WEBVTT 00:00:00.255 --> 00:00:04.714 What I want to do in this video is order these fractions from least to greatest 00:00:04.714 --> 00:00:10.379 And, the easiest way--and the way that people are sure to get the right answer-- 00:00:10.379 --> 00:00:14.002 is to find a common denominator, because if we can't find a common denominator, 00:00:14.002 --> 00:00:21.432 these fractions are difficult to compare: 4/9 v. 3/4 v. 4/5, 11/12, 13/15. 00:00:21.432 --> 00:00:25.844 You can try to estimate them, but you'll be able to directly compare them if 00:00:25.844 --> 00:00:32.467 they all have the same denominator. So, the trick here is to first find the common denominator. 00:00:32.467 --> 00:00:36.432 And there is many ways to do it, you could just pick one of these numbers, 00:00:36.432 --> 00:00:42.051 and take all of its multiples until you find a multiple that is divisible by all of the rest. 00:00:42.051 --> 00:00:45.667 Another way to do it is to look at the prime factorization of each of these numbers. 00:00:45.667 --> 00:00:52.067 and then the 'least common multiple' of them would have each of those prime numbers in it. 00:00:52.067 --> 00:00:58.630 Let's do it that second way, and then verify it. 00:00:58.630 --> 00:01:08.429 So, 9 is 33, so our LCM is going to have at least one 33 in it. 00:01:08.429 --> 00:01:12.191 And then 4 is the same thing as 2*2. 00:01:12.191 --> 00:01:17.810 So, we will also have 2*2 in our prime factorization (LCM). 00:01:17.810 --> 00:01:22.361 5 is a prime number, so we'll put 5 right there. 00:01:22.361 --> 00:01:31.185 And then, 12 is the same thing as 26, and 6 = 23. 00:01:31.185 --> 00:01:40.867 So, in our LCM, we have to have two 2's, but we already have two 2's, and we already have one 3. 00:01:40.867 --> 00:01:48.182 Another way to think about it, is that something that is divisible by both 9 and 4 00:01:48.182 --> 00:01:50.200 is going to be divisible by 12. 00:01:50.200 --> 00:01:58.770 And then finally, we need it to be divisible by 15's prime factors. 00:01:58.770 --> 00:02:03.971 15 is the same thing as 3*5. 00:02:03.971 --> 00:02:09.312 So once again, we already have 3 and 5. 00:02:09.312 --> 00:02:15.163 So, this is our least common multiple (LCM). 00:02:15.163 --> 00:02:45.256 So, LCM is going to be equal to 33225 =180 00:02:45.256 --> 00:02:52.873 So, our LCM is 180. So, we want to rewrite all of these fractions with 180 in the denominator. 00:02:52.873 --> 00:02:59.467 So, our first fraction, 4/9, is what over 180? 00:02:59.467 --> 00:03:04.065 To go from 9 to 180, we have to multiple 9 by 20. 00:03:04.065 --> 00:03:16.836 So, to get the denominator to equal 180, we multiple by 20. 00:03:16.836 --> 00:03:21.851 Since we don't want to change the value of the fraction, we should also multiple by the 4 by 20. 00:03:21.851 --> 00:03:28.863 4*20 = 80. So, 4/9 is the same thing as 80/180. 00:03:28.863 --> 00:03:37.200 Now, let's do 3/4. What do we have to multiple the denominator by to equal 180? 00:03:37.200 --> 00:03:42.656 You can divide 4 into 180 (180/4 = x) to figure that out. 00:03:42.656 --> 00:03:54.452 4*45 = 180. Now, you also have to multiple the numerator by 45. 00:03:54.452 --> 00:04:09.200 3*45 = 135. So, 3/4 equals 135/180. 00:04:09.200 --> 00:04:31.929 Now let's do 4/5. To get 180 from 5, multiple 5 by 36. 00:04:31.929 --> 00:04:35.133 Have to multiple numerator by same number, 36. 00:04:35.133 --> 00:04:46.325 So, 144/180. 00:04:46.325 --> 00:04:50.180 And then we have only two more to do. 00:04:50.180 --> 00:05:25.846 180/12 = 15. Same for numerator, 15. So, 11/12 = 165/180. 00:05:25.846 --> 00:05:28.067 And then finally, we have 13/15. 00:05:28.067 --> 00:05:51.434 To get 180 from 15, multiply 15 by 12--1510 = 150, 30 remaining for 180. 152 = 30. So, 15*12 = 180. 00:05:51.434 --> 00:05:54.128 Multiple numerator by same number, 13. 00:05:54.128 --> 00:06:01.233 We know 12*12 = 144, so just add one more 12 = 156. 00:06:01.233 --> 00:06:08.431 So, we've rewritten each of these fractions with the new common denominator. 00:06:08.431 --> 00:06:13.029 Now, it is very easy to compare them. We only have to look at their numerators. 00:06:13.029 --> 00:06:21.434 Foe example, the smallest numerator is 80, so 4/9 is the least of these numbers. 00:06:21.434 --> 00:07:04.438 The next smallest number looks like 135, which was 3/4. 00:07:04.438 --> 00:07:08.524 And then the next one is going to be the 144/180, which was 4/5. 00:07:08.524 --> 00:07:20.831 Next is 156/180, which was 13/15. 00:07:20.831 --> 00:07:35.970 Finally, we have 165/180, which was 11/12. 00:07:35.970 --> 99:59:59.999 And, we're done! We have finished our ordering.