Understand Fractions & Their Meaning - Multiplying Fractions & Adding Fractions - [31] - Free Educational videos for Students in K-12 | Lumos Learning

Understand Fractions & Their Meaning - Multiplying Fractions & Adding Fractions - [31] - Free Educational videos for Students in k-12


Understand Fractions & Their Meaning - Multiplying Fractions & Adding Fractions - [31] - By Math and Science



Transcript
00:00 Hello . Welcome back . The title here is called
00:02 fractions as multiples . This is part one . The
00:05 driving purpose of this section is for you to understand
00:08 that the fractions that we have been working with ,
00:10 all of the fractions that we've been working with ,
00:12 you can think of them as you can break apart
00:15 the fractions and express them as multiples of a of
00:18 a smaller fraction , and that's a little hard to
00:21 understand by words , but it'll be really simple once
00:23 they get it on the board . Actually , I've
00:25 been emphasizing this whole concept from the very first fraction
00:29 lesson we've done . So when you look at this
00:31 , you might think you already know that . Well
00:32 , that's because I've been emphasizing it from the beginning
00:35 to try to make it easier to understand . Let's
00:37 just jump right in . Let's take the fraction 2/8
00:41 . I've been telling you since we started that what
00:44 this means is two pieces out of eight of a
00:46 pizza . Cut a pizza into eight slices . That
00:50 means every slice would be 1/8 but you don't have
00:52 1/8 you have 2/8 . So I've been teaching you
00:56 to think of these slices of the pizza like this
00:58 is a slice of the pizza . To think of
01:00 these slices as things that you count , you count
01:03 them as you go around . This is 1/8 .
01:05 If you have two of them it's to eight and
01:07 then 3/8 and then 48 So you've been counting uh
01:10 these slices of the pizza , counting in eighth the
01:12 whole time . So what I want to do to
01:14 to illustrate the point here is I want us to
01:17 write this fraction two eights . I want us to
01:19 write it two different ways . The first way I
01:21 want to write it as a multiplication equation or something
01:25 involving multiplication . And then the second way we're going
01:28 to write it in terms of addition . So we're
01:30 gonna write two different ways . We're going to write
01:32 an equation with multiplication and an equation with addition .
01:36 It's going to be very very simple . Let me
01:38 ask you to 8th . It's going to be easier
01:41 for us to get to the punch line and then
01:43 go from there for this one for our multiplication equation
01:46 we can say that 2/8 is equal to what ?
01:50 1/8 but times two , that's what 1/8 is times
01:56 two you get to eight . So you can kind
01:58 of like rip this apart and the two can go
02:01 over as a whole number and the 1/8 can come
02:03 over here because remember there's like an invisible being this
02:07 over one . I can write this as to over
02:09 one times 18 and when I multiply one times two
02:13 is 21 times eight is eight . So it makes
02:16 perfect sense that I can say that this fraction is
02:19 equal to the fraction 18 times two . That's why
02:22 it's called multiples . I want you to think of
02:25 28 and 3/8 and 4/8 is just like multiplying 1/8
02:30 times two or multiplying diffraction 18 times three or whatever
02:34 this is called a multiple . And so I can
02:37 show you that with a uh with a fraction or
02:40 with a with a model we can say this is
02:43 the fraction two eights . That's what this is .
02:45 This is the fraction to AIDS . But I can
02:46 write that as the fraction 1/8 times to write .
02:52 And that's another way of of of writing that 18
02:55 the fraction 18 times . To the other way we
02:57 want to write it is in terms of addition ,
02:59 we can say that 2/8 is equal to just like
03:02 two times 1/8 . We can write it as 1/8
03:04 plus 1/8 because remember all multiplication can be written as
03:09 addition . So these are the two answers I'm going
03:11 to give you a fraction . And our goal is
03:14 to write it as the multiplication of something and then
03:16 also to write it as the addition of something .
03:18 And every problem will be the same . This two
03:21 eights means the fraction 1/8 times to just like this
03:25 . And then we can also think of these as
03:26 being just added together . 1/8 plus 1/8 gives you
03:29 2/8 . Because if you add these you keep the
03:32 same denominator , add enumerators , you get the 2/8
03:35 . If you multiply this , you multiply the tops
03:38 , multiply the bottoms . Of course the bottom of
03:39 the one here and so you get the same thing
03:41 back . All right now that all of that talking
03:44 is out of the way , It's gonna be much
03:47 , much easier for us to just jump in and
03:49 understand the rest . Let's write the fraction . 4
03:53 5th . We're gonna write it two different ways .
03:56 We're gonna write it first . It's multiplication , And
03:59 then we're gonna write it as edition . So ,
04:01 4/5 . What does this mean ? It means we
04:03 have four pieces out of five . It means we
04:06 have four slices , each of which is 1/5 .
04:09 It means that we can take the fraction 1/5 which
04:12 is a small fraction . And we can multiply it
04:14 times four , Right ? Four times 1/5 . Because
04:18 that's what we're doing . We're basically going and saying
04:20 we have a fraction is 1/5 and we replicate it
04:22 . And we multiply it times four and that's what
04:24 4/5 is . So , let's take this . We
04:28 have uh here we have the fraction 4/5 there's 1/5
04:33 there's 2/5 there's 3/5 There's 4/5 , there's a fraction
04:37 4/5 . But that's the same thing as just taking
04:40 the fraction 1/5 and multiplying it times four . I
04:44 guess I can flip this over like this 1/5 times
04:47 for the representing it . This way , it's the
04:49 same amount of pizza as uh when you when you
04:54 kind of wrap it around like this , it's the
04:55 same . Exactly the same thing , whether you spread
04:57 it out or you put it into a circle is
04:59 the same thing . This front , 4/5 is the
05:01 fraction 1/5 times four . That's what 4/5 is actually
05:05 equal to . And we can also then write it
05:08 . In terms of edition , we can say that
05:10 4/5 is going to be equal . What ? Thinking
05:12 about this , we can say 1/5 plus 1/5 plus
05:17 1/5 plus 1/5 +1234 times . Because multiplication is the
05:24 same thing as adding the thing that many times .
05:27 So this whole fraction which is 4/5 can be thought
05:30 of as 1/5 plus 1/5 plus 1/5 plus 1/5 .
05:33 That's all we're saying . It can also be thought
05:36 of as 1/5 times . four , same thing .
05:39 So , we circle all of these . All right
05:43 , Let's take a look at problem # three .
05:47 What about the fraction 56 ? How do we write
05:49 that as multiplication . And how do we write it
05:52 as edition ? Well , what we're saying here is
05:55 that we have the fraction 56 can be written as
05:58 five times the fraction 1/6 . And if you can
06:02 think about it , if you think about five being
06:04 5/1 , then five times one is five and the
06:08 one that's down here , one time six is six
06:10 . So this equation is true and we can also
06:13 write that 56 is equal to 1/6 plus 1/6 plus
06:18 1/6 plus 1/6 plus 1/6 +12345 times . So we're
06:25 just adding them together . So let's see if that
06:28 makes sense in terms of six , let's put the
06:31 fraction on the board . There's 1/6 there's +26 we'll
06:34 add that , there's 3/6 there's 46 and then of
06:39 course we have 56 All we're saying here is whether
06:43 or not I keep it tucked into a circle like
06:45 this , or if I spread it out , if
06:48 I add all of these sixes together , it equals
06:51 the 56 Or if I take 16 times five It
06:55 equals what we already know 56 to be . So
06:57 I want you to start thinking of fractions As yes
07:01 it's five out of six slices but it's also like
07:03 taking 1/6 and just adding it to itself that many
07:07 times . Or multiplying times that many numbers there .
07:11 So that's all we're trying to do in this lesson
07:15 . Let's take a look At the fraction . 5/12
07:20 . Let's write it as a multiplication first . Well
07:23 we can say 5/12 is the same thing as 1/12
07:29 Right ? Multiplied by five . Right ? Because if
07:32 I put it put this over one it would be
07:34 five times one is five and then one down here
07:36 times 12 is 12 . So this is how to
07:38 write it as a multiplication . But also we can
07:41 write it as what ? 1/12 plus 1/12 plus 1
07:48 12 Plus 1 12th . That's four times plus 1
07:54 12 . So we're basically doing the multiplication , we're
07:56 representing it as addition . And if you add these
07:59 fractions together , the denominator will be the same and
08:02 you'll add all the ones and you'll get 5/12 .
08:05 So we can do the same thing . Here's 1/12
08:09 . 2 12 , 3 12 , 4 12 5/12
08:13 . That's what we It's five out of 12 pieces
08:16 , but we can also represent it as being 1
08:18 12 , just just multiplied by five . It's a
08:22 multiple This fraction 5 12 is a multiple of the
08:25 fraction . 1 12 . It's just a smaller fraction
08:28 . 1/12 replicated and multiplied times five . So ,
08:31 it's a multiple of the smaller fraction . It's like
08:34 the smaller fractions the core fraction . And then we
08:38 make it a multiple of this by multiplying by five
08:42 and it becomes then 5 12 . Or you can
08:43 think of it as addition . 1 12 plus 1
08:45 12 plus 1 12 plus 1 12 plus 1 12
08:51 . All right . How many more do we have
08:53 ? Only two more ? How do we write the
08:56 fraction ? 2/4 . In terms of multiplication ? We
09:02 can write that as the fraction 1 4th times two
09:07 or two times 1/4 . However , you want to
09:08 write it because this too is really to over one
09:11 and then two times one is two and then the
09:13 one times four is four . So it's like taking
09:16 the smaller fraction 1/4 and just multiplying by two .
09:19 That's what the larger fraction is . And we can
09:22 also represent that as simple . In addition we can
09:26 say its 1/4 plus 1/4 . We do it two
09:31 times and adam together . So the fraction 2/4 is
09:34 this this is the fraction to fourth , two out
09:37 of four pieces . It's the same thing as saying
09:40 , here's the fraction 1/4 times to that equals to
09:44 fourth or the fraction 1/4 plus 1/4 That equals the
09:48 2/4 . So this concept should be pretty familiar now
09:54 because as we've been going through this , I've been
09:55 kind of emphasizing this without really saying it . Last
09:59 problem . 4/10 . Let's write it as a multiplication
10:04 . Well , we can say that that's 1/10 times
10:07 four , because if this were 4/1 , 4 times
10:11 one is 41 times 10 is 10 . We can
10:13 also represent 4/10 as 1/10 since it's times 4 .
10:18 1/10 we'll just add it four times plus 1/10 plus
10:22 1/10 plus one 10th . Let's see if that makes
10:28 sense . What I'm saying here is that we have
10:30 1/10 from here , 1/10 from here and 1/10 from
10:33 here and 1/10 from here . And if we add
10:36 all of these together we get the fraction 4/10 that's
10:39 all we're saying . Same thing is thinking about it
10:42 in multiplication . This larger fraction 4/10 is just equal
10:45 to one of these small ones and multiplying it times
10:49 the top number times for so it's not 1/10 it's
10:53 4/10 because we've multiplied the small fraction times four .
10:57 So here in this lesson we're just trying to get
10:59 you to think about fractions in different ways . Yes
11:01 it is four out of 10 slices of a pizza
11:04 but it can also be thought of as 1/10 multiplied
11:08 by four or 1/10 plus 1 10 plus 1 10
11:11 plus 1/10 . We can think about fractions in different
11:13 ways and sometimes the different ways we think about them
11:16 are helpful in different in different problems . So I'd
11:19 like you to practices yourself when you feel like you
11:22 understand it . Follow me on to the next lesson
11:23 . We're gonna give you a little bit more practice
11:25 with this concept
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