[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.80,0:00:05.32,Default,,0000,0000,0000,,We have negative 3/4\Nminus 7/6 minus 3/6.
Dialogue: 0,0:00:05.32,0:00:06.79,Default,,0000,0000,0000,,And there's many\Nways to do this.
Dialogue: 0,0:00:06.79,0:00:08.52,Default,,0000,0000,0000,,But it immediately\Njumps out at me
Dialogue: 0,0:00:08.52,0:00:11.40,Default,,0000,0000,0000,,that these last two numbers\Nhave a 6 in the denominator.
Dialogue: 0,0:00:11.40,0:00:13.27,Default,,0000,0000,0000,,So I'm going to worry\Nabout these first.
Dialogue: 0,0:00:13.27,0:00:17.39,Default,,0000,0000,0000,,I'm going to view this as\Nnegative 7/6 minus 3/6.
Dialogue: 0,0:00:17.39,0:00:21.54,Default,,0000,0000,0000,,So if we have negative\N7/6 minus 3/6,
Dialogue: 0,0:00:21.54,0:00:24.93,Default,,0000,0000,0000,,that's going to be the same\Nthing as negative 7 minus 3
Dialogue: 0,0:00:24.93,0:00:26.62,Default,,0000,0000,0000,,over 6.
Dialogue: 0,0:00:26.62,0:00:28.79,Default,,0000,0000,0000,,And of course, we\Nhave this negative 3/4
Dialogue: 0,0:00:28.79,0:00:30.90,Default,,0000,0000,0000,,out front that\Nwe're going to add
Dialogue: 0,0:00:30.90,0:00:32.11,Default,,0000,0000,0000,,to whatever we get over here.
Dialogue: 0,0:00:32.11,0:00:35.98,Default,,0000,0000,0000,,So this is these two terms\Nthat I'm adding together.
Dialogue: 0,0:00:35.98,0:00:39.77,Default,,0000,0000,0000,,Negative 7 minus\N3 is negative 10.
Dialogue: 0,0:00:39.77,0:00:42.61,Default,,0000,0000,0000,,So it's negative 10 over 6.
Dialogue: 0,0:00:42.61,0:00:45.23,Default,,0000,0000,0000,,And then I'm going to have\Nto add that to negative 3/4.
Dialogue: 0,0:00:52.55,0:00:56.62,Default,,0000,0000,0000,,And now I have to worry about\Nfinding a common denominator.
Dialogue: 0,0:00:56.62,0:01:02.80,Default,,0000,0000,0000,,Let me write that so\Nthey have a similar size.
Dialogue: 0,0:01:02.80,0:01:05.39,Default,,0000,0000,0000,,So now I have to worry about\Nfinding a common denominator.
Dialogue: 0,0:01:05.39,0:01:09.69,Default,,0000,0000,0000,,What is the smallest number that\Nis a multiple of both 4 and 6?
Dialogue: 0,0:01:09.69,0:01:11.62,Default,,0000,0000,0000,,Well, it might jump out\Nat you that it's 12.
Dialogue: 0,0:01:11.62,0:01:14.04,Default,,0000,0000,0000,,You can literally just go\Nthrough the multiples of 4.
Dialogue: 0,0:01:14.04,0:01:15.89,Default,,0000,0000,0000,,Or you could look at\Nthe prime factorization
Dialogue: 0,0:01:15.89,0:01:16.85,Default,,0000,0000,0000,,of both of these numbers.
Dialogue: 0,0:01:16.85,0:01:18.31,Default,,0000,0000,0000,,And what's the\Nsmallest number that
Dialogue: 0,0:01:18.31,0:01:20.95,Default,,0000,0000,0000,,has all of the prime\Nfactors of both of these?
Dialogue: 0,0:01:20.95,0:01:25.38,Default,,0000,0000,0000,,So you need two 2s, and\Nyou need a 2 and a 3.
Dialogue: 0,0:01:25.38,0:01:29.57,Default,,0000,0000,0000,,So if you have two 2s and a\N3, that's 4 times 3 is 12.
Dialogue: 0,0:01:29.57,0:01:34.52,Default,,0000,0000,0000,,So let's rewrite this\Nas something over 12
Dialogue: 0,0:01:34.52,0:01:37.50,Default,,0000,0000,0000,,plus something over 12.
Dialogue: 0,0:01:40.76,0:01:43.00,Default,,0000,0000,0000,,Well, to get your\Ndenominator from 4 to 12,
Dialogue: 0,0:01:43.00,0:01:44.86,Default,,0000,0000,0000,,you have to multiply by 3.
Dialogue: 0,0:01:44.86,0:01:47.41,Default,,0000,0000,0000,,So let's multiply our\Nnumerator by 3 as well.
Dialogue: 0,0:01:47.41,0:01:50.12,Default,,0000,0000,0000,,So if we multiply\Nnegative 3 times 3,
Dialogue: 0,0:01:50.12,0:01:52.13,Default,,0000,0000,0000,,you're going to have negative 9.
Dialogue: 0,0:01:52.13,0:01:54.26,Default,,0000,0000,0000,,And to get your\Ndenominator from 6 to 12,
Dialogue: 0,0:01:54.26,0:01:56.27,Default,,0000,0000,0000,,you have to multiply by 2.
Dialogue: 0,0:01:56.27,0:01:58.32,Default,,0000,0000,0000,,So let's multiply our\Nnumerator by 2 as well so
Dialogue: 0,0:01:58.32,0:02:00.28,Default,,0000,0000,0000,,that we don't change the\Nvalue of the fraction.
Dialogue: 0,0:02:00.28,0:02:02.89,Default,,0000,0000,0000,,So that's going\Nto be negative 20.
Dialogue: 0,0:02:02.89,0:02:04.49,Default,,0000,0000,0000,,And now we're ready to add.
Dialogue: 0,0:02:04.49,0:02:07.38,Default,,0000,0000,0000,,Our common denominator is 12.
Dialogue: 0,0:02:07.38,0:02:12.69,Default,,0000,0000,0000,,And so this is going to be\Nnegative 9 plus negative 20,
Dialogue: 0,0:02:12.69,0:02:15.53,Default,,0000,0000,0000,,or we could even write\Nthat as minus 20,
Dialogue: 0,0:02:15.53,0:02:18.78,Default,,0000,0000,0000,,over 12, which is equal to--\Nand we deserve a drum roll now.
Dialogue: 0,0:02:18.78,0:02:23.98,Default,,0000,0000,0000,,This is negative 29 over 12.
Dialogue: 0,0:02:23.98,0:02:26.98,Default,,0000,0000,0000,,And 29 is a prime\Nnumber, so it's not
Dialogue: 0,0:02:26.98,0:02:30.09,Default,,0000,0000,0000,,going to share any common\Nfactors other than 1 with 12.
Dialogue: 0,0:02:30.09,0:02:34.79,Default,,0000,0000,0000,,So we also have this in\Nthe most simplified form.