Lesson 1 - Multiply Whole Numbers By Fractions (5th Grade Math) - By Lumos Learning
Transcript
| 00:01 | Hello . Welcome to this lesson of mastering fifth grade | |
| 00:03 | math . My name is Jason . I'll be your | |
| 00:04 | host in your teacher in this batch of lessons , | |
| 00:07 | and what we're going to focus on now is primarily | |
| 00:10 | on how to multiply and divide fractions . Now you | |
| 00:14 | already have learned how to add and subtract fractions . | |
| 00:16 | We've been doing that . We've also learned how to | |
| 00:18 | simplify fractions . We've done that as previous material . | |
| 00:21 | So if you're unsure how to add or subtract or | |
| 00:23 | simplify fractions , go to the previous lessons . To | |
| 00:26 | get that here , we're going to start to learn | |
| 00:27 | how to multiply and divide fractions . Now the key | |
| 00:32 | to learning how to multiply fractions , which is what | |
| 00:34 | we're basically starting in this lesson , um , is | |
| 00:37 | it's actually easier than adding or subtracting fractions . To | |
| 00:41 | be truthful , multiplying and dividing them is actually easier | |
| 00:44 | . And that's because in order to multiply , divide | |
| 00:47 | fractions . You do not have to worry about a | |
| 00:49 | common denominator . See , that's what we had to | |
| 00:51 | do with adding and subtracting fractions . I kept telling | |
| 00:53 | you , common denominator common denominator . But here when | |
| 00:57 | we multiply fractions , we multiply whole numbers , times | |
| 01:00 | , fractions , which is what we're doing here . | |
| 01:02 | We do not have to worry about common denominators makes | |
| 01:05 | it much simpler . So let's just jump into that | |
| 01:08 | . What if I asked ? You multiply three times | |
| 01:11 | the fraction two thirds . All right , Now you | |
| 01:15 | would look at this and you would probably say I | |
| 01:17 | have no idea how to do that . But then | |
| 01:19 | you should remember something from a previous lesson that we | |
| 01:21 | have discussed and that is that any whole number that | |
| 01:25 | you have , whether it's three or five or seven | |
| 01:28 | or 10 or anything else , you can always write | |
| 01:31 | it as the number divided by one or the number | |
| 01:33 | over one . Because fractions this is a fraction here | |
| 01:37 | is really also represented by division . We talked about | |
| 01:40 | that many times before , So if you want to | |
| 01:42 | represent the number three , you can always write it | |
| 01:44 | as a fraction simply 3/1 . Because that's three divided | |
| 01:48 | by one , which is just three . So this | |
| 01:50 | the number three and this the Fraction 3/1 is exactly | |
| 01:54 | the same thing , because this is like division here | |
| 01:56 | . 3/1 is three , right ? So we're still | |
| 01:59 | multiplying by two thirds and we want to show you | |
| 02:02 | how do we calculate that . So I said before | |
| 02:05 | , when you multiply fractions together and also you'll learn | |
| 02:08 | later when you divide fractions , you do not have | |
| 02:10 | to worry about a common denominator . So it's actually | |
| 02:13 | easier . These denominators are different . You have a | |
| 02:15 | one and you have a three . But that's OK | |
| 02:17 | . All you do to multiply fractions is you do | |
| 02:21 | three times two on the top , we multiply the | |
| 02:24 | numerator and one times three on the bottom , we | |
| 02:27 | just multiply the denominator . So on the top you | |
| 02:30 | will get six . And on the bottom you will | |
| 02:32 | get three . That is the answer . Six thirds | |
| 02:36 | . But you have to ask yourself , Is this | |
| 02:39 | simplified ? You always check your fraction when you're done | |
| 02:42 | to see if it's fully simplified . And this one | |
| 02:45 | we have a 6/3 , Uh , so we can | |
| 02:48 | try to simplify it . But then we realized this | |
| 02:50 | is the same as six . Divided by three and | |
| 02:53 | six , divided by three is too six divided by | |
| 02:57 | three is two and two is the answer . So | |
| 02:59 | you might ask yourself , Well , how is it | |
| 03:02 | you take three times a fraction and what you get | |
| 03:04 | at the end is just a number . Well , | |
| 03:06 | think of it this way . We know that you | |
| 03:08 | can multiply regular old fractions by numbers , and you | |
| 03:13 | can sometimes end up with numbers . For instance , | |
| 03:15 | if I have half of a pizza and then multiply | |
| 03:18 | that times two , what do I get ? A | |
| 03:21 | whole pizza ? Let's show you how that would work | |
| 03:23 | if we're actually gonna do that problem . If we | |
| 03:26 | have two times one half of a pizza , how | |
| 03:31 | would we do that ? Well , you know , | |
| 03:32 | the answer is one whole pizza . But let's show | |
| 03:34 | how you do it with the math here . And | |
| 03:36 | the way you do that is the two . You | |
| 03:39 | just write it as to over one . We're still | |
| 03:42 | multiplying one by one half , all right . And | |
| 03:46 | then what you do is you multiply the numerator is | |
| 03:48 | two times one and then the denominators one times two | |
| 03:53 | . So what you get over here on the top | |
| 03:55 | is too , and on the bottom , you also | |
| 03:57 | get to . And if you remember , two divided | |
| 03:59 | by two gives you one . So you know , | |
| 04:02 | from your experience that two times a half of something | |
| 04:05 | should give you a whole pizza or a whole peanut | |
| 04:08 | butter and jelly sandwich or whatever it is you're talking | |
| 04:10 | about , this is how you do it in terms | |
| 04:12 | of the math . So that's how you can get | |
| 04:14 | this . In this case , if you measure two | |
| 04:16 | thirds of the pizza out and you take two thirds | |
| 04:19 | of the pizza from one box and then two thirds | |
| 04:21 | of the pizza from a second box from second Pizza | |
| 04:23 | and then two thirds of a pizza from another box | |
| 04:26 | and you arrange all of those slices together , you're | |
| 04:28 | gonna end up with two whole pizzas . It's the | |
| 04:30 | same exact concept . The fundamental key thing here is | |
| 04:34 | to remember that when you are multiplying a fraction times | |
| 04:37 | , a whole number , you write the whole number | |
| 04:39 | over one and then you multiply the fractions by multiplying | |
| 04:42 | the tops , multiplying the bottoms . So let's get | |
| 04:45 | some more practice with this . What if we have | |
| 04:46 | the number 12 times ? One third , 12 times | |
| 04:50 | a third ? Well , the first thing we wanna | |
| 04:51 | do we cannot multiply these unless we're multiplying two fractions | |
| 04:55 | . So we represent . The 12 is 12/1 . | |
| 04:57 | We're still multiplying by one third . Alright , Now | |
| 05:01 | , up here we end up with 12 times one | |
| 05:05 | on the top and on the bottom . We end | |
| 05:07 | up with one times three and so on the top | |
| 05:11 | 12 times . One gives you 12 on the bottom | |
| 05:13 | . One times three gives you three and you try | |
| 05:15 | to simplify this . But then you realize I can | |
| 05:17 | divide this 12 divided by three is going to give | |
| 05:20 | me four . So the answer is just four . | |
| 05:22 | So , so far , for every time we've multiplied | |
| 05:25 | a fraction by a whole number , we've always gotten | |
| 05:28 | a whole number back . But that's not always the | |
| 05:30 | case . Let's do one win . That's not the | |
| 05:33 | case . What if we have 2/5 times five Now | |
| 05:37 | here . We've had the whole number of times , | |
| 05:39 | the fraction whole number of times the fraction . Here | |
| 05:41 | we have it backwards , the fraction times the whole | |
| 05:44 | number . But you do exactly the same thing . | |
| 05:46 | I mean , there's no difference . You write it | |
| 05:48 | as 2/5 times , and then the five becomes a | |
| 05:51 | 5/1 . You always write whole numbers as fractions , | |
| 05:56 | and then what you have is two times five on | |
| 05:58 | the top , and here you have five times , | |
| 06:00 | one on the bottom . You do not have to | |
| 06:02 | worry about getting any kind of common denominator to multiply | |
| 06:05 | fractions . What you get on the top two times | |
| 06:08 | five is 10 . On the bottom . You will | |
| 06:10 | get five times . One is five . And this | |
| 06:14 | is one of those cases where you're gonna get a | |
| 06:15 | whole number 10 divided by five is going to give | |
| 06:19 | you 2 10 . Divided by five is gonna give | |
| 06:22 | you two . Now , let's do one . Where | |
| 06:24 | when we do the multiplication , we don't actually end | |
| 06:27 | up with a whole number at the end . All | |
| 06:30 | right , let's say we're doing the fraction 3/5 times | |
| 06:34 | . Four . Okay . All right . And we | |
| 06:36 | want to multiply this . So the first thing we | |
| 06:38 | do is we write 3/5 times and we write The | |
| 06:41 | four is for over one . So now we have | |
| 06:45 | a fraction times a fraction . So then we multiply | |
| 06:48 | the tops three times four , we multiply the bottoms | |
| 06:52 | five times one and what we get on the top | |
| 06:54 | three times four is 12 and on the bottom five | |
| 06:57 | times one is five . So that's the answer . | |
| 06:59 | But we always try to simplify it . The first | |
| 07:02 | thing we look for is we say , Can we | |
| 07:04 | say 12 divided by five ? Well , it doesn't | |
| 07:06 | really divide evenly so we can't get a whole number | |
| 07:09 | , as we have for the other fractions . Secondly | |
| 07:11 | , we try to simplify it . Can we divide | |
| 07:13 | top and bottom by any single number to make this | |
| 07:16 | simpler ? And we can't do that , either . | |
| 07:18 | We can't divide by two or by three for both | |
| 07:21 | of these guys because we have that pesky five on | |
| 07:23 | the bottom that's not going to let us do that | |
| 07:25 | . So basically , you could circle . This is | |
| 07:27 | the answer , But then we also realize that this | |
| 07:30 | is an improper fraction . All right , we can | |
| 07:32 | always convert improper fractions to mix numbers . How many | |
| 07:36 | times will five go into 12 ? Well , it'll | |
| 07:39 | go two times because five times two is 10 now | |
| 07:43 | , the difference between 12 and 10 is only two | |
| 07:46 | . So that's the remainder . And we write it | |
| 07:48 | over the denominator , which is five . So the | |
| 07:52 | answer that we get from this multiplication can be written | |
| 07:55 | as an improper Fraction 12/5 , or you can write | |
| 07:59 | it as two and 2/5 . They both represent exactly | |
| 08:02 | the same thing because , you know , mixed numbers | |
| 08:05 | and improper fractions , we can always switch back and | |
| 08:07 | forth . Okay , Now , what if we have | |
| 08:10 | 2/5 times 12 . We want to do that one | |
| 08:16 | . So we have the same sort of thing . | |
| 08:18 | We take 2/5 times , 12/1 we write . The | |
| 08:22 | whole number is 12/1 , 2 times 12 on the | |
| 08:26 | top and five times one on the bottom . Now | |
| 08:30 | , if you remember from your multiplication tables 12 times | |
| 08:34 | two is 24 on the top and five times one | |
| 08:36 | is five on the bottom . So you get 24/5 | |
| 08:40 | . So we try to simplify this , and we | |
| 08:43 | really can't divide it 24/5 evenly . And we can't | |
| 08:46 | really pick a number to simplify the fraction so we | |
| 08:48 | could circle it like this . But then we also | |
| 08:50 | realize that this is also an improper fraction so we | |
| 08:53 | can convert to mix number . So six times five | |
| 08:56 | is 30 . That's too many times . Five times | |
| 08:58 | five is 25 . That's too many times four times | |
| 09:01 | five is 20 so this can be divided into their | |
| 09:04 | 2045 by five can go a whole four times . | |
| 09:07 | That gives us 20 . The difference between 24 20 | |
| 09:10 | is four , and we always write it over the | |
| 09:12 | bottom number here . So we get four and 4/5 | |
| 09:16 | . If you're having problems converting from improper fraction to | |
| 09:20 | mix numbers , then go back to some of the | |
| 09:22 | previous lessons and the fifth grade series . We have | |
| 09:25 | a lot of practice with how to go back and | |
| 09:27 | forth between mixed numbers and improper fractions . So when | |
| 09:31 | I circle both of these answers , basically you can | |
| 09:34 | write it . Either way , you're getting exactly the | |
| 09:35 | same answer . All right . Now I have a | |
| 09:40 | couple more days to get a little more practice . | |
| 09:42 | What about the number one ? Sixth times ? Three | |
| 09:45 | ? Well , boy , we would write . That | |
| 09:46 | is 1/6 times we'd write . The three is 3/1 | |
| 09:51 | , and then we multiply . The numerator is one | |
| 09:53 | times three and then six times one . All right | |
| 09:58 | . And so then if I switch colors here on | |
| 10:00 | the top , I'm gonna get three . One times | |
| 10:03 | 33 on the bottom . I'm gonna get sick . | |
| 10:04 | So you could say that That's the answer . But | |
| 10:07 | then we realized right away we try to simplify it | |
| 10:09 | . This is not not an improper fraction , but | |
| 10:12 | I can simplify this by dividing bottom the top by | |
| 10:15 | three . And also the bottom by three . So | |
| 10:18 | three divided by three gives us one on the top | |
| 10:21 | six . Divided by three gives us two on the | |
| 10:24 | bottom so you get one half . So this is | |
| 10:27 | the final answer . One half if you take 1/6 | |
| 10:30 | of a pizza and you do that three times from | |
| 10:32 | three different pizzas and arrange them together . What you | |
| 10:34 | actually have at the end of the day is half | |
| 10:36 | of a pizza . If you arrange all the slices | |
| 10:38 | . Alright , The final problem we're gonna do in | |
| 10:41 | this set here is to seventh times 2 to 7 | |
| 10:46 | times too . So what you do is you keep | |
| 10:48 | the fraction to seventh and you write the whole number | |
| 10:52 | is 2/1 and then you multiply the numerator two times | |
| 10:56 | two and then you multiply the denominator seven times one | |
| 11:01 | and what you'll get when you do both of those | |
| 11:02 | things on the top . Two times two is four | |
| 11:05 | and seven times one is seven . And so you | |
| 11:08 | look at this and you say , can I simplify | |
| 11:09 | it anymore ? And the answer is you really cannot | |
| 11:12 | . 4/7 is the final answer . I cannot divide | |
| 11:15 | top and bottom by anything to simplify that . It's | |
| 11:18 | also not improper , so I can't really do anything | |
| 11:20 | with that . So this is the final answer . | |
| 11:22 | If you have any problems simplifying a fraction to one | |
| 11:26 | half like we did here or converting to mix numbers | |
| 11:29 | or something like that , then you need to take | |
| 11:31 | a few minutes and go back to my previous lessons | |
| 11:33 | . We learned how to simplify fractions , and we | |
| 11:35 | learned how to convert to mix numbers . Because those | |
| 11:37 | skills we're gonna use and all of these problems every | |
| 11:40 | time we multiply fractions , we get the answer . | |
| 11:42 | We always check to see if we can simplify it | |
| 11:44 | , so you have to know how to do this | |
| 11:46 | stuff . So here is an introduction to the first | |
| 11:49 | concept here where we're multiplying a whole number times a | |
| 11:52 | fraction , and you've seen that the way you do | |
| 11:54 | that is you always convert the whole number two a | |
| 11:57 | fraction by changing it from the number over the number | |
| 11:59 | over one . And then once you have it as | |
| 12:02 | fraction times , fraction , you always multiply the numerator | |
| 12:05 | . You always multiply the denominators and you simplify the | |
| 12:08 | results . Very simple . You do not have to | |
| 12:11 | worry about finding a common denominator when you multiply or | |
| 12:14 | divide fractions . So keep that in mind . Make | |
| 12:16 | sure you understand this and these problems work the worksheet | |
| 12:20 | problems that we have for you and then follow me | |
| 12:21 | on to the next lesson where we'll gain some practice | |
| 12:24 | with doing this and gaining additional practice solving problems in | |
| 12:28 | fifth grade math . |
Summarizer
DESCRIPTION:
This is just a few minutes of a complete course. Get all lessons & more subjects at: http://www.MathTutorDVD.comâ. In this lesson the student will learn how to multiply a whole number by a fraction and simplify the result.
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Lesson 1 - Multiply Whole Numbers By Fractions (5th Grade Math) is a free educational video by Lumos Learning.
This page not only allows students and teachers view Lesson 1 - Multiply Whole Numbers By Fractions (5th Grade Math) videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.
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