0:00:06.659,0:00:11.250 Hi and welcome to Math Antics. This video is all about dividing fractions, 0:00:11.350,0:00:14.090 But in order to understand how dividing fractions works, 0:00:14.100,0:00:17.180 we first need to learn about something called reciprocals. 0:00:17.360,0:00:17.370 0:00:17.360,0:00:21.030 A reciprocal is just a fancy math term for what you get 0:00:21.040,0:00:23.799 when you switch the top and bottom numbers of a fraction. 0:00:24.180,0:00:27.120 For example, if you have the fraction 1/2 0:00:27.290,0:00:30.860 and then switch the top and bottom numbers, you'll end up with 2/1. 0:00:31.309,0:00:38.479 2/1 is the reciprocal of 1/2 and 1/2 is the reciprocal of 2/1. 0:00:39.180,0:00:43.119 And an interesting thing about reciprocals is multiplying a fraction 0:00:43.130,0:00:46.479 by its own reciprocal will always give you one. 0:00:46.869,0:00:50.799 That's because you'll have the same multiplication problem on the top and bottom. 0:00:50.830,0:00:54.000 So you'll end up with a whole fraction, which is always one. 0:00:55.000,0:00:56.220 OK, that's nice. 0:00:56.330,0:00:59.189 But what do reciprocals have to do with dividing fractions? 0:00:59.250,0:01:04.110 Well, reciprocals let us do a really cool trick that makes dividing fractions easy. 0:01:04.680,0:01:06.919 Whenever you have to divide something by a fraction, 0:01:07.040,0:01:10.500 you can just multiply it by the reciprocal of that fraction instead 0:01:10.620,0:01:12.300 and you'll get the correct answer. 0:01:12.690,0:01:16.239 And that's great news because multiplying fractions is so simple. 0:01:16.889,0:01:19.720 This trick of multiplying by the reciprocal works 0:01:19.730,0:01:22.690 because fractions are really just mini-division problems. 0:01:22.879,0:01:25.389 So when you multiply something by 1/2, 0:01:25.610,0:01:30.069 it's the same as dividing by two, since two is below the fraction's division line. 0:01:30.580,0:01:35.589 And dividing by two is the same as dividing by 2/1 because you can turn 0:01:35.599,0:01:39.080 any number into a fraction by just writing a one as the bottom number, 0:01:39.089,0:01:39.349 right? 0:01:40.019,0:01:46.529 But look, reciprocals. That's why multiplying by 1/2 is the same as dividing by 2/1. 0:01:46.730,0:01:48.550 And it's true the other way around too. 0:01:49.239,0:01:50.059 So really, 0:01:50.220,0:01:52.629 it's kind of like you never have to divide fractions. 0:01:52.830,0:01:55.069 You can just rewrite your division problems so 0:01:55.080,0:01:57.620 that you're multiplying by the reciprocal instead. 0:01:57.980,0:02:02.029 Then when you multiply, you'll get the answer for the original division problem. 0:02:02.459,0:02:05.660 As always, let's see a couple examples of how this works 0:02:05.669,0:02:07.059 so you'll really understand. 0:02:07.550,0:02:11.520 Let's try this problem: 3/4 divided by 2/7. 0:02:11.789,0:02:12.350 OK, 0:02:12.490,0:02:15.500 so the first thing we want to do is rewrite our problem. 0:02:15.660,0:02:20.179 Instead of dividing by 2/7, we can multiply by the reciprocal instead. 0:02:20.960,0:02:24.179 The reciprocal of 2/7 is 7/2. 0:02:24.550,0:02:28.820 So our problem becomes 3/4 times 7/2. 0:02:29.699,0:02:32.119 Oh, I should mention a mistake that a lot of 0:02:32.130,0:02:34.770 students make when they first learn to divide fractions. 0:02:34.899,0:02:38.169 Sometimes students take the reciprocal of the first fraction, 0:02:38.179,0:02:42.059 the one that's being divided or even the reciprocal of both fractions. 0:02:42.309,0:02:45.770 But you only want to take the reciprocal of the second fraction, 0:02:45.779,0:02:47.360 the one you're dividing by. 0:02:48.000,0:02:52.020 OK, now that our problem has been changed to multiplication, it's easy. 0:02:52.029,0:02:55.559 Just multiply the tops, three times seven equals 21, 0:02:55.639,0:02:58.559 and multiply the bottoms, four times two equals eight. 0:02:58.869,0:03:01.919 And we have the answer to our fraction division problem. 0:03:02.350,0:03:06.899 So 3/4 divided by 2/7 is 21/8. 0:03:07.169,0:03:08.360 So that's pretty easy, 0:03:08.399,0:03:14.300 but let's try one more example. Let's try 15/16 divided by 9/22. 0:03:14.309,0:03:17.820 Again, the first thing we want to do is rewrite our problem. 0:03:17.869,0:03:23.020 We'll change the divided by 9/22 into times 22/9. 0:03:23.259,0:03:25.139 Now, all we have to do is multiply, 0:03:25.470,0:03:29.009 but since these numbers are kind of big, I'm going to use my calculator to help. 0:03:29.020,0:03:30.220 Let's see here. 0:03:30.619,0:03:32.559 So we have, all right, 0:03:33.240,0:03:37.580 on the top, we have 15 times 22 equals 330. 0:03:37.820,0:03:41.910 And on the bottom, we have 16 times nine equals 144. 0:03:42.470,0:03:47.199 So the answer to our division problem is 330/144. 0:03:47.279,0:03:50.649 Of course, that could be simplified for your final answer on a test, 0:03:50.660,0:03:53.279 but we cover simplifying fractions in another video. 0:03:53.850,0:03:54.520 All right, 0:03:54.639,0:03:56.160 that's how you divide fractions. 0:03:56.169,0:03:59.240 You just multiply by the reciprocal and you have your answer. 0:03:59.509,0:04:01.330 But there's one more thing I want to show you. 0:04:01.770,0:04:04.600 You already know that the line between the top and bottom number 0:04:04.610,0:04:07.899 of a fraction is just another form of the division symbol. 0:04:07.929,0:04:08.539 Well, 0:04:08.550,0:04:12.160 that means you'll sometimes see fraction division problems written like this. 0:04:12.639,0:04:18.519 This shows the top fraction, 2/3, being divided by the bottom fraction, 4/5. 0:04:18.570,0:04:21.970 It's really just that we have a fraction made up from other fractions. 0:04:22.239,0:04:25.260 The top number is a fraction and the bottom number is a fraction. 0:04:25.600,0:04:29.079 It just looks a little confusing because we have all these fraction lines here. 0:04:29.600,0:04:31.640 But we can make it look a lot better. 0:04:31.649,0:04:34.200 Let's rewrite this as a multiplication problem by 0:04:34.209,0:04:36.390 taking the reciprocal of the bottom number, 0:04:36.399,0:04:38.059 the fraction that we're dividing by, 0:04:38.309,0:04:40.500 and multiplying it by the fraction on top. 0:04:41.390,0:04:45.059 Tthere, that looks easier to do. And it's really the same problem. 0:04:45.070,0:04:47.000 We just need to multiply to get the answer. 0:04:47.299,0:04:49.160 So two times five equals 10 0:04:49.470,0:04:51.239 and three times four equals 12. 0:04:51.829,0:04:53.600 Ok. So there you have it. 0:04:53.609,0:04:58.160 What sounded really hard turns out to be as easy as flipping fractions upside down. 0:04:58.329,0:05:01.640 If you can multiply fractions, then you can divide fractions too. 0:05:02.190,0:05:03.920 Don't forget to practice what you've learned 0:05:03.929,0:05:05.839 by doing the exercises for this section. 0:05:06.130,0:05:08.239 Thanks for watching and I'll see you next time. 0:05:09.700,0:05:11.950 Learn more at mathantics.com.