WEBVTT 00:00:06.659 --> 00:00:11.250 Hi and welcome to Math Antics. This video is all about dividing fractions, 00:00:11.350 --> 00:00:14.090 But in order to understand how dividing fractions works, 00:00:14.100 --> 00:00:17.180 we first need to learn about something called reciprocals. 00:00:17.360 --> 00:00:17.370 00:00:17.360 --> 00:00:21.030 A reciprocal is just a fancy math term for what you get 00:00:21.040 --> 00:00:23.799 when you switch the top and bottom numbers of a fraction. 00:00:24.180 --> 00:00:27.120 For example, if you have the fraction 1/2 00:00:27.290 --> 00:00:30.860 and then switch the top and bottom numbers, you'll end up with 2/1. 00:00:31.309 --> 00:00:38.479 2/1 is the reciprocal of 1/2 and 1/2 is the reciprocal of 2/1. 00:00:39.180 --> 00:00:43.119 And an interesting thing about reciprocals is multiplying a fraction 00:00:43.130 --> 00:00:46.479 by its own reciprocal will always give you one. 00:00:46.869 --> 00:00:50.799 That's because you'll have the same multiplication problem on the top and bottom. 00:00:50.830 --> 00:00:54.000 So you'll end up with a whole fraction, which is always one. 00:00:55.000 --> 00:00:56.220 OK, that's nice. 00:00:56.330 --> 00:00:59.189 But what do reciprocals have to do with dividing fractions? 00:00:59.250 --> 00:01:04.110 Well, reciprocals let us do a really cool trick that makes dividing fractions easy. 00:01:04.680 --> 00:01:06.919 Whenever you have to divide something by a fraction, 00:01:07.040 --> 00:01:10.500 you can just multiply it by the reciprocal of that fraction instead 00:01:10.620 --> 00:01:12.300 and you'll get the correct answer. 00:01:12.690 --> 00:01:16.239 And that's great news because multiplying fractions is so simple. 00:01:16.889 --> 00:01:19.720 This trick of multiplying by the reciprocal works 00:01:19.730 --> 00:01:22.690 because fractions are really just mini-division problems. 00:01:22.879 --> 00:01:25.389 So when you multiply something by 1/2, 00:01:25.610 --> 00:01:30.069 it's the same as dividing by two, since two is below the fraction's division line. 00:01:30.580 --> 00:01:35.589 And dividing by two is the same as dividing by 2/1 because you can turn 00:01:35.599 --> 00:01:39.080 any number into a fraction by just writing a one as the bottom number, 00:01:39.089 --> 00:01:39.349 right? 00:01:40.019 --> 00:01:46.529 But look, reciprocals. That's why multiplying by 1/2 is the same as dividing by 2/1. 00:01:46.730 --> 00:01:48.550 And it's true the other way around too. 00:01:49.239 --> 00:01:50.059 So really, 00:01:50.220 --> 00:01:52.629 it's kind of like you never have to divide fractions. 00:01:52.830 --> 00:01:55.069 You can just rewrite your division problems so 00:01:55.080 --> 00:01:57.620 that you're multiplying by the reciprocal instead. 00:01:57.980 --> 00:02:02.029 Then when you multiply, you'll get the answer for the original division problem. 00:02:02.459 --> 00:02:05.660 As always, let's see a couple examples of how this works 00:02:05.669 --> 00:02:07.059 so you'll really understand. 00:02:07.550 --> 00:02:11.520 Let's try this problem: 3/4 divided by 2/7. 00:02:11.789 --> 00:02:12.350 OK, 00:02:12.490 --> 00:02:15.500 so the first thing we want to do is rewrite our problem. 00:02:15.660 --> 00:02:20.179 Instead of dividing by 2/7, we can multiply by the reciprocal instead. 00:02:20.960 --> 00:02:24.179 The reciprocal of 2/7 is 7/2. 00:02:24.550 --> 00:02:28.820 So our problem becomes 3/4 times 7/2. 00:02:29.699 --> 00:02:32.119 Oh, I should mention a mistake that a lot of 00:02:32.130 --> 00:02:34.770 students make when they first learn to divide fractions. 00:02:34.899 --> 00:02:38.169 Sometimes students take the reciprocal of the first fraction, 00:02:38.179 --> 00:02:42.059 the one that's being divided or even the reciprocal of both fractions. 00:02:42.309 --> 00:02:45.770 But you only want to take the reciprocal of the second fraction, 00:02:45.779 --> 00:02:47.360 the one you're dividing by. 00:02:48.000 --> 00:02:52.020 OK, now that our problem has been changed to multiplication, it's easy. 00:02:52.029 --> 00:02:55.559 Just multiply the tops, three times seven equals 21, 00:02:55.639 --> 00:02:58.559 and multiply the bottoms, four times two equals eight. 00:02:58.869 --> 00:03:01.919 And we have the answer to our fraction division problem. 00:03:02.350 --> 00:03:06.899 So 3/4 divided by 2/7 is 21/8. 00:03:07.169 --> 00:03:08.360 So that's pretty easy, 00:03:08.399 --> 00:03:14.300 but let's try one more example. Let's try 15/16 divided by 9/22. 00:03:14.309 --> 00:03:17.820 Again, the first thing we want to do is rewrite our problem. 00:03:17.869 --> 00:03:23.020 We'll change the divided by 9/22 into times 22/9. 00:03:23.259 --> 00:03:25.139 Now, all we have to do is multiply, 00:03:25.470 --> 00:03:29.009 but since these numbers are kind of big, I'm going to use my calculator to help. 00:03:29.020 --> 00:03:30.220 Let's see here. 00:03:30.619 --> 00:03:32.559 So we have, all right, 00:03:33.240 --> 00:03:37.580 on the top, we have 15 times 22 equals 330. 00:03:37.820 --> 00:03:41.910 And on the bottom, we have 16 times nine equals 144. 00:03:42.470 --> 00:03:47.199 So the answer to our division problem is 330/144. 00:03:47.279 --> 00:03:50.649 Of course, that could be simplified for your final answer on a test, 00:03:50.660 --> 00:03:53.279 but we cover simplifying fractions in another video. 00:03:53.850 --> 00:03:54.520 All right, 00:03:54.639 --> 00:03:56.160 that's how you divide fractions. 00:03:56.169 --> 00:03:59.240 You just multiply by the reciprocal and you have your answer. 00:03:59.509 --> 00:04:01.330 But there's one more thing I want to show you. 00:04:01.770 --> 00:04:04.600 You already know that the line between the top and bottom number 00:04:04.610 --> 00:04:07.899 of a fraction is just another form of the division symbol. 00:04:07.929 --> 00:04:08.539 Well, 00:04:08.550 --> 00:04:12.160 that means you'll sometimes see fraction division problems written like this. 00:04:12.639 --> 00:04:18.519 This shows the top fraction, 2/3, being divided by the bottom fraction, 4/5. 00:04:18.570 --> 00:04:21.970 It's really just that we have a fraction made up from other fractions. 00:04:22.239 --> 00:04:25.260 The top number is a fraction and the bottom number is a fraction. 00:04:25.600 --> 00:04:29.079 It just looks a little confusing because we have all these fraction lines here. 00:04:29.600 --> 00:04:31.640 But we can make it look a lot better. 00:04:31.649 --> 00:04:34.200 Let's rewrite this as a multiplication problem by 00:04:34.209 --> 00:04:36.390 taking the reciprocal of the bottom number, 00:04:36.399 --> 00:04:38.059 the fraction that we're dividing by, 00:04:38.309 --> 00:04:40.500 and multiplying it by the fraction on top. 00:04:41.390 --> 00:04:45.059 Tthere, that looks easier to do. And it's really the same problem. 00:04:45.070 --> 00:04:47.000 We just need to multiply to get the answer. 00:04:47.299 --> 00:04:49.160 So two times five equals 10 00:04:49.470 --> 00:04:51.239 and three times four equals 12. 00:04:51.829 --> 00:04:53.600 Ok. So there you have it. 00:04:53.609 --> 00:04:58.160 What sounded really hard turns out to be as easy as flipping fractions upside down. 00:04:58.329 --> 00:05:01.640 If you can multiply fractions, then you can divide fractions too. 00:05:02.190 --> 00:05:03.920 Don't forget to practice what you've learned 00:05:03.929 --> 00:05:05.839 by doing the exercises for this section. 00:05:06.130 --> 00:05:08.239 Thanks for watching and I'll see you next time. 00:05:09.700 --> 00:05:11.950 Learn more at mathantics.com.