WEBVTT 00:00:00.570 --> 00:00:02.680 We're asked to rewrite the following two 00:00:02.680 --> 00:00:06.720 fractions as fractions with a least common denominator. 00:00:10.960 --> 00:00:13.260 So a least common denominator for two fractions 00:00:13.260 --> 00:00:17.250 is really just going to be the least common multiple of both 00:00:17.250 --> 00:00:19.630 of these denominators over here. 00:00:19.630 --> 00:00:21.480 And the value of doing that is then 00:00:21.480 --> 00:00:24.530 if you can make these a common denominator, 00:00:24.530 --> 00:00:26.400 then you can add the two fractions. 00:00:26.400 --> 00:00:28.046 And we'll see that in other videos. 00:00:28.046 --> 00:00:30.545 But first of all, let's just find the least common multiple. 00:00:33.330 --> 00:00:35.920 Let me write it out because sometimes LCD 00:00:35.920 --> 00:00:37.400 could meet other things. 00:00:37.400 --> 00:00:48.160 So least common denominator of these two things 00:00:48.160 --> 00:00:51.360 is going to be the same thing as the least common multiple 00:00:51.360 --> 00:00:53.580 of the two denominators over here. 00:00:53.580 --> 00:00:57.342 The least common multiple of 8 and 6. 00:00:57.342 --> 00:00:59.800 And a couple of ways to think about least common multiple-- 00:00:59.800 --> 00:01:02.380 you literally could just take the multiples of 8 and 6 00:01:02.380 --> 00:01:05.370 and see what they're smallest common multiple is. 00:01:05.370 --> 00:01:07.180 So let's do it that way first. 00:01:07.180 --> 00:01:13.760 So multiples of six are 6, 12, 18, 24 30. 00:01:13.760 --> 00:01:17.050 And I could keep going if we don't find any common multiples 00:01:17.050 --> 00:01:20.360 out of this group here with any of the multiples in eight. 00:01:20.360 --> 00:01:25.687 And the multiples of eight are 8, 16, 24, 00:01:25.687 --> 00:01:26.895 and it looks like we're done. 00:01:26.895 --> 00:01:29.150 And we could keep going obviously-- 32, 00:01:29.150 --> 00:01:30.490 so on and so forth. 00:01:30.490 --> 00:01:32.290 But I found a common multiple and this 00:01:32.290 --> 00:01:33.740 is their smallest common multiple. 00:01:33.740 --> 00:01:38.050 They have other common multiples-- 48 and 72, 00:01:38.050 --> 00:01:40.050 and we could keep adding more and more multiple. 00:01:40.050 --> 00:01:41.841 But this is their smallest common multiple, 00:01:41.841 --> 00:01:44.400 their least common multiple. 00:01:44.400 --> 00:01:47.550 So it is 24. 00:01:47.550 --> 00:01:50.420 Another way that you could have found at least common multiple 00:01:50.420 --> 00:01:52.910 is you could have taken the prime factorization of six 00:01:52.910 --> 00:01:55.330 and you say, hey, that's 2, and 3. 00:01:55.330 --> 00:02:00.810 So the least common multiple has to have at least 1, 2, and 1, 3 00:02:00.810 --> 00:02:02.700 in its prime factorization in order for it 00:02:02.700 --> 00:02:04.440 to be divisible by 6. 00:02:04.440 --> 00:02:07.610 And you could have said, what's the prime factorization of 8? 00:02:07.610 --> 00:02:11.190 It is 2 times 4 and 4 is 2 times 2. 00:02:11.190 --> 00:02:12.820 So in order to be divisible by 8, 00:02:12.820 --> 00:02:16.760 you have to have at least three 2's in the prime factorization. 00:02:16.760 --> 00:02:21.607 So to be divisible by 6, you have to have a 2 times a 3. 00:02:21.607 --> 00:02:24.190 And then to be divisible by 8, you have to have at least three 00:02:24.190 --> 00:02:25.900 2's. 00:02:25.900 --> 00:02:27.810 You have to have two times itself three times 00:02:27.810 --> 00:02:28.690 I should say. 00:02:28.690 --> 00:02:32.070 Well, we have one 2 and let's throw in a couple more. 00:02:32.070 --> 00:02:34.830 So then you have another 2 and then another 2. 00:02:34.830 --> 00:02:38.190 So this part right over here makes it divisible by 8. 00:02:38.190 --> 00:02:41.260 And this part right over here makes it divisible by 6. 00:02:41.260 --> 00:02:48.206 If I take 2 times 2 times 2 times 3, that does give me 24. 00:02:48.206 --> 00:02:49.872 So our least common multiple of 8 and 6, 00:02:49.872 --> 00:02:52.590 which is also the least common denominator of these two 00:02:52.590 --> 00:02:54.790 fractions is going to be 24. 00:02:54.790 --> 00:02:57.200 So what we want to do is rewrite each of these fractions 00:02:57.200 --> 00:02:59.570 with 24 as the denominator. 00:02:59.570 --> 00:03:01.790 So I'll start with 2 over 8. 00:03:01.790 --> 00:03:04.790 And I want to write that as something over 24. 00:03:08.790 --> 00:03:11.180 Well, to get the denominator be 24, 00:03:11.180 --> 00:03:13.350 we have to multiply it by 3. 00:03:13.350 --> 00:03:15.126 8 times 3 is 24. 00:03:15.126 --> 00:03:16.500 And so if we don't want to change 00:03:16.500 --> 00:03:17.920 the value of the fraction, we have 00:03:17.920 --> 00:03:21.560 to multiply the numerator and denominator by the same thing. 00:03:21.560 --> 00:03:24.740 So let's multiply the numerator by 3 as well. 00:03:24.740 --> 00:03:26.870 2 times 3 is 6. 00:03:26.870 --> 00:03:29.936 So 2/8 is the exact same thing as 6/24. 00:03:29.936 --> 00:03:31.310 To see that a little bit clearer, 00:03:31.310 --> 00:03:37.040 you say, look, if I have 2/8, and if I multiply this times 3 00:03:37.040 --> 00:03:39.635 over 3, that gives me 6/24. 00:03:42.370 --> 00:03:45.970 And this are the same fraction because 3 over 3 00:03:45.970 --> 00:03:47.970 is really just 1. 00:03:47.970 --> 00:03:49.540 It's one whole. 00:03:49.540 --> 00:03:53.600 So 2/8 is 6/24 let's do the same thing with 5/6. 00:03:56.590 --> 00:04:03.150 So 5 over 6 is equal to something over 24. 00:04:03.150 --> 00:04:05.740 Let me do that in a different color. 00:04:05.740 --> 00:04:07.430 I'll do it in blue. 00:04:07.430 --> 00:04:09.590 Something over 24. 00:04:09.590 --> 00:04:11.910 To get the denominator from 6 to 24, 00:04:11.910 --> 00:04:14.230 we have to multiply it by 4. 00:04:14.230 --> 00:04:16.240 So if we don't want to change the value of 5/6, 00:04:16.240 --> 00:04:18.281 we have to multiply the numerator and denominator 00:04:18.281 --> 00:04:19.190 by the same thing. 00:04:19.190 --> 00:04:22.190 So let's multiply the numerator times 4. 00:04:22.190 --> 00:04:24.610 5 times 4 is 20. 00:04:24.610 --> 00:04:26.820 5/6 is the same thing as 20/24. 00:04:26.820 --> 00:04:27.700 So we're done. 00:04:27.700 --> 00:04:31.902 We've written 2/8 as 6/24 and we've written 5/6 as 20/24. 00:04:31.902 --> 00:04:34.110 If we wanted to add them now, we could literally just 00:04:34.110 --> 00:04:36.849 add 6/24 to 20/24. 00:04:36.849 --> 00:04:38.390 And I'll leave you there because they 00:04:38.390 --> 00:04:41.140 didn't ask us to actually do that.