[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:06.66,0:00:11.25,Default,,0000,0000,0000,,Hi and welcome to Math Antics. This video is all about dividing fractions,
Dialogue: 0,0:00:11.35,0:00:14.09,Default,,0000,0000,0000,,But in order to understand how dividing fractions works,
Dialogue: 0,0:00:14.10,0:00:17.18,Default,,0000,0000,0000,,we first need to learn about something called reciprocals.
Dialogue: 0,0:00:17.36,0:00:17.37,Default,,0000,0000,0000,,
Dialogue: 0,0:00:17.36,0:00:21.03,Default,,0000,0000,0000,,A reciprocal is just a fancy math term for what you get
Dialogue: 0,0:00:21.04,0:00:23.80,Default,,0000,0000,0000,,when you switch the top and bottom numbers of a fraction.
Dialogue: 0,0:00:24.18,0:00:27.12,Default,,0000,0000,0000,,For example, if you have the fraction 1/2
Dialogue: 0,0:00:27.29,0:00:30.86,Default,,0000,0000,0000,,and then switch the top and bottom numbers, you'll end up with 2/1.
Dialogue: 0,0:00:31.31,0:00:38.48,Default,,0000,0000,0000,,2/1 is the reciprocal of 1/2 and 1/2 is the reciprocal of 2/1.
Dialogue: 0,0:00:39.18,0:00:43.12,Default,,0000,0000,0000,,And an interesting thing about reciprocals is multiplying a fraction
Dialogue: 0,0:00:43.13,0:00:46.48,Default,,0000,0000,0000,,by its own reciprocal will always give you one.
Dialogue: 0,0:00:46.87,0:00:50.80,Default,,0000,0000,0000,,That's because you'll have the same multiplication problem on the top and bottom.
Dialogue: 0,0:00:50.83,0:00:54.00,Default,,0000,0000,0000,,So you'll end up with a whole fraction, which is always one.
Dialogue: 0,0:00:55.00,0:00:56.22,Default,,0000,0000,0000,,OK, that's nice.
Dialogue: 0,0:00:56.33,0:00:59.19,Default,,0000,0000,0000,,But what do reciprocals have to do with dividing fractions?
Dialogue: 0,0:00:59.25,0:01:04.11,Default,,0000,0000,0000,,Well, reciprocals let us do a really cool trick that makes dividing fractions easy.
Dialogue: 0,0:01:04.68,0:01:06.92,Default,,0000,0000,0000,,Whenever you have to divide something by a fraction,
Dialogue: 0,0:01:07.04,0:01:10.50,Default,,0000,0000,0000,,you can just multiply it by the reciprocal of that fraction instead
Dialogue: 0,0:01:10.62,0:01:12.30,Default,,0000,0000,0000,,and you'll get the correct answer.
Dialogue: 0,0:01:12.69,0:01:16.24,Default,,0000,0000,0000,,And that's great news because multiplying fractions is so simple.
Dialogue: 0,0:01:16.89,0:01:19.72,Default,,0000,0000,0000,,This trick of multiplying by the reciprocal works
Dialogue: 0,0:01:19.73,0:01:22.69,Default,,0000,0000,0000,,because fractions are really just mini-division problems.
Dialogue: 0,0:01:22.88,0:01:25.39,Default,,0000,0000,0000,,So when you multiply something by 1/2,
Dialogue: 0,0:01:25.61,0:01:30.07,Default,,0000,0000,0000,,it's the same as dividing by two, since two is below the fraction's division line.
Dialogue: 0,0:01:30.58,0:01:35.59,Default,,0000,0000,0000,,And dividing by two is the same as dividing by 2/1 because you can turn
Dialogue: 0,0:01:35.60,0:01:39.08,Default,,0000,0000,0000,,any number into a fraction by just writing a one as the bottom number,
Dialogue: 0,0:01:39.09,0:01:39.35,Default,,0000,0000,0000,,right?
Dialogue: 0,0:01:40.02,0:01:46.53,Default,,0000,0000,0000,,But look, reciprocals. That's why multiplying by 1/2 is the same as dividing by 2/1.
Dialogue: 0,0:01:46.73,0:01:48.55,Default,,0000,0000,0000,,And it's true the other way around too.
Dialogue: 0,0:01:49.24,0:01:50.06,Default,,0000,0000,0000,,So really,
Dialogue: 0,0:01:50.22,0:01:52.63,Default,,0000,0000,0000,,it's kind of like you never have to divide fractions.
Dialogue: 0,0:01:52.83,0:01:55.07,Default,,0000,0000,0000,,You can just rewrite your division problems so
Dialogue: 0,0:01:55.08,0:01:57.62,Default,,0000,0000,0000,,that you're multiplying by the reciprocal instead.
Dialogue: 0,0:01:57.98,0:02:02.03,Default,,0000,0000,0000,,Then when you multiply, you'll get the answer for the original division problem.
Dialogue: 0,0:02:02.46,0:02:05.66,Default,,0000,0000,0000,,As always, let's see a couple examples of how this works
Dialogue: 0,0:02:05.67,0:02:07.06,Default,,0000,0000,0000,,so you'll really understand.
Dialogue: 0,0:02:07.55,0:02:11.52,Default,,0000,0000,0000,,Let's try this problem: 3/4 divided by 2/7.
Dialogue: 0,0:02:11.79,0:02:12.35,Default,,0000,0000,0000,,OK,
Dialogue: 0,0:02:12.49,0:02:15.50,Default,,0000,0000,0000,,so the first thing we want to do is rewrite our problem.
Dialogue: 0,0:02:15.66,0:02:20.18,Default,,0000,0000,0000,,Instead of dividing by 2/7, we can multiply by the reciprocal instead.
Dialogue: 0,0:02:20.96,0:02:24.18,Default,,0000,0000,0000,,The reciprocal of 2/7 is 7/2.
Dialogue: 0,0:02:24.55,0:02:28.82,Default,,0000,0000,0000,,So our problem becomes 3/4 times 7/2.
Dialogue: 0,0:02:29.70,0:02:32.12,Default,,0000,0000,0000,,Oh, I should mention a mistake that a lot of
Dialogue: 0,0:02:32.13,0:02:34.77,Default,,0000,0000,0000,,students make when they first learn to divide fractions.
Dialogue: 0,0:02:34.90,0:02:38.17,Default,,0000,0000,0000,,Sometimes students take the reciprocal of the first fraction,
Dialogue: 0,0:02:38.18,0:02:42.06,Default,,0000,0000,0000,,the one that's being divided or even the reciprocal of both fractions.
Dialogue: 0,0:02:42.31,0:02:45.77,Default,,0000,0000,0000,,But you only want to take the reciprocal of the second fraction,
Dialogue: 0,0:02:45.78,0:02:47.36,Default,,0000,0000,0000,,the one you're dividing by.
Dialogue: 0,0:02:48.00,0:02:52.02,Default,,0000,0000,0000,,OK, now that our problem has been changed to multiplication, it's easy.
Dialogue: 0,0:02:52.03,0:02:55.56,Default,,0000,0000,0000,,Just multiply the tops, three times seven equals 21,
Dialogue: 0,0:02:55.64,0:02:58.56,Default,,0000,0000,0000,,and multiply the bottoms, four times two equals eight.
Dialogue: 0,0:02:58.87,0:03:01.92,Default,,0000,0000,0000,,And we have the answer to our fraction division problem.
Dialogue: 0,0:03:02.35,0:03:06.90,Default,,0000,0000,0000,,So 3/4 divided by 2/7 is 21/8.
Dialogue: 0,0:03:07.17,0:03:08.36,Default,,0000,0000,0000,,So that's pretty easy,
Dialogue: 0,0:03:08.40,0:03:14.30,Default,,0000,0000,0000,,but let's try one more example. Let's try 15/16 divided by 9/22.
Dialogue: 0,0:03:14.31,0:03:17.82,Default,,0000,0000,0000,,Again, the first thing we want to do is rewrite our problem.
Dialogue: 0,0:03:17.87,0:03:23.02,Default,,0000,0000,0000,,We'll change the divided by 9/22 into times 22/9.
Dialogue: 0,0:03:23.26,0:03:25.14,Default,,0000,0000,0000,,Now, all we have to do is multiply,
Dialogue: 0,0:03:25.47,0:03:29.01,Default,,0000,0000,0000,,but since these numbers are kind of big, I'm going to use my calculator to help.
Dialogue: 0,0:03:29.02,0:03:30.22,Default,,0000,0000,0000,,Let's see here.
Dialogue: 0,0:03:30.62,0:03:32.56,Default,,0000,0000,0000,,So we have, all right,
Dialogue: 0,0:03:33.24,0:03:37.58,Default,,0000,0000,0000,,on the top, we have 15 times 22 equals 330.
Dialogue: 0,0:03:37.82,0:03:41.91,Default,,0000,0000,0000,,And on the bottom, we have 16 times nine equals 144.
Dialogue: 0,0:03:42.47,0:03:47.20,Default,,0000,0000,0000,,So the answer to our division problem is 330/144.
Dialogue: 0,0:03:47.28,0:03:50.65,Default,,0000,0000,0000,,Of course, that could be simplified for your final answer on a test,
Dialogue: 0,0:03:50.66,0:03:53.28,Default,,0000,0000,0000,,but we cover simplifying fractions in another video.
Dialogue: 0,0:03:53.85,0:03:54.52,Default,,0000,0000,0000,,All right,
Dialogue: 0,0:03:54.64,0:03:56.16,Default,,0000,0000,0000,,that's how you divide fractions.
Dialogue: 0,0:03:56.17,0:03:59.24,Default,,0000,0000,0000,,You just multiply by the reciprocal and you have your answer.
Dialogue: 0,0:03:59.51,0:04:01.33,Default,,0000,0000,0000,,But there's one more thing I want to show you.
Dialogue: 0,0:04:01.77,0:04:04.60,Default,,0000,0000,0000,,You already know that the line between the top and bottom number
Dialogue: 0,0:04:04.61,0:04:07.90,Default,,0000,0000,0000,,of a fraction is just another form of the division symbol.
Dialogue: 0,0:04:07.93,0:04:08.54,Default,,0000,0000,0000,,Well,
Dialogue: 0,0:04:08.55,0:04:12.16,Default,,0000,0000,0000,,that means you'll sometimes see fraction division problems written like this.
Dialogue: 0,0:04:12.64,0:04:18.52,Default,,0000,0000,0000,,This shows the top fraction, 2/3, being divided by the bottom fraction, 4/5.
Dialogue: 0,0:04:18.57,0:04:21.97,Default,,0000,0000,0000,,It's really just that we have a fraction made up from other fractions.
Dialogue: 0,0:04:22.24,0:04:25.26,Default,,0000,0000,0000,,The top number is a fraction and the bottom number is a fraction.
Dialogue: 0,0:04:25.60,0:04:29.08,Default,,0000,0000,0000,,It just looks a little confusing because we have all these fraction lines here.
Dialogue: 0,0:04:29.60,0:04:31.64,Default,,0000,0000,0000,,But we can make it look a lot better.
Dialogue: 0,0:04:31.65,0:04:34.20,Default,,0000,0000,0000,,Let's rewrite this as a multiplication problem by
Dialogue: 0,0:04:34.21,0:04:36.39,Default,,0000,0000,0000,,taking the reciprocal of the bottom number,
Dialogue: 0,0:04:36.40,0:04:38.06,Default,,0000,0000,0000,,the fraction that we're dividing by,
Dialogue: 0,0:04:38.31,0:04:40.50,Default,,0000,0000,0000,,and multiplying it by the fraction on top.
Dialogue: 0,0:04:41.39,0:04:45.06,Default,,0000,0000,0000,,Tthere, that looks easier to do. And it's really the same problem.
Dialogue: 0,0:04:45.07,0:04:47.00,Default,,0000,0000,0000,,We just need to multiply to get the answer.
Dialogue: 0,0:04:47.30,0:04:49.16,Default,,0000,0000,0000,,So two times five equals 10
Dialogue: 0,0:04:49.47,0:04:51.24,Default,,0000,0000,0000,,and three times four equals 12.
Dialogue: 0,0:04:51.83,0:04:53.60,Default,,0000,0000,0000,,Ok. So there you have it.
Dialogue: 0,0:04:53.61,0:04:58.16,Default,,0000,0000,0000,,What sounded really hard turns out to be as easy as flipping fractions upside down.
Dialogue: 0,0:04:58.33,0:05:01.64,Default,,0000,0000,0000,,If you can multiply fractions, then you can divide fractions too.
Dialogue: 0,0:05:02.19,0:05:03.92,Default,,0000,0000,0000,,Don't forget to practice what you've learned
Dialogue: 0,0:05:03.93,0:05:05.84,Default,,0000,0000,0000,,by doing the exercises for this section.
Dialogue: 0,0:05:06.13,0:05:08.24,Default,,0000,0000,0000,,Thanks for watching and I'll see you next time.
Dialogue: 0,0:05:09.70,0:05:11.95,Default,,0000,0000,0000,,Learn more at mathantics.com.