Math Antics - Dividing Fractions - By mathantics
Transcript
| 00:03 | Uh huh . Hi and welcome to Math Antics . | |
| 00:08 | This video is all about dividing fractions , but in | |
| 00:11 | order to understand how dividing fractions works , we first | |
| 00:14 | need to learn about something called reciprocal . A reciprocal | |
| 00:18 | is just a fancy math term for what you get | |
| 00:20 | when you switch the top and bottom numbers of a | |
| 00:22 | fraction . For example , if you have the fraction | |
| 00:25 | 1/2 and then switch the top and bottom numbers , | |
| 00:28 | you'll end up with 2/1 to over one is the | |
| 00:32 | reciprocal of 1/2 and 1/2 is the reciprocal of 2/1 | |
| 00:38 | . And an interesting thing about reciprocal . Xyz multiplying | |
| 00:42 | a fraction by its own . Reciprocal will always give | |
| 00:45 | you one that's because you'll have the same multiplication problem | |
| 00:48 | on the top and bottom . So you'll end up | |
| 00:51 | with a whole fraction which is always one . Okay | |
| 00:54 | , that's nice . But what do reciprocal is have | |
| 00:57 | to do with dividing fractions ? Well , reciprocal let | |
| 01:00 | us do a really cool trick . That makes dividing | |
| 01:02 | fractions easy . Whenever you have to divide something by | |
| 01:05 | a fraction , you can just multiply it by the | |
| 01:08 | reciprocal of that fraction instead , and you'll get the | |
| 01:10 | correct answer . And that's great news because multiplying fractions | |
| 01:14 | is so simple . This trick of multiplying by the | |
| 01:18 | reciprocal works because fractions are really just many division problems | |
| 01:22 | . So when you multiply something by 1/2 , it's | |
| 01:25 | the same as dividing by two , since two is | |
| 01:27 | below the fractions division line and dividing by two is | |
| 01:31 | the same as dividing by 2/1 . Because you can | |
| 01:34 | turn any number into a fraction by just writing a | |
| 01:37 | one as the bottom number , right ? But look | |
| 01:40 | reciprocal , that's why multiplying by 1/2 is the same | |
| 01:44 | as dividing by 2/1 . And it's true the other | |
| 01:47 | way around too . So really it's kind of like | |
| 01:50 | you never have to divide fractions , you can just | |
| 01:52 | rewrite your division problems so that you're multiplying by the | |
| 01:55 | reciprocal instead . Then when you multiply you'll get the | |
| 01:59 | answer for the original division problem as always . Let's | |
| 02:03 | see a couple examples of how this works . So | |
| 02:05 | you'll really understand . Let's try this problem . 3/4 | |
| 02:09 | , divided by 2/7 . Okay , so the first | |
| 02:12 | thing we wanna do is rewrite our problem instead of | |
| 02:15 | dividing by 2/7 , we can multiply by the reciprocal | |
| 02:19 | instead . The reciprocal of 2/7 is 7/2 . So | |
| 02:24 | our problem becomes 3/4 times 7/2 . Oh , I | |
| 02:30 | should mention a mistake that a lot of students make | |
| 02:32 | when they first learned to divide fractions . Sometimes students | |
| 02:35 | take the reciprocal of the first fraction , the one | |
| 02:38 | that's being divided , or even the reciprocal of both | |
| 02:40 | fractions , but you only want to take the reciprocal | |
| 02:43 | of the second fraction , the one you're dividing by | |
| 02:47 | . Okay , now that our problem has been changed | |
| 02:49 | to multiplication , it's easy just multiply the tops three | |
| 02:53 | times seven equals 21 multiply the bottoms four times two | |
| 02:57 | equals eight . And we have the answer to our | |
| 02:59 | fraction division problem . So 3/4 , divided by 2/7 | |
| 03:04 | is 21/8 . So that's pretty easy . But let's | |
| 03:08 | try one more example , Let's try 15/16 , divided | |
| 03:12 | by 9/22 . Again , the first thing we want | |
| 03:15 | to do is rewrite our problem Will change the divided | |
| 03:18 | by 9/22 into times 22/9 . Now , all we | |
| 03:23 | have to do is multiply . But since these numbers | |
| 03:25 | are kind of big , I'm gonna use my calculator | |
| 03:28 | to help . Let's see here . So we have | |
| 03:31 | all right on the top we have 15 times 22 | |
| 03:35 | equals 330 . And on the bottom we have 16 | |
| 03:39 | times nine equals 144 . So , the answer to | |
| 03:42 | our division problem is 330 over 144 . Of course | |
| 03:47 | . That could be simplified for your final answer on | |
| 03:49 | a test . But we cover simplifying fractions in another | |
| 03:52 | video . All right . That's how you divide fractions | |
| 03:55 | . You just multiply by the reciprocal and you have | |
| 03:58 | your answer . But there's one more thing I want | |
| 04:00 | to show you . You already know that the line | |
| 04:02 | between the top and bottom number of a fraction is | |
| 04:05 | just another form of the division symbol . Well , | |
| 04:08 | that means you'll sometimes see fraction division problems written like | |
| 04:11 | this . This shows the top fraction 2/3 being divided | |
| 04:15 | by the bottom fraction 4/5 . It's really just that | |
| 04:18 | we have a fraction made up from other fractions . | |
| 04:21 | The top number is a fraction and the bottom number | |
| 04:24 | is a fraction . It just looks a little confusing | |
| 04:26 | because we have all these fraction lines here but we | |
| 04:29 | can make it look a lot better . Let's rewrite | |
| 04:31 | this as a multiplication problem by taking the reciprocal of | |
| 04:34 | the bottom number , the fraction that we're dividing by | |
| 04:37 | and multiplying it by the fraction on top there . | |
| 04:41 | That looks easier to do . And it's really the | |
| 04:43 | same problem . We just need to multiply to get | |
| 04:45 | the answer . So two times five equals 10 and | |
| 04:49 | three times four equals 12 . Okay , so there | |
| 04:52 | you have it . What sounded really hard turns out | |
| 04:54 | to be as easy as flipping fractions upside down . | |
| 04:57 | If you can multiply fractions then you can divide fractions | |
| 05:00 | too . Don't forget to practice what you've learned by | |
| 05:03 | doing the exercises for this section . Thanks for watching | |
| 05:06 | . And I'll see you next time . Mhm . | |
| 05:09 | Learn more at math Antics dot com . |
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