04 - Simplify Fractions to Lowest Terms (Simplifying & Reducing Fractions) - Part 2 - Free Educational videos for Students in K-12 | Lumos Learning

04 - Simplify Fractions to Lowest Terms (Simplifying & Reducing Fractions) - Part 2 - Free Educational videos for Students in k-12


04 - Simplify Fractions to Lowest Terms (Simplifying & Reducing Fractions) - Part 2 - By Math and Science



Transcript
00:00 Hello . Welcome back . We're working on simplifying fractions
00:03 . This is part two . So in the last
00:05 lesson we have learned that to simplify a fraction into
00:08 what we call lowest terms or simplest form . All
00:11 you have to do is pick a number that you
00:12 can divide the top by and the bottom by the
00:15 numerator and the denominator divided by the same number and
00:19 simplify the fraction . So you have to divide by
00:21 the same number on the top and the bottom that
00:23 divides evenly . So what you do is try to
00:27 pick the largest number that you can divide into the
00:29 top and the bottom and that will give you the
00:31 smallest number of steps . But even if you don't
00:34 pick the perfect number , just pick anything that you
00:36 can divide the top and the bottom into . And
00:38 eventually you will get down to the simplest form or
00:41 lowest terms . So let's talk about that by going
00:44 over a concrete example , let's say I give you
00:46 the fraction 15/30 , what does this mean ? It
00:50 means if I take a pizza and cut it into
00:53 30 pieces , that's a lot of tiny pieces ,
00:55 right ? And I take 15 of those pieces .
00:58 That is the fraction that I have . So ,
01:00 we want to simplify that amount of pizza to a
01:03 simpler form , but it's going to represent the same
01:05 amount of pizza is what we have here . So
01:07 , we want to pick a number that we can
01:09 divide the top and the bottom evenly . So what
01:12 we're gonna do is we're gonna rewrite the fraction 15
01:15 30th , But we're going to extend this guy .
01:18 So we're going to extend the fraction bar and we
01:21 want to divide the top and the bottom by some
01:22 number . Now we have 15 and we have 30
01:25 . We know from 5 , 10 15 2025 30
01:28 35 40 . We know that we can divide top
01:31 and bottom by five . All right . So let's
01:34 do that . Because immediately we see we know we
01:36 can divide the top by five and we can divide
01:39 the bottom by five . So what happens if we
01:42 do that ? 15 divided by five is three ?
01:46 How do I know that ? Because three times five
01:48 is 15 , right ? 30 ? Divided by five
01:51 is six . How do I know that ? Because
01:53 six times five is 30 . Right ? So I've
01:56 divided the top and I've divided the bottom and I
01:58 get an answer of 3/6 . But I look at
02:00 this answer and I say , is this the lowest
02:03 terms ? Is this the simplest form ? In other
02:06 words , can I divide 36 by something on the
02:09 top and something on the bottom dividing evenly to make
02:12 this fraction even simpler . And the answer is yes
02:15 . I can divide the top by three and I
02:17 can also divide the bottom by three . Notice that
02:20 first I divided the top and bottom by five .
02:22 I did it the same number top and bottom .
02:24 That's totally legal . Now here I look and say
02:26 can I divide the top and bottom by something ?
02:28 I'm gonna pick the number three because I can divide
02:30 the top by three in the bottom by three .
02:32 So let me start over here by 36 and we're
02:36 going to extend this guy and we're going to divide
02:39 the top by three and the bottom by three .
02:43 What do I get ? Three divided by three is
02:45 one because one times three is three and then six
02:49 divided by three . Is to why ? Because two
02:52 times three is six . So this is what we
02:55 call lowest terms because this means I've have half of
03:00 the pizza which I'm saying is exactly the same thing
03:03 is taking 15 out of 30 slices . If I
03:05 slice a pizza into 30 pieces and I take 15
03:08 of them , I get exactly the same amount of
03:11 actual food . And if I take a pizza and
03:13 cut it into two pieces and only take half and
03:16 notice that along the way we went through this fraction
03:20 right here , 336 which were also saying is the
03:23 same . So let's go and check this . Uh
03:25 one half is if I were to take a pizza
03:29 and cut it into two pieces , right ? But
03:31 I only have one of those pieces , so that's
03:33 how much I have . This is what we call
03:35 half of a pizza , right ? Is it the
03:37 same as 36 here ? So let me go ahead
03:40 and make a pizza , cutting it into six equal
03:44 pieces here , and let's see how much we have
03:47 here . So let me kind of put them all
03:48 together , so that's a whole pizza . But we
03:49 only have we cut them into six pieces , but
03:52 we only have three of those pieces . 123 that's
03:55 what we have the rest of it , I'm gonna
03:57 throw it away . And what we're claiming is that
03:59 363 out of six pieces is the same as one
04:02 out of two . And you can see that that's
04:04 exactly the same amount of pizza . These two fractions
04:07 are exactly the same thing and they're also the same
04:11 thing as 15 out of 30 . I don't have
04:13 a magnet that was sliced into 30 pieces and see
04:16 this is sliced into six pieces . I don't have
04:19 a magnet to show you sliced into 30 pieces ,
04:21 but if I did have a magnet sliced into 30
04:24 tiny little pieces , but I took 15 of them
04:27 , it would be exactly the same amount of pizza
04:29 . Is this ? So what we have figured out
04:31 is that 15 30th is exactly the same as 3/6
04:37 and that's also exactly the same as one half .
04:40 But one half is the lowest terms or the simplest
04:43 form because I cannot divide anything top and bottom to
04:46 make this any simpler . I can't think of a
04:48 number to make it any simpler than that . So
04:51 I'm done . So when I get to this step
04:53 I try and divide . In this time I pick
04:55 three and then I get to simplest form . Now
04:59 I want to solve the problem one more time .
05:01 Let's talk about 15 30th and let's think about this
05:05 again . Right in this case I knew it divided
05:09 by five and five . So that's what I did
05:11 and then I did the process again . But is
05:13 there a different number that I could divide the top
05:15 and the bottom by a larger number than dividing by
05:19 five ? Is there anything else you can think of
05:21 ? It might take you a minute . But if
05:22 you actually divide the top by 15 And also divide
05:27 the bottom by 15 , right ? Then actually 15
05:31 divided by 15 is one and 30 divided by 15
05:35 is actually too because if you take two and multiply
05:38 it by 15 , you're actually going to get 30
05:41 . I know some of you may not have remembered
05:44 that or know that , But if you go off
05:46 to the side and take 15 times two You're going
05:49 to get 30 . So you see if I think
05:52 in my mind if I if I pick the largest
05:54 number two , divide by then in this case I'm
05:57 going to come up with dividing 15 , divided by
05:59 15 . I'm going to get one half as the
06:00 answer in only one step , right ? And I
06:04 notice it's the same exact answer as I got before
06:06 . But if you don't remember that you can divide
06:08 by 15 or you just don't know right , then
06:11 pick any number you want that goes evenly into the
06:13 top and the bottom and you're gonna get some answer
06:15 and then you ask yourself , can I do it
06:17 again , Can I pick another number and divide it
06:19 again ? And in this case I pick three and
06:21 I get down to the exact same answer . So
06:23 my point is is I don't care what you divide
06:26 the top and the bottom by . Actually you're going
06:28 to save steps . If you can pick the biggest
06:30 number , you can divide the top and the bottom
06:32 by because it only took one step here . But
06:35 if you don't remember that and you have to do
06:36 it multiple times . Just keep asking yourself can I
06:39 simplify it again ? Can I simplify it again and
06:42 so on ? Eventually you will get to exactly the
06:44 same answer . All right . Exactly the same answer
06:48 . So , let's go and uh crank through a
06:51 bunch of additional problems and see if we can get
06:53 some more practice . Let's say that we have the
06:56 number 18 the fraction 18 2021st , or 1821 .
07:03 However , you want to say it ? All right
07:04 . Um What we have here is a pizza cut
07:07 into 21 pieces and we have 18 of those slices
07:10 . So we need to think of a number that
07:13 we can divide the top and the bottom by any
07:16 number that we want . Uh But it's gonna save
07:18 us time if we can come up with the biggest
07:20 number and we want to divide the top and the
07:22 bottom by the same number . If we divide by
07:25 two , this is an even number . So it
07:27 will divide by two . But this one will not
07:28 divide by two . But then we think about it
07:30 and we say , well actually we can divide this
07:32 by three and we can divide this also by three
07:35 . What is 18 divided by 3 , 18 divided
07:38 by three is six because six times three is 18
07:42 , 21 , divided by three is actually seven because
07:44 seven times three is 21 . And so we get
07:47 down to this and we ask ourselves can we simplify
07:49 this further , cannot divide the top and the bottom
07:52 by something to make these numbers simpler . And I
07:54 can't there is no way to make that simpler .
07:56 So , the answer is 6/7 . Yeah . All
08:01 right . Let's take a look at the fraction .
08:04 26th . 26th . So we rewrite the fraction as
08:08 10 16 . Give us a little more room and
08:12 we ask ourselves All right , what can we divide
08:14 the top and the bottom by ? Well , we
08:15 immediately see these are both even numbers . So we
08:18 know that I can divide the top by two and
08:20 I can divide the bottom by two . For sure
08:23 . 10 divided by two is five because five times
08:26 two is 10 16 divided by two is eight because
08:30 eight times two is 16 . And so I get
08:33 the answer . Five eights . This is the final
08:35 answer . Because I ask myself can I make this
08:37 simpler ? Can I divide the top and the bottom
08:40 by a different number ? By ? Well , by
08:42 the same number , divide five by the same number
08:45 . And divide it by the same number . And
08:47 get it simpler . And I can't There's nothing I
08:49 can pick . So this is called simplest form or
08:51 lowest terms . All right , then . Of course
08:55 we come across this problem that we've just done .
08:58 Which I've already I actually solved that one first because
09:00 I wanted to use the magnets for it . Let's
09:02 take a look at the fraction . 12 21st .
09:07 21st . All right . So we rewrite it 12
09:10 21st and we ask ourselves what can we divide top
09:13 and bottom by . Can we divide by two ?
09:15 Well , we really can't because 21 divided by two
09:17 doesn't work . Can we divide by three ? Well
09:20 , we can divide this by three . And we
09:21 can also divide this by three because we know our
09:23 multiplication tables and we know that 12 divided by three
09:26 is four because four times three is 12 , 21
09:30 divided by three is seven because seven times three is
09:33 21 . And then we say , is this simplest
09:35 form , can I divide top and bottom by some
09:37 number . Can divide by two . Can divide by
09:39 three . Can divide by four . I mean it
09:41 works here , but it doesn't work here . Can
09:43 divide by five or any any other number I can
09:45 think of . So that's simplest form four sevens .
09:50 And what we're basically saying for all of these problems
09:52 is that four out of seven slices of pizza is
09:55 exactly the same as taking 12 out of 21 slices
09:59 . Five out of eight slices of pizza is exactly
10:02 the same as taking 10 out of 16 slices .
10:05 So that is what the process really means here .
10:08 Now let's take a look at the next one carefully
10:10 because we have a couple of choices . Let's take
10:12 a look at 28 And the Fractions 28 , 30
10:16 seconds . So we have 32 slices of a pizza
10:19 , but we only take 28 of them . How
10:21 can we simplify this ? 28 , 32 . All
10:25 right , there's a bunch of different choices . The
10:26 first thing I noticed right away is that I can
10:30 uh go through my multiplication tables and I say ,
10:32 Okay , well , I can divide this by four
10:35 because seven times four is 28 , and I can
10:37 divide this by what can I divide also by four
10:41 ? Because eight times four is 32 . So ,
10:43 I know that I can divide both by four .
10:46 So , if I go through and I say ,
10:48 well , what is 28 divided by four ? I
10:49 know the answer seven because seven times four is 28
10:53 And I know this is 32 , divided by four
10:55 , 32 , divided by four is eight because eight
10:58 times four is 32 . And I know this is
11:00 simplest form because I cannot divide the top and the
11:03 bottom by anything else . To make it simpler .
11:06 Now that's if you happen to remember that I can
11:08 divide by four . But let me solve the problem
11:10 again . Let's start over again . 28 , 32
11:14 . Let's say that you didn't realize you could divide
11:16 by four , you just didn't think of it .
11:18 I know that this is an even number and this
11:20 is also an even number . So I know that
11:22 I can divide this by two and I can also
11:24 divide that by two . Now what is 28 divided
11:28 by two ? You might not know that off the
11:30 top of your head because it's a big number .
11:32 But 28 divided by two actually turns out to be
11:36 14 , right And 32 divided by two actually turns
11:41 out to be 16 . How do you know I
11:44 mean ? Really ? I know because I know my
11:46 multiplication tables , but if you don't remember 14 times
11:48 two should be 28 . 14 times two . So
11:52 four times two is 82 times one is two .
11:55 So 14 times two is 28 . And then to
11:58 go down here , you can say 16 times two
12:01 , six times two is 12 , carry the one
12:04 . Uh And then you have two times one is
12:06 two , and then plus one is three , So
12:08 16 times two is 32 . So when I divide
12:11 through , I know that these are the right numbers
12:13 . But then I ask myself can I take this
12:15 fraction and make it any simpler ? And I can
12:17 because I see that these are also even numbers .
12:20 So 14 , 16 , what can I divide top
12:23 and bottom by ? Well , I can divide it
12:25 again by two and again by two . And I
12:27 know that 14 divided by two is seven And I
12:30 know that 16 divided by two is eight because seven
12:33 times two is 14 and eight times two is 16
12:36 . So the answer I get is again 78 exactly
12:39 the same thing as I got here . The reason
12:41 I'm showing you two ways here is because when you're
12:43 simplifying a fraction , sometimes you don't know what to
12:46 divide by . When I'm trying to tell you is
12:48 I don't care what you divide by . As long
12:50 as it divides an even number of times the shortest
12:53 way to solve the problem is just to divide by
12:55 four . It only takes one step and you get
12:57 to the answer . If you divide by the biggest
13:00 thing you can that works for both top and bottom
13:02 number then you're going to solve the problem faster .
13:05 But if you don't think of that number or if
13:07 you can't if you don't remember that , you can
13:09 see that these are even just divide by to get
13:11 the answer , then you say , well I can
13:13 do it again and I can divide by two again
13:15 and get the answer . I'm going to get to
13:16 the exact same place no matter what I do .
13:19 All right , That was problem five . We are
13:23 halfway done . Let's take a look at the fraction
13:27 15/18 . So what I'm gonna do is divide top
13:33 and the bottom by some number , what am I
13:36 going to pick ? Well , I can't divide by
13:37 two because this doesn't divide by two . This divides
13:42 by two , but this doesn't uh If I divide
13:44 by three , does that work ? I say yes
13:45 . Actually it can because I know that this is
13:47 divisible by three and that's divisible by three . 15
13:50 divided by three is five because five times three is
13:54 15 18 divided by three is six . Why ?
13:58 Because six times three is 18 ? And this is
14:01 the final answer . Because when I look at 56
14:04 I cannot come up with another number that I can
14:06 divide top and bottom by evenly and make it any
14:09 simpler . So that is the final answer and it's
14:11 only one step . All right , so we only
14:15 have a few more and we will be done .
14:18 Let's take a look at 12 18th . So 18
14:24 slices of a pizza . I only take 12 of
14:27 them . What fraction is equivalent to this ? That's
14:30 simpler . Well , I can see that there are
14:32 even numbers immediately . So I'm gonna go ahead and
14:35 divide by two . I'm gonna divide by two because
14:38 I see that I can divide by two and they're
14:41 both even . So that makes sense to me .
14:42 12 divided by two is six . six times 2
14:46 is 12 18 , divided by two is nine because
14:49 nine times two is 18 . So I'm saying ok
14:51 , am I done ? And I said well no
14:53 , I actually I'm not done because I can do
14:54 the process again , I can divide the top and
14:56 the bottom by something to make that fraction simpler .
15:00 So let's go over here and say 6/9 . What
15:03 can I divide the top and the bottom by Well
15:06 I can divide the top , not by two .
15:08 That doesn't divide into the bottom , it divides into
15:10 the top , but I can divide by three on
15:12 both of these . Six , divided by three is
15:14 two and nine divided by three is three . Why
15:18 ? Because three times three is nine and two times
15:20 three is six . And this is the final answer
15:22 because this fraction cannot be simplified any further . So
15:25 you see how it took two steps . I didn't
15:27 have to wrestle or stress out about what to divide
15:30 by . I just saw that they were even numbers
15:32 . So I divide by two . I get this
15:34 and then I say well I can do some ,
15:36 I can divide again by something else and I'll get
15:38 down to the point where eventually I'll do it enough
15:40 times , I'll get to the final answer . But
15:42 because it actually took two times here , I now
15:45 know that I can actually do this in one step
15:48 . 12 divided by 18 . Is there another number
15:51 ? I could divide the original problem by ? Well
15:54 , I picked to initially because I knew that they
15:58 were they were even numbers . But I think about
16:01 it further and I know that if I divide by
16:03 a bigger number , I'll save time so I can
16:06 divide by three and by three , Right , 12
16:09 divided by three is 4 , right ? And 18
16:13 divided by three is what , 18 ? Five by
16:15 three ? Six ? Because six times three is 18
16:17 and four times three is 12 . Right ? So
16:20 actually I got this , but then I'm like I
16:22 look at this and I'm like well wait a minute
16:23 , I'm not done here , I can actually take
16:25 the 4/6 yes , and I can divide what by
16:29 two , and I can divide by two to simplify
16:32 this further . Two divided by two is two because
16:35 two times two is 4 and six divided by two
16:38 is three . And so I get a final answer
16:40 of two thirds which matches exactly before here . So
16:43 if I divide by two , I get this and
16:45 then I divide that answer by something else , that
16:47 I get this and I divide this by three and
16:50 get this and then take the answer divided by two
16:51 . I get to the same place and I'll do
16:53 it one last time Just to drive the point home
16:56 . Let's start over with the original problem again .
16:58 12/18 . So here I divided by two . Here
17:01 I divided by three . What else can I divide
17:04 by ? What is the biggest number I can divide
17:06 by ? The biggest number I can think of is
17:08 six . Mhm Right , 12 divided by six is
17:12 two because two times uh six is 12 and 18
17:15 divided by six is three because three times six is
17:17 18 , this again is the same answer . So
17:20 I'm trying to show you several different examples where if
17:23 you think of the biggest number two divide by ,
17:26 you only have one step , but if you can't
17:28 think of that , just pick something else and keep
17:30 doing the process and you'll always get to the same
17:33 correct answer . Alright , for our next problem ,
17:37 let's take a look at 27 30th . Want to
17:41 put that into simplest form . So let's think about
17:43 what can we divide by on the top and the
17:45 bottom . I cannot divide by two on the top
17:49 of the bottom because this is not an even number
17:50 , it won't divide . But I can divide the
17:52 top and bottom by three . On the top 27
17:56 divided by three is nine . And on the bottom
17:58 30 divided by three is 10 because 10 times three
18:01 is 30 and nine times three is 27 . So
18:05 , the answer you get here is 9/10 and I
18:07 can't simplify that further . So , that actually is
18:09 the final answer . All right . When we have
18:13 two more problems . Uh huh . Let's take a
18:17 look at 14 20th . What can we divide top
18:22 and bottom by uh to make our lives to make
18:26 this simpler ? Well , I see that they're both
18:27 even numbers . So I'm going to divide the top
18:29 and bottom by two right away . 14 divided by
18:32 two is seven and 20 divided by two is 10
18:36 because 10 times two is 20 and seven times two
18:38 is 14 and the answer is 7/10 because uh and
18:42 this is the simplest form because I cannot divide top
18:44 and bottom again by anything else to make it simpler
18:47 . All right . Here is our last problem .
18:51 Let's take a look at 6/30 . Mhm Right .
18:56 6/30 . So let's think about what can we divide
18:59 six by and 35 ? Well , we know that
19:03 these are both even numbers . So if we divide
19:06 by two , we know that we're going to be
19:08 able to get down to the answer , but we're
19:10 going to save time . If we can think of
19:11 the largest number , we can divide by right ?
19:14 So we know that actually we can divide the top
19:17 by six and also the bottom by six . That's
19:19 the biggest number we can think of because six divided
19:21 by six is one and 30 divided by six is
19:24 five . So the answer is 1 51 times 6265
19:28 times six is 30 . So the answer is 1/5
19:30 . I cannot simplify that anymore . Now just for
19:33 giggles , let's go down here and simplify a different
19:36 way . 36 30 is let's say we didn't think
19:39 of this and we just divided by two . What
19:42 do we get here ? Six divided by two is
19:44 three and 30 divided by two . If you actually
19:47 think about it and do some multiplication off to the
19:49 side 30 divided by two is actually 15 . Right
19:53 ? But I can simplify this further because if I
19:56 take the three and I divide by three and the
19:59 15 and divide by three though I top and bottom
20:01 by three what I will get is three divided by
20:03 three is one and 15 divided by three is five
20:06 because five times three is 15 and one times three
20:09 is three and I get exactly the same thing 1/5
20:11 . So the bottom line of this lesson is when
20:13 you're simplifying fractions you will save time if you can
20:16 think of the biggest number that you can divide the
20:18 top and the bottom by to simplify it . But
20:21 if you can't think of the biggest number it's okay
20:23 just if it's even divide by two , if you
20:26 know you can divide both by three , divide by
20:27 three and you may have to do the process two
20:30 or three times , but eventually you will get down
20:32 to exactly the same place . I've shown you several
20:35 times that you'll always get to the same place ,
20:37 so don't stress out about what to divide by .
20:39 Just pick something that works and keep on working from
20:41 there . So that was the topic of simplifying fractions
20:44 . It's crucially important . I want you to practice
20:46 all of these lessons are all these problems and then
20:49 follow me on to the next lesson will continue building
20:51 your skills step by step .
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