WEBVTT 00:00:00.303 --> 00:00:03.046 - [Voiceover] Let's say that we have the fraction 9/10, 00:00:03.046 --> 00:00:08.046 and I want to add to that the fraction 1/6. 00:00:09.567 --> 00:00:13.039 What is this, what is this going to equal? 00:00:13.839 --> 00:00:14.827 So when you first look at this, you say, 00:00:14.827 --> 00:00:16.602 "Oh, I have different denominators here. 00:00:16.602 --> 00:00:18.599 It's not obvious how I add these." 00:00:18.599 --> 00:00:21.038 And you'd be right and the way to actually 00:00:21.038 --> 00:00:23.546 move forward is to find a common denominator, 00:00:23.546 --> 00:00:26.181 to convert both of these fractions into 00:00:26.181 --> 00:00:28.536 fractions that have a common denominator. 00:00:28.536 --> 00:00:30.498 So how do you think about a common denominator? 00:00:30.498 --> 00:00:32.125 Well, a common denominator's gonna have to be 00:00:32.125 --> 00:00:36.478 a common multiple of these two denominators of 10 and six. 00:00:36.478 --> 00:00:38.638 So what's a common multiple of 10 and six? 00:00:38.638 --> 00:00:41.436 And it's usually simplest to find the least common multiple, 00:00:41.436 --> 00:00:43.502 and a good way of doing that is start with the larger 00:00:43.502 --> 00:00:47.312 denominator here, 10, and say, okay is 10 divisible by six? 00:00:47.952 --> 00:00:50.978 No. Okay, now, is 20 divisible by six? 00:00:51.588 --> 00:00:56.005 No. Is 30 divisible by six? Yes. 30 is divisible by six. 00:00:56.005 --> 00:00:57.722 So I'm just going through the multiples of 10 00:00:57.722 --> 00:00:59.556 and saying, "Well what is the smallest multiple of 10 00:00:59.556 --> 00:01:03.644 that is divisible by six?" And that's going to be 30. 00:01:03.644 --> 00:01:05.639 So I could rewrite both of these fractions 00:01:05.639 --> 00:01:07.605 as something over 30. 00:01:07.605 --> 00:01:10.296 So nine over 10. How would I write that as 00:01:10.296 --> 00:01:11.898 something over 30? Well I multiply 00:01:11.898 --> 00:01:15.984 the denominator, I'm multiplying the denominator by three. 00:01:17.074 --> 00:01:19.617 So I've just multiplied the denominator by three. 00:01:19.617 --> 00:01:22.088 So if I don't want to change the value of the fraction, 00:01:22.088 --> 00:01:23.586 I have to do the same thing to the numerator. 00:01:23.586 --> 00:01:26.186 I have to multiply that by three as well 00:01:26.996 --> 00:01:29.854 because now I'm just multiplying the numerator by three 00:01:29.854 --> 00:01:31.433 and the denominator by three, and that doesn't change 00:01:31.433 --> 00:01:32.954 the value of the fraction. 00:01:32.954 --> 00:01:35.751 So nine times three is 27. 00:01:35.751 --> 00:01:38.549 So once again, 9/10 and 27/30 00:01:38.549 --> 00:01:40.964 represent the same number. 00:01:40.964 --> 00:01:43.564 I've just written it now with a denominator of 30, 00:01:43.564 --> 00:01:45.631 and that's useful because I can also write 1/6 00:01:45.631 --> 00:01:49.100 with a denominator of 30. Let's do that. 00:01:49.100 --> 00:01:51.621 So 1/6 is what over 30? 00:01:51.621 --> 00:01:52.724 I encourage you to pause the video 00:01:52.724 --> 00:01:53.850 and try to think about it. 00:01:53.850 --> 00:01:56.149 So what did we do go from six to 30? 00:01:56.149 --> 00:01:59.248 We had to multiply by five. 00:01:59.908 --> 00:02:01.628 So if we multiply the denominator by five, 00:02:01.628 --> 00:02:04.623 we have to multiply the numerator by five as well, 00:02:04.623 --> 00:02:09.623 so one times five, one times five is five. 00:02:11.008 --> 00:02:13.749 So 9/10 is the same thing as 27/30, 00:02:13.749 --> 00:02:16.453 and 1/6 is the same thing as 5/30. 00:02:16.453 --> 00:02:20.226 And now we can add, now we can add 00:02:20.226 --> 00:02:21.817 and it's fairly straightforward. 00:02:21.817 --> 00:02:23.267 We have a certain number of 30ths, 00:02:23.267 --> 00:02:25.335 added to another number of 30ths, 00:02:25.335 --> 00:02:30.062 so 27/30 + 5/30, well that's going to be 00:02:30.062 --> 00:02:35.062 27, that's going to be 27 plus five, 00:02:35.471 --> 00:02:40.201 plus five, plus 5/30, 00:02:41.181 --> 00:02:43.583 plus 5/30, which of course 00:02:43.583 --> 00:02:47.361 going to be equal to 32/30. 00:02:47.361 --> 00:02:50.781 32 over 30, and 00:02:50.781 --> 00:02:54.321 if we want, we could try to reduce this fraction. 00:02:54.801 --> 00:02:56.805 We have a common factor of 32 and 30, 00:02:56.805 --> 00:03:00.196 they're both divisible by two. 00:03:00.196 --> 00:03:03.505 So if we divide the numerator and the denominator by two, 00:03:03.505 --> 00:03:06.118 numerator divided by two is 16, 00:03:06.118 --> 00:03:08.902 denominator divided by two is 15. 00:03:09.452 --> 00:03:12.640 So, this is the same thing as 16/15, and if I wanted 00:03:12.640 --> 00:03:16.215 to write this as a mixed number, 15 goes into 16 one time 00:03:16.215 --> 00:03:17.574 with a remainder one. 00:03:17.574 --> 00:03:20.255 So this is the same thing as 1 1/15. 00:03:20.795 --> 00:03:22.534 Let's do another example. 00:03:22.534 --> 00:03:27.018 Let's say that we wanted to add, we wanted to add 00:03:27.018 --> 00:03:31.881 1/2 to 00:03:31.881 --> 00:03:36.881 to 11/12, to 11 over 12. 00:03:36.893 --> 00:03:38.033 And I encourage you to pause the video 00:03:38.033 --> 00:03:40.864 and see if you could work this out. 00:03:40.864 --> 00:03:42.502 Well like we saw before, we wanna find 00:03:42.502 --> 00:03:43.883 a common denominator. 00:03:43.883 --> 00:03:45.102 If these had the same denominator, 00:03:45.102 --> 00:03:46.264 we could just add them immediately, 00:03:46.264 --> 00:03:48.527 but we wanna find a common denominator 00:03:48.527 --> 00:03:50.222 because right now they're not the same. 00:03:50.902 --> 00:03:53.468 Well what we wanna find is a multiple, 00:03:53.468 --> 00:03:55.794 a common multiple of two and 12, and ideally 00:03:55.794 --> 00:03:58.164 we'll find the lowest common multiple of two and 12, 00:03:58.164 --> 00:04:00.264 and just like we did before, let's start with the larger 00:04:00.264 --> 00:04:01.901 of the two numbers, 12. 00:04:01.901 --> 00:04:05.291 Now we could just say well 12 times one is 12, 00:04:05.291 --> 00:04:07.949 so that we could view that as the lowest multiple of 12. 00:04:07.949 --> 00:04:10.632 And is that divisible by two? Yeah, sure. 00:04:10.632 --> 00:04:12.790 12 is divisible by two. 00:04:12.790 --> 00:04:15.855 So 12 is actually the least common multiple of two and 12, 00:04:15.855 --> 00:04:17.213 so we could write both of these 00:04:17.213 --> 00:04:19.013 fractions as something over 12. 00:04:19.013 --> 00:04:21.625 So 1/2 is what over 12? 00:04:21.625 --> 00:04:24.446 Well to go from two to 12, you multiply by six, 00:04:24.446 --> 00:04:27.104 so we'll also multiply the numerator by six. 00:04:27.104 --> 00:04:30.588 Now we see 1/2, and 6/12, these are the same thing. 00:04:30.588 --> 00:04:33.954 One is half of two, six is half of 12. 00:04:34.914 --> 00:04:38.485 And how would we write 11/12 as something over 12? 00:04:38.485 --> 00:04:40.855 Well it's already written as something over 12, 00:04:40.855 --> 00:04:43.258 11/12 already has 12 in the denominator, 00:04:43.258 --> 00:04:45.029 so we don't have to change that. 00:04:45.615 --> 00:04:48.268 11/12, and now we're ready to add. 00:04:48.600 --> 00:04:51.350 So this is going to be equal to six, 00:04:52.520 --> 00:04:55.820 this is going to be equal to six plus 11, 00:04:56.510 --> 00:05:01.510 six plus 11 over 12. 00:05:02.378 --> 00:05:06.021 Over 12. We have 6/12 plus 11/12, 00:05:06.021 --> 00:05:09.318 it's gonna be six plus 11 over 12, 00:05:10.728 --> 00:05:15.087 which is equal to, six plus 11 is 17/12. 00:05:15.087 --> 00:05:16.504 If we wanted to write it as a mixed number, 00:05:16.504 --> 00:05:19.487 that is what, 12 goes into 17 one time with 00:05:19.487 --> 00:05:24.487 a remainder of five, so 1 5/12. 00:05:24.530 --> 00:05:25.710 Let's do one more of these. 00:05:25.710 --> 00:05:29.007 This is strangely fun. Alright. 00:05:29.007 --> 00:05:31.043 Let's say that we wanted to add, 00:05:31.523 --> 00:05:35.894 We're gonna add 3/4 to, 00:05:36.504 --> 00:05:40.584 we're gonna add 3/4 to 1/5. 00:05:41.414 --> 00:05:43.974 To one over five. 00:05:43.974 --> 00:05:44.659 What is this going to be? 00:05:44.659 --> 00:05:46.157 And once again, pause the video and 00:05:46.157 --> 00:05:47.870 see if you could work it out. 00:05:47.870 --> 00:05:49.291 Well we have different denominators here, 00:05:49.291 --> 00:05:52.052 and we wanna find, we wanna rewrite these 00:05:52.052 --> 00:05:53.457 so they have the same denominators, 00:05:53.457 --> 00:05:54.792 so we have to find a common multiple, 00:05:54.792 --> 00:05:57.095 ideally the least common multiple. 00:05:57.095 --> 00:05:59.738 So what's the least common multiple of four and five? 00:06:00.548 --> 00:06:01.862 Well let's start with the larger number, 00:06:01.862 --> 00:06:04.718 and let's look at its multiples and keep increasing 00:06:04.718 --> 00:06:07.061 them until we get one that's divisible by four. 00:06:07.061 --> 00:06:10.064 So five is not divisible by four. 00:06:10.064 --> 00:06:13.622 10 is not divisible by four, or perfectly divisible by four 00:06:13.622 --> 00:06:14.702 is what we care about. 00:06:14.702 --> 00:06:17.059 15 is not perfectly divisible by four. 00:06:17.059 --> 00:06:20.763 20 is divisible by four, in fact, that is five times four. 00:06:20.763 --> 00:06:23.514 That is 20. So what we could do is, we could write 00:06:23.514 --> 00:06:27.460 both of these fractions as having 20 in the denominator, 00:06:27.460 --> 00:06:28.714 or 20 as the denominator. 00:06:29.454 --> 00:06:32.266 So we could write 3/4 is something over 20. 00:06:32.996 --> 00:06:35.319 So to go from four to 20 in the denominator, 00:06:35.319 --> 00:06:36.949 we multiplied by five. 00:06:36.949 --> 00:06:38.466 So we also do that to the numerator. 00:06:38.466 --> 00:06:41.398 We multiply by three times five to get 15. 00:06:41.398 --> 00:06:44.183 All I did to go from four to 20, multiplied by five. 00:06:44.183 --> 00:06:45.820 So I have to do the same thing to the numerator, 00:06:45.820 --> 00:06:47.736 three times five is 15. 00:06:47.736 --> 00:06:52.658 3/4 is the same thing as 15/20, and over here. 00:06:52.658 --> 00:06:55.004 1/5. What is that over 20? 00:06:55.004 --> 00:06:58.358 Well to go from five to 20, you have to multiply by four. 00:06:58.358 --> 00:06:59.995 So we have to do the same thing to the numerator. 00:06:59.995 --> 00:07:03.861 I have to multiply this numerator times four to get 4/20. 00:07:04.451 --> 00:07:07.181 So now I've rewritten this instead of 3/4 plus 1/5, 00:07:07.181 --> 00:07:10.815 it's now written as 15/20 plus 4/20. 00:07:10.815 --> 00:07:12.973 And what is that going to be? 00:07:12.973 --> 00:07:17.932 Well that's going to be 15 plus four is 19/20. 00:07:17.932 --> 00:07:22.024 19/20, and we're done.