[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.00,0:00:00.38,Default,,0000,0000,0000,, Dialogue: 0,0:00:00.38,0:00:04.55,Default,,0000,0000,0000,,We're asked to add 4/9 and 11/12\Nand to write our answer Dialogue: 0,0:00:04.55,0:00:07.31,Default,,0000,0000,0000,,as a mixed number, and then\Nsimplify and write our answer Dialogue: 0,0:00:07.31,0:00:09.24,Default,,0000,0000,0000,,as a mixed number. Dialogue: 0,0:00:09.24,0:00:11.97,Default,,0000,0000,0000,,So here we have two fractions\Nwe're adding together, but we Dialogue: 0,0:00:11.97,0:00:13.70,Default,,0000,0000,0000,,have different denominators. Dialogue: 0,0:00:13.70,0:00:15.80,Default,,0000,0000,0000,,So whenever you add fractions,\Nthe first thing you have to do Dialogue: 0,0:00:15.80,0:00:16.88,Default,,0000,0000,0000,,is check the denominators. Dialogue: 0,0:00:16.88,0:00:18.84,Default,,0000,0000,0000,,If they're the same, you can\Nadd, but if they're different Dialogue: 0,0:00:18.84,0:00:21.60,Default,,0000,0000,0000,,like this, you have to make\Nthem have the same Dialogue: 0,0:00:21.60,0:00:22.58,Default,,0000,0000,0000,,denominator. Dialogue: 0,0:00:22.58,0:00:27.86,Default,,0000,0000,0000,,So what we have to do is find\Na number that both 9 and 12 Dialogue: 0,0:00:27.86,0:00:30.89,Default,,0000,0000,0000,,will divide into, and that\Nwill be our common Dialogue: 0,0:00:30.89,0:00:33.80,Default,,0000,0000,0000,,denominator, and you'll see\Nwhy both 9 and 12 have to Dialogue: 0,0:00:33.80,0:00:34.97,Default,,0000,0000,0000,,divide into it. Dialogue: 0,0:00:34.97,0:00:37.07,Default,,0000,0000,0000,,So let's think about what that\Nnumber is, and there's two Dialogue: 0,0:00:37.07,0:00:39.79,Default,,0000,0000,0000,,ways of coming up with that\Nwhat we could call a least Dialogue: 0,0:00:39.79,0:00:44.30,Default,,0000,0000,0000,,common multiple, the smallest\Nmultiple of both 9 Dialogue: 0,0:00:44.30,0:00:46.54,Default,,0000,0000,0000,,and 12 that is common. Dialogue: 0,0:00:46.54,0:00:49.31,Default,,0000,0000,0000,,One way is just to kind of look\Nat the multiples of 9 and Dialogue: 0,0:00:49.31,0:00:51.45,Default,,0000,0000,0000,,see if any of them are\Ndivisible by 12. Dialogue: 0,0:00:51.45,0:00:54.80,Default,,0000,0000,0000,,So if you start with 9--\Nwe can do it over here. Dialogue: 0,0:00:54.80,0:00:57.23,Default,,0000,0000,0000,,So you have 9, that's\Nnot divisible by 12. Dialogue: 0,0:00:57.23,0:00:59.81,Default,,0000,0000,0000,,18 isn't divisible by 12. Dialogue: 0,0:00:59.81,0:01:02.81,Default,,0000,0000,0000,,27 isn't divisible by 12. Dialogue: 0,0:01:02.81,0:01:05.67,Default,,0000,0000,0000,,36, well, that is\Ndivisible by 12. Dialogue: 0,0:01:05.67,0:01:07.48,Default,,0000,0000,0000,,That is 12 times 3. Dialogue: 0,0:01:07.48,0:01:11.56,Default,,0000,0000,0000,,So 9 goes into 36 and\N12 goes into 36. Dialogue: 0,0:01:11.56,0:01:13.62,Default,,0000,0000,0000,,So what we want to do is write\Na common denominator. Dialogue: 0,0:01:13.62,0:01:17.87,Default,,0000,0000,0000,,So we're going to write 4/9 as\Nsomething over 36, and we're Dialogue: 0,0:01:17.87,0:01:23.50,Default,,0000,0000,0000,,going to write 11/12 as\Nsomething over 36. Dialogue: 0,0:01:23.50,0:01:27.37,Default,,0000,0000,0000,,Now, to turn your 9 into\Na 36, you have to Dialogue: 0,0:01:27.37,0:01:32.72,Default,,0000,0000,0000,,multiply it by 4, right? Dialogue: 0,0:01:32.72,0:01:37.62,Default,,0000,0000,0000,,9 times 4 is equal to 36. Dialogue: 0,0:01:37.62,0:01:40.24,Default,,0000,0000,0000,,Now, you can't just multiply\Nthe denominator by 4. Dialogue: 0,0:01:40.24,0:01:43.56,Default,,0000,0000,0000,,You also have to multiply the\Nnumerator by the same thing. Dialogue: 0,0:01:43.56,0:01:45.60,Default,,0000,0000,0000,,So if you multiply the numerator\Nby 4, you get 4 Dialogue: 0,0:01:45.60,0:01:48.09,Default,,0000,0000,0000,,times 4 is 16. Dialogue: 0,0:01:48.09,0:01:52.46,Default,,0000,0000,0000,,So 4/9 is the exact same\Nthing as 16/36. Dialogue: 0,0:01:52.46,0:01:55.55,Default,,0000,0000,0000,,If you wanted to simplify this\None to 4/9, you divide the Dialogue: 0,0:01:55.55,0:01:58.02,Default,,0000,0000,0000,,numerator and the denominator\Nby 4. Dialogue: 0,0:01:58.02,0:02:00.01,Default,,0000,0000,0000,,Now, we do the same\Nthing over here. Dialogue: 0,0:02:00.01,0:02:07.80,Default,,0000,0000,0000,,36, 12 times 3, so we're\Nmultiplying 12 by 3 to get 36. Dialogue: 0,0:02:07.80,0:02:10.03,Default,,0000,0000,0000,,Well, if we did that to the\Ndenominator, we also have to Dialogue: 0,0:02:10.03,0:02:14.18,Default,,0000,0000,0000,,do that to the numerator,\Nso 11 times 3 is 33. Dialogue: 0,0:02:14.18,0:02:16.66,Default,,0000,0000,0000,,And just like that, we've now\Nrewritten each of the Dialogue: 0,0:02:16.66,0:02:19.66,Default,,0000,0000,0000,,fractions so that they have\Nthe same denominator. Dialogue: 0,0:02:19.66,0:02:22.57,Default,,0000,0000,0000,,Both of their denominators\Nis 36. Dialogue: 0,0:02:22.57,0:02:23.94,Default,,0000,0000,0000,,So now we're ready to add. Dialogue: 0,0:02:23.94,0:02:29.17,Default,,0000,0000,0000,,If you add these two things,\Nwe'll have 36, because we're Dialogue: 0,0:02:29.17,0:02:33.11,Default,,0000,0000,0000,,considering kind of parts of\N36 or fractions of 36, and Dialogue: 0,0:02:33.11,0:02:35.47,Default,,0000,0000,0000,,then we have 16 plus 33\Nin the numerator. Dialogue: 0,0:02:35.47,0:02:36.42,Default,,0000,0000,0000,,Let me write that down. Dialogue: 0,0:02:36.42,0:02:41.19,Default,,0000,0000,0000,,16 plus 33 in the numerator. Dialogue: 0,0:02:41.19,0:02:44.62,Default,,0000,0000,0000,,And 16 plus 33 is what? Dialogue: 0,0:02:44.62,0:02:48.02,Default,,0000,0000,0000,,6 plus 33 would be 39\Nand then you have Dialogue: 0,0:02:48.02,0:02:49.77,Default,,0000,0000,0000,,another 10, so it's 49. Dialogue: 0,0:02:49.77,0:02:57.39,Default,,0000,0000,0000,,So it's equal to 49/36. Dialogue: 0,0:02:57.39,0:02:59.36,Default,,0000,0000,0000,,Now, can we simplify this? Dialogue: 0,0:02:59.36,0:03:03.65,Default,,0000,0000,0000,,49, it's 7 squared, so it has\N1, 7 and 49 as factors. Dialogue: 0,0:03:03.65,0:03:06.00,Default,,0000,0000,0000,,This has 1-- it has a bunch\Nof numbers, but it's not Dialogue: 0,0:03:06.00,0:03:12.77,Default,,0000,0000,0000,,divisible by 7, so this is\Nactually in simplest form, but Dialogue: 0,0:03:12.77,0:03:14.40,Default,,0000,0000,0000,,this is an improper fraction. Dialogue: 0,0:03:14.40,0:03:16.26,Default,,0000,0000,0000,,The numerator is larger\Nthan the denominator. Dialogue: 0,0:03:16.26,0:03:18.48,Default,,0000,0000,0000,,So let's write it as\Na proper fraction. Dialogue: 0,0:03:18.48,0:03:24.68,Default,,0000,0000,0000,,To do that, we divide\N36 into 49. Dialogue: 0,0:03:24.68,0:03:26.85,Default,,0000,0000,0000,,36 goes into 49 how\Nmany times? Dialogue: 0,0:03:26.85,0:03:29.44,Default,,0000,0000,0000,,Well, it only goes one\Ntime, so it equals 1. Dialogue: 0,0:03:29.44,0:03:31.11,Default,,0000,0000,0000,,And how much will\Nbe left over? Dialogue: 0,0:03:31.11,0:03:36.13,Default,,0000,0000,0000,,If I divide 36 into 49 one time,\Nor 1 times 36 is 36, Dialogue: 0,0:03:36.13,0:03:38.75,Default,,0000,0000,0000,,then I have 13 left\Nover to get to 49. Dialogue: 0,0:03:38.75,0:03:43.46,Default,,0000,0000,0000,,So it's 1 and 13/36. Dialogue: 0,0:03:43.46,0:03:46.10,Default,,0000,0000,0000,,And you can do that manually,\Nif you like you. Dialogue: 0,0:03:46.10,0:03:48.96,Default,,0000,0000,0000,,You'd say 36 into 49. Dialogue: 0,0:03:48.96,0:03:50.68,Default,,0000,0000,0000,,36 goes into 49 one time. Dialogue: 0,0:03:50.68,0:03:54.13,Default,,0000,0000,0000,,1 times 36 is 36, and\Nthen you subtract. Dialogue: 0,0:03:54.13,0:03:55.77,Default,,0000,0000,0000,,9 minus 6 is 3. Dialogue: 0,0:03:55.77,0:03:58.31,Default,,0000,0000,0000,,4 minus 3 is 1. Dialogue: 0,0:03:58.31,0:04:00.74,Default,,0000,0000,0000,,You have a remainder of 13. Dialogue: 0,0:04:00.74,0:04:04.09,Default,,0000,0000,0000,,So that's our answer:\N1 and 13/36. Dialogue: 0,0:04:04.09,0:04:05.33,Default,,0000,0000,0000,,