 times 5, and now both\Nof these are prime.
Dialogue: 0,0:02:43.45,0:02:48.21,Default,,0000,0000,0000,,So we need something that has\Ntwo 2's and a 3, so let's look
Dialogue: 0,0:02:48.21,0:02:49.31,Default,,0000,0000,0000,,at the 12 right there.
Dialogue: 0,0:02:49.31,0:02:55.16,Default,,0000,0000,0000,,So our denominator has to have\Nat least two 2's and a 3, so
Dialogue: 0,0:02:55.16,0:02:56.08,Default,,0000,0000,0000,,let's write that down.
Dialogue: 0,0:02:56.08,0:02:59.53,Default,,0000,0000,0000,,So it has to be 2\Ntimes 2 times 3.
Dialogue: 0,0:02:59.53,0:03:01.39,Default,,0000,0000,0000,,It has to have at least that.
Dialogue: 0,0:03:01.39,0:03:04.12,Default,,0000,0000,0000,,Now, it also has to have\Na 5 there, right?
Dialogue: 0,0:03:04.12,0:03:06.38,Default,,0000,0000,0000,,Because it has to be a\Ncommon multiple of 5.
Dialogue: 0,0:03:06.38,0:03:09.05,Default,,0000,0000,0000,,5's another one of those prime\Nfactors, so it's got to have a
Dialogue: 0,0:03:09.05,0:03:09.90,Default,,0000,0000,0000,,5 in there.
Dialogue: 0,0:03:09.90,0:03:11.67,Default,,0000,0000,0000,,It didn't already have a 5.
Dialogue: 0,0:03:11.67,0:03:14.39,Default,,0000,0000,0000,,And then it also has to\Nhave a 3 and a 5.
Dialogue: 0,0:03:14.39,0:03:16.55,Default,,0000,0000,0000,,Well, we already have a 5.
Dialogue: 0,0:03:16.55,0:03:20.44,Default,,0000,0000,0000,,We already have a 3 from the\N12, and we already have a 5
Dialogue: 0,0:03:20.44,0:03:24.09,Default,,0000,0000,0000,,from the 5, so this number will\Nbe divisible by all of
Dialogue: 0,0:03:24.09,0:03:26.35,Default,,0000,0000,0000,,them, and you can see that\Nbecause you can see it has a
Dialogue: 0,0:03:26.35,0:03:30.57,Default,,0000,0000,0000,,12 in it, it has a 5 in it,\Nand it has a 15 in it.
Dialogue: 0,0:03:30.57,0:03:31.79,Default,,0000,0000,0000,,So what is this number?
Dialogue: 0,0:03:31.79,0:03:33.81,Default,,0000,0000,0000,,2 times 2 is 4.
Dialogue: 0,0:03:33.81,0:03:36.46,Default,,0000,0000,0000,,4 times 3 is 12.
Dialogue: 0,0:03:36.46,0:03:38.64,Default,,0000,0000,0000,,12 times 5 is 60.
Dialogue: 0,0:03:38.64,0:03:43.09,Default,,0000,0000,0000,,So the least common multiple\Nof 12, 5 and 15 is 60.
Dialogue: 0,0:03:43.09,0:03:45.00,Default,,0000,0000,0000,,So this is going to be plus.
Dialogue: 0,0:03:45.00,0:03:47.49,Default,,0000,0000,0000,,We're going to be over 60.
Dialogue: 0,0:03:47.49,0:03:51.04,Default,,0000,0000,0000,,So all of these are going\Nto be over 60.
Dialogue: 0,0:03:51.04,0:03:54.16,Default,,0000,0000,0000,,All of these three fractions\Nare over 60.
Dialogue: 0,0:03:54.16,0:03:56.85,Default,,0000,0000,0000,,Now, to go from 12 to 60,\Nwe have to multiply the
Dialogue: 0,0:03:56.85,0:04:00.11,Default,,0000,0000,0000,,denominator by 5, so we also\Nhave to multiply the numerator
Dialogue: 0,0:04:00.11,0:04:02.93,Default,,0000,0000,0000,,by 5, so 1 times 5 is 5.
Dialogue: 0,0:04:02.93,0:04:05.90,Default,,0000,0000,0000,,5/60 is the same\Nthing as 1/12.
Dialogue: 0,0:04:05.90,0:04:08.20,Default,,0000,0000,0000,,To go from 5 to 60 in the\Ndenominator, we have to
Dialogue: 0,0:04:08.20,0:04:10.49,Default,,0000,0000,0000,,multiply by 12, so we\Nhave to do the same
Dialogue: 0,0:04:10.49,0:04:11.58,Default,,0000,0000,0000,,thing for the numerator.
Dialogue: 0,0:04:11.58,0:04:15.15,Default,,0000,0000,0000,,12 times 2 is 24.
Dialogue: 0,0:04:15.15,0:04:18.74,Default,,0000,0000,0000,,The last one, 15 to 60, you have\Nto multiply by 4, so you
Dialogue: 0,0:04:18.74,0:04:20.34,Default,,0000,0000,0000,,have to do the same thing\Nin the numerator.
Dialogue: 0,0:04:20.34,0:04:27.12,Default,,0000,0000,0000,,4 times 3 is 12.
Dialogue: 0,0:04:27.12,0:04:29.02,Default,,0000,0000,0000,,And now we have the\Nsame denominator.
Dialogue: 0,0:04:29.02,0:04:33.46,Default,,0000,0000,0000,,We are ready to add.
Dialogue: 0,0:04:33.46,0:04:34.38,Default,,0000,0000,0000,,So let's do that.
Dialogue: 0,0:04:34.38,0:04:40.97,Default,,0000,0000,0000,,So this is going to be 18 plus,\Nand then over 60, we
Dialogue: 0,0:04:40.97,0:04:45.45,Default,,0000,0000,0000,,have 5 plus 24, which is 29.
Dialogue: 0,0:04:45.45,0:04:52.32,Default,,0000,0000,0000,,29 plus 12, let's see, 29\Nplus 10 would be 39
Dialogue: 0,0:04:52.32,0:04:55.42,Default,,0000,0000,0000,,plus 2 would be 41.
Dialogue: 0,0:04:55.42,0:04:57.94,Default,,0000,0000,0000,,It would be 41.
Dialogue: 0,0:04:57.94,0:05:01.80,Default,,0000,0000,0000,,And as far as I can tell,\N41 and 60 do not
Dialogue: 0,0:05:01.80,0:05:04.03,Default,,0000,0000,0000,,have any common factors.
Dialogue: 0,0:05:04.03,0:05:06.23,Default,,0000,0000,0000,,41 actually looks prime to me.
Dialogue: 0,0:05:06.23,0:05:12.22,Default,,0000,0000,0000,,So the final answer\Nis 18 and 41/60.
Dialogue: 0,0:05:12.22,0:05:15.40,Default,,0000,0000,0000,,