1 00:00:00,255 --> 00:00:04,714 What I want to do in this video is order these fractions from least to greatest 2 00:00:04,714 --> 00:00:10,379 And, the easiest way--and the way that people are sure to get the right answer-- 3 00:00:10,379 --> 00:00:14,002 is to find a common denominator, because if we can't find a common denominator, 4 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. 5 00:00:21,432 --> 00:00:25,844 You can try to estimate them, but you'll be able to directly compare them if 6 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. 7 00:00:32,467 --> 00:00:36,432 And there is many ways to do it, you could just pick one of these numbers, 8 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. 9 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. 10 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. 11 00:00:52,067 --> 00:00:58,630 Let's do it that second way, and then verify it. 12 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. 13 00:01:08,429 --> 00:01:12,191 And then 4 is the same thing as 2*2. 14 00:01:12,191 --> 00:01:17,810 So, we will also have 2*2 in our prime factorization (LCM). 15 00:01:17,810 --> 00:01:22,361 5 is a prime number, so we'll put 5 right there. 16 00:01:22,361 --> 00:01:31,185 And then, 12 is the same thing as 26, and 6 = 23. 17 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. 18 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 19 00:01:48,182 --> 00:01:50,200 is going to be divisible by 12. 20 00:01:50,200 --> 00:01:58,770 And then finally, we need it to be divisible by 15's prime factors. 21 00:01:58,770 --> 00:02:03,971 15 is the same thing as 3*5. 22 00:02:03,971 --> 00:02:09,312 So once again, we already have 3 and 5. 23 00:02:09,312 --> 00:02:15,163 So, this is our least common multiple (LCM). 24 00:02:15,163 --> 00:02:45,256 So, LCM is going to be equal to 33225 =180 25 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. 26 00:02:52,873 --> 00:02:59,467 So, our first fraction, 4/9, is what over 180? 27 00:02:59,467 --> 00:03:04,065 To go from 9 to 180, we have to multiple 9 by 20. 28 00:03:04,065 --> 00:03:16,836 So, to get the denominator to equal 180, we multiple by 20. 29 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. 30 00:03:21,851 --> 00:03:28,863 4*20 = 80. So, 4/9 is the same thing as 80/180. 31 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? 32 00:03:37,200 --> 00:03:42,656 You can divide 4 into 180 (180/4 = x) to figure that out. 33 00:03:42,656 --> 00:03:54,452 4*45 = 180. Now, you also have to multiple the numerator by 45. 34 00:03:54,452 --> 00:04:09,200 3*45 = 135. So, 3/4 equals 135/180. 35 00:04:09,200 --> 00:04:31,929 Now let's do 4/5. To get 180 from 5, multiple 5 by 36. 36 00:04:31,929 --> 00:04:35,133 Have to multiple numerator by same number, 36. 37 00:04:35,133 --> 00:04:46,325 So, 144/180. 38 00:04:46,325 --> 00:04:50,180 And then we have only two more to do. 39 00:04:50,180 --> 00:05:25,846 180/12 = 15. Same for numerator, 15. So, 11/12 = 165/180. 40 00:05:25,846 --> 00:05:28,067 And then finally, we have 13/15. 41 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. 42 00:05:51,434 --> 00:05:54,128 Multiple numerator by same number, 13. 43 00:05:54,128 --> 00:06:01,233 We know 12*12 = 144, so just add one more 12 = 156. 44 00:06:01,233 --> 00:06:08,431 So, we've rewritten each of these fractions with the new common denominator. 45 00:06:08,431 --> 00:06:13,029 Now, it is very easy to compare them. We only have to look at their numerators. 46 00:06:13,029 --> 00:06:21,434 Foe example, the smallest numerator is 80, so 4/9 is the least of these numbers. 47 00:06:21,434 --> 00:07:04,438 The next smallest number looks like 135, which was 3/4. 48 00:07:04,438 --> 00:07:08,524 And then the next one is going to be the 144/180, which was 4/5. 49 00:07:08,524 --> 00:07:20,831 Next is 156/180, which was 13/15. 50 00:07:20,831 --> 00:07:35,970 Finally, we have 165/180, which was 11/12. 51 00:07:35,970 --> 99:59:59,999 And, we're done! We have finished our ordering.