[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.57,0:00:02.68,Default,,0000,0000,0000,,We're asked to rewrite\Nthe following two
Dialogue: 0,0:00:02.68,0:00:06.72,Default,,0000,0000,0000,,fractions as fractions with\Na least common denominator.
Dialogue: 0,0:00:10.96,0:00:13.26,Default,,0000,0000,0000,,So a least common\Ndenominator for two fractions
Dialogue: 0,0:00:13.26,0:00:17.25,Default,,0000,0000,0000,,is really just going to be the\Nleast common multiple of both
Dialogue: 0,0:00:17.25,0:00:19.63,Default,,0000,0000,0000,,of these denominators over here.
Dialogue: 0,0:00:19.63,0:00:21.48,Default,,0000,0000,0000,,And the value of\Ndoing that is then
Dialogue: 0,0:00:21.48,0:00:24.53,Default,,0000,0000,0000,,if you can make these\Na common denominator,
Dialogue: 0,0:00:24.53,0:00:26.40,Default,,0000,0000,0000,,then you can add\Nthe two fractions.
Dialogue: 0,0:00:26.40,0:00:28.05,Default,,0000,0000,0000,,And we'll see that\Nin other videos.
Dialogue: 0,0:00:28.05,0:00:30.54,Default,,0000,0000,0000,,But first of all, let's just\Nfind the least common multiple.
Dialogue: 0,0:00:33.33,0:00:35.92,Default,,0000,0000,0000,,Let me write it out\Nbecause sometimes LCD
Dialogue: 0,0:00:35.92,0:00:37.40,Default,,0000,0000,0000,,could meet other things.
Dialogue: 0,0:00:37.40,0:00:48.16,Default,,0000,0000,0000,,So least common denominator\Nof these two things
Dialogue: 0,0:00:48.16,0:00:51.36,Default,,0000,0000,0000,,is going to be the same thing\Nas the least common multiple
Dialogue: 0,0:00:51.36,0:00:53.58,Default,,0000,0000,0000,,of the two\Ndenominators over here.
Dialogue: 0,0:00:53.58,0:00:57.34,Default,,0000,0000,0000,,The least common\Nmultiple of 8 and 6.
Dialogue: 0,0:00:57.34,0:00:59.80,Default,,0000,0000,0000,,And a couple of ways to think\Nabout least common multiple--
Dialogue: 0,0:00:59.80,0:01:02.38,Default,,0000,0000,0000,,you literally could just\Ntake the multiples of 8 and 6
Dialogue: 0,0:01:02.38,0:01:05.37,Default,,0000,0000,0000,,and see what they're\Nsmallest common multiple is.
Dialogue: 0,0:01:05.37,0:01:07.18,Default,,0000,0000,0000,,So let's do it that way first.
Dialogue: 0,0:01:07.18,0:01:13.76,Default,,0000,0000,0000,,So multiples of six\Nare 6, 12, 18, 24 30.
Dialogue: 0,0:01:13.76,0:01:17.05,Default,,0000,0000,0000,,And I could keep going if we\Ndon't find any common multiples
Dialogue: 0,0:01:17.05,0:01:20.36,Default,,0000,0000,0000,,out of this group here with\Nany of the multiples in eight.
Dialogue: 0,0:01:20.36,0:01:25.69,Default,,0000,0000,0000,,And the multiples of\Neight are 8, 16, 24,
Dialogue: 0,0:01:25.69,0:01:26.90,Default,,0000,0000,0000,,and it looks like we're done.
Dialogue: 0,0:01:26.90,0:01:29.15,Default,,0000,0000,0000,,And we could keep\Ngoing obviously-- 32,
Dialogue: 0,0:01:29.15,0:01:30.49,Default,,0000,0000,0000,,so on and so forth.
Dialogue: 0,0:01:30.49,0:01:32.29,Default,,0000,0000,0000,,But I found a common\Nmultiple and this
Dialogue: 0,0:01:32.29,0:01:33.74,Default,,0000,0000,0000,,is their smallest\Ncommon multiple.
Dialogue: 0,0:01:33.74,0:01:38.05,Default,,0000,0000,0000,,They have other common\Nmultiples-- 48 and 72,
Dialogue: 0,0:01:38.05,0:01:40.05,Default,,0000,0000,0000,,and we could keep adding\Nmore and more multiple.
Dialogue: 0,0:01:40.05,0:01:41.84,Default,,0000,0000,0000,,But this is their\Nsmallest common multiple,
Dialogue: 0,0:01:41.84,0:01:44.40,Default,,0000,0000,0000,,their least common multiple.
Dialogue: 0,0:01:44.40,0:01:47.55,Default,,0000,0000,0000,,So it is 24.
Dialogue: 0,0:01:47.55,0:01:50.42,Default,,0000,0000,0000,,Another way that you could have\Nfound at least common multiple
Dialogue: 0,0:01:50.42,0:01:52.91,Default,,0000,0000,0000,,is you could have taken the\Nprime factorization of six
Dialogue: 0,0:01:52.91,0:01:55.33,Default,,0000,0000,0000,,and you say, hey,\Nthat's 2, and 3.
Dialogue: 0,0:01:55.33,0:02:00.81,Default,,0000,0000,0000,,So the least common multiple has\Nto have at least 1, 2, and 1, 3
Dialogue: 0,0:02:00.81,0:02:02.70,Default,,0000,0000,0000,,in its prime factorization\Nin order for it
Dialogue: 0,0:02:02.70,0:02:04.44,Default,,0000,0000,0000,,to be divisible by 6.
Dialogue: 0,0:02:04.44,0:02:07.61,Default,,0000,0000,0000,,And you could have said, what's\Nthe prime factorization of 8?
Dialogue: 0,0:02:07.61,0:02:11.19,Default,,0000,0000,0000,,It is 2 times 4\Nand 4 is 2 times 2.
Dialogue: 0,0:02:11.19,0:02:12.82,Default,,0000,0000,0000,,So in order to be\Ndivisible by 8,
Dialogue: 0,0:02:12.82,0:02:16.76,Default,,0000,0000,0000,,you have to have at least three\N2's in the prime factorization.
Dialogue: 0,0:02:16.76,0:02:21.61,Default,,0000,0000,0000,,So to be divisible by 6, you\Nhave to have a 2 times a 3.
Dialogue: 0,0:02:21.61,0:02:24.19,Default,,0000,0000,0000,,And then to be divisible by 8,\Nyou have to have at least three
Dialogue: 0,0:02:24.19,0:02:25.90,Default,,0000,0000,0000,,2's.
Dialogue: 0,0:02:25.90,0:02:27.81,Default,,0000,0000,0000,,You have to have two\Ntimes itself three times
Dialogue: 0,0:02:27.81,0:02:28.69,Default,,0000,0000,0000,,I should say.
Dialogue: 0,0:02:28.69,0:02:32.07,Default,,0000,0000,0000,,Well, we have one 2 and\Nlet's throw in a couple more.
Dialogue: 0,0:02:32.07,0:02:34.83,Default,,0000,0000,0000,,So then you have another\N2 and then another 2.
Dialogue: 0,0:02:34.83,0:02:38.19,Default,,0000,0000,0000,,So this part right over here\Nmakes it divisible by 8.
Dialogue: 0,0:02:38.19,0:02:41.26,Default,,0000,0000,0000,,And this part right over\Nhere makes it divisible by 6.
Dialogue: 0,0:02:41.26,0:02:48.21,Default,,0000,0000,0000,,If I take 2 times 2 times 2\Ntimes 3, that does give me 24.
Dialogue: 0,0:02:48.21,0:02:49.87,Default,,0000,0000,0000,,So our least common\Nmultiple of 8 and 6,
Dialogue: 0,0:02:49.87,0:02:52.59,Default,,0000,0000,0000,,which is also the least common\Ndenominator of these two
Dialogue: 0,0:02:52.59,0:02:54.79,Default,,0000,0000,0000,,fractions is going to be 24.
Dialogue: 0,0:02:54.79,0:02:57.20,Default,,0000,0000,0000,,So what we want to do is\Nrewrite each of these fractions
Dialogue: 0,0:02:57.20,0:02:59.57,Default,,0000,0000,0000,,with 24 as the denominator.
Dialogue: 0,0:02:59.57,0:03:01.79,Default,,0000,0000,0000,,So I'll start with 2 over 8.
Dialogue: 0,0:03:01.79,0:03:04.79,Default,,0000,0000,0000,,And I want to write that\Nas something over 24.
Dialogue: 0,0:03:08.79,0:03:11.18,Default,,0000,0000,0000,,Well, to get the\Ndenominator be 24,
Dialogue: 0,0:03:11.18,0:03:13.35,Default,,0000,0000,0000,,we have to multiply it by 3.
Dialogue: 0,0:03:13.35,0:03:15.13,Default,,0000,0000,0000,,8 times 3 is 24.
Dialogue: 0,0:03:15.13,0:03:16.50,Default,,0000,0000,0000,,And so if we don't\Nwant to change
Dialogue: 0,0:03:16.50,0:03:17.92,Default,,0000,0000,0000,,the value of the\Nfraction, we have
Dialogue: 0,0:03:17.92,0:03:21.56,Default,,0000,0000,0000,,to multiply the numerator and\Ndenominator by the same thing.
Dialogue: 0,0:03:21.56,0:03:24.74,Default,,0000,0000,0000,,So let's multiply the\Nnumerator by 3 as well.
Dialogue: 0,0:03:24.74,0:03:26.87,Default,,0000,0000,0000,,2 times 3 is 6.
Dialogue: 0,0:03:26.87,0:03:29.94,Default,,0000,0000,0000,,So 2/8 is the exact\Nsame thing as 6/24.
Dialogue: 0,0:03:29.94,0:03:31.31,Default,,0000,0000,0000,,To see that a\Nlittle bit clearer,
Dialogue: 0,0:03:31.31,0:03:37.04,Default,,0000,0000,0000,,you say, look, if I have 2/8,\Nand if I multiply this times 3
Dialogue: 0,0:03:37.04,0:03:39.64,Default,,0000,0000,0000,,over 3, that gives me 6/24.
Dialogue: 0,0:03:42.37,0:03:45.97,Default,,0000,0000,0000,,And this are the same\Nfraction because 3 over 3
Dialogue: 0,0:03:45.97,0:03:47.97,Default,,0000,0000,0000,,is really just 1.
Dialogue: 0,0:03:47.97,0:03:49.54,Default,,0000,0000,0000,,It's one whole.
Dialogue: 0,0:03:49.54,0:03:53.60,Default,,0000,0000,0000,,So 2/8 is 6/24 let's do\Nthe same thing with 5/6.
Dialogue: 0,0:03:56.59,0:04:03.15,Default,,0000,0000,0000,,So 5 over 6 is equal\Nto something over 24.
Dialogue: 0,0:04:03.15,0:04:05.74,Default,,0000,0000,0000,,Let me do that in\Na different color.
Dialogue: 0,0:04:05.74,0:04:07.43,Default,,0000,0000,0000,,I'll do it in blue.
Dialogue: 0,0:04:07.43,0:04:09.59,Default,,0000,0000,0000,,Something over 24.
Dialogue: 0,0:04:09.59,0:04:11.91,Default,,0000,0000,0000,,To get the denominator\Nfrom 6 to 24,
Dialogue: 0,0:04:11.91,0:04:14.23,Default,,0000,0000,0000,,we have to multiply it by 4.
Dialogue: 0,0:04:14.23,0:04:16.24,Default,,0000,0000,0000,,So if we don't want to\Nchange the value of 5/6,
Dialogue: 0,0:04:16.24,0:04:18.28,Default,,0000,0000,0000,,we have to multiply the\Nnumerator and denominator
Dialogue: 0,0:04:18.28,0:04:19.19,Default,,0000,0000,0000,,by the same thing.
Dialogue: 0,0:04:19.19,0:04:22.19,Default,,0000,0000,0000,,So let's multiply the\Nnumerator times 4.
Dialogue: 0,0:04:22.19,0:04:24.61,Default,,0000,0000,0000,,5 times 4 is 20.
Dialogue: 0,0:04:24.61,0:04:26.82,Default,,0000,0000,0000,,5/6 is the same thing as 20/24.
Dialogue: 0,0:04:26.82,0:04:27.70,Default,,0000,0000,0000,,So we're done.
Dialogue: 0,0:04:27.70,0:04:31.90,Default,,0000,0000,0000,,We've written 2/8 as 6/24 and\Nwe've written 5/6 as 20/24.
Dialogue: 0,0:04:31.90,0:04:34.11,Default,,0000,0000,0000,,If we wanted to add them\Nnow, we could literally just
Dialogue: 0,0:04:34.11,0:04:36.85,Default,,0000,0000,0000,,add 6/24 to 20/24.
Dialogue: 0,0:04:36.85,0:04:38.39,Default,,0000,0000,0000,,And I'll leave you\Nthere because they
Dialogue: 0,0:04:38.39,0:04:41.14,Default,,0000,0000,0000,,didn't ask us to\Nactually do that.