Lesson 1 - Multiply Whole Numbers By Fractions (5th Grade Math) - Free Educational videos for Students in K-12 | Lumos Learning

Lesson 1 - Multiply Whole Numbers By Fractions (5th Grade Math) - Free Educational videos for Students in k-12


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.com​. 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.

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