Writing simple algebric expressions - Free Educational videos for Students in K-12 | Lumos Learning

Writing simple algebric expressions - Free Educational videos for Students in k-12


Writing simple algebric expressions - By tecmath



Transcript
00:0-1 Good day . Welcome to Tech Math Channel . What
00:02 we're going to be having a look at in this
00:03 video is we're going to continue to look at algebra
00:05 . Um Now in the first video we're looking algebra
00:08 , we're basically doing some very introductory sort of things
00:10 , looking at how algebraic expressions were put together and
00:15 writing some very basic ones . As well as simplifying
00:17 the this sort of leads on from there . We're
00:19 going to have a look at how to actually write
00:21 some algebraic expressions from worded sort of problems before we
00:24 get to the next stage of algebra . Yeah ,
00:28 I'll give you some examples here . We've only got
00:29 a few examples here , but they sort of sum
00:33 up what we should be up to so far .
00:34 Just say we have this sort of question . Allah
00:36 has four bags apples . Okay , so we've got
00:41 two parts of this about each bag has nine apples
00:43 , How many apples does she have ? And we're
00:46 gonna go into each bag has X . Apples .
00:48 And this is where it's maybe a varied part of
00:50 , you know that could change how many apples as
00:52 you have . So , I'm going to start off
00:54 looking at this With nine apples . So an example
00:57 here , what I'll do is I will draw these
01:01 four bags . Okay , for this paradise . Each
01:04 one has 9 apples in it . Okay , there's
01:07 my bags and each one has nine apples . So
01:11 you might be able to work out how many apples
01:12 she has altogether . She has four groups Have 9-4
01:18 times nine , Which is equal to 36 apples .
01:22 Okay , now let's do this algebraic lee . So
01:26 what we say , what we actually have now is
01:28 we have these four bags and told you all these
01:30 four bags they want to three . Cool . And
01:37 instead of actually knowing that they have nine , that
01:38 we actually now have this variable a mountain . And
01:41 okay , so it might be one apple in each
01:43 bag . It might be five apples in each bag
01:45 . It might be nine apples in each bag .
01:46 It might be a 126 apples in each bag .
01:49 We're looking for an expression that covers this , an
01:52 algebraic expression . So like this one was up here
01:55 was four times 9 instead of this were actually the
01:58 changes for times X . Okay , there's four groups
02:03 of X . This is how we would write it
02:06 . Okay . Which would actually brought Even closer is
02:10 four x . Because this is the way we can
02:13 write an algebraic expression with multiplication . We're going to
02:17 another exam to say here we have this type of
02:22 question . We have . Just get rid of that
02:25 there . And we have this one here . We
02:29 have nick is 15 years old . How old will
02:32 he be in five years ? And how old will
02:35 he be in X years ? Okay . Actually how
02:37 will he be ? That's the same way as saying
02:39 , how old would he be in one or five
02:40 or 10 or 90 years . Okay . Is there
02:43 a general sort of rule ? We can write our
02:45 bravely . So let's start out with the number that
02:47 we do know . And you're gonna see that algebra
02:50 is a lot like with the letters were it's a
02:52 lot like just doing normal bats , you treat them
02:54 exactly the same . It's just instead of using letters
02:57 . So how old will he be in five years
02:59 ? So nick at the moment is 15 , So
03:03 we get 15 and we add five to it ,
03:05 we're going to get that . He's 20 years old
03:09 . Okay . How you , should we go with
03:13 that ? Now when we're doing this algebra basically we
03:16 can do this a similar thing . We're starting out
03:18 where he's 15 , but now we're saying not in
03:21 five years , we were saying in X years ,
03:24 so not plus five , got a B plus ng
03:26 X onto it , saying 90 years in 20 years
03:29 and 30 years , whatever years , how old will
03:32 we be ? So it's gonna be , this is
03:35 the answer here is going to be 15 plus X
03:37 . Or the way we typically write this is we
03:40 might even write this as you might see this written
03:42 as X plus 15 . I know it's sort of
03:44 the same thing and it is exactly the same thing
03:46 . They just tend to like to write these are
03:49 pro numeral , these algebraic expressions first . They tend
03:51 to like to put these ones with no letters in
03:54 the blast . Okay , so that's the way that
03:57 you can write the soldier bravely , by the way
03:59 each of these is equally as correct . Okay so
04:03 an example of this , we could then say a
04:05 bit later on we can say , well what happens
04:07 if X . Is 12 years ? Okay well how
04:10 old they've been 12 ? So we can say X
04:12 plus 15 . He will be 12 plus 15 plus
04:18 15 and he would be 27 . Okay . We
04:24 could say how old we been . 21 years .
04:27 Okay . 21 plus 15 equals 36 . Okay ,
04:33 that's where algebraic expressions are really powerful because you can
04:37 sort of create rules where you can create rules which
04:39 you can end up this substituting values in without having
04:42 to do the same calculations again and again and again
04:45 and again . Okay . What about we have a
04:48 look at Another question here we have Peter and Allen
04:52 and they have $30 between them . If Peter has
04:56 $12 is the first part . If Peter has $12
04:59 how much does alan had ? And the second part
05:00 is Peter has X . Dollars . Okay . X
05:03 . Dollars . How much does Alan have ? Okay
05:07 so let's have a look at this first part .
05:10 If Peter has $12 so that between them they got
05:13 $30 . 30 and Peter's amount of money equals .
05:22 Okay $12 . How much is Alan Have ? Between
05:25 that ? 30-30 ? We can take away 12 amount
05:28 . Peter has to work in our challenge has .
05:30 Okay so 30 take away 12 . And if we
05:32 do this we get the answer of $18 . Okay
05:36 . And yes I haven't put dollar signs in their
05:38 possibly sure but I'm not going to do that for
05:40 the minute . So this is a fairly easier sort
05:44 of question to work out . Yeah . Say for
05:48 instance we decided as algebraic . We we don't know
05:50 exactly how much Peter has but we do know this
05:53 . Okay . We do know between them . They
05:55 have $30 . So instead of saying he has $12
05:58 , we say that played a has Extols . So
06:01 instead of taking 12 we're taking X . Okay .
06:04 We just say that Ellen has 30 target way X
06:08 . Okay . Peter has X . And Allen has
06:12 30 take away . So this is Allen's and Peter
06:20 has eggs and between them They have $30 . Okay
06:24 , I'll give you an example here , we can
06:25 substitute some values in here . Say we say that
06:28 Peter has $10 . Okay , so 30 take away
06:31 10 , he would have $20 and As we said
06:34 he had $10 at 10 past 20 is 30 .
06:38 So you can try this out . It's worth when
06:39 you're first doing these substituting a few values just to
06:42 make yourself feel comfortable with them . Okay , now
06:46 the last question , we're going to have a look
06:48 at this one And this is a bit more of
06:50 a difficult sort of one . Okay , the length
06:52 of a rectangle was 10 cm and the width is
06:56 This one here ? It's four plus X cm .
06:59 Okay , so X might be one and so be
07:02 one plus four is five or it might be seven
07:05 and seven plus four is 11 . In fact ,
07:08 what about I'll draw this triangle just to start you
07:11 out . Okay , so we have this and we
07:13 have Length of 10 cm and we have this width
07:19 of four plus Biggs . Okay , so what's the
07:27 perimeter of this rectangle ? That's the first part and
07:31 they're going to work out the area . Okay ,
07:33 so let's see here you go with this . So
07:34 give it a go . Maybe maybe come back to
07:36 this . Anyway , I'm going to answer this right
07:39 now . So what's the river to this ? So
07:41 you're gonna realize that we've got two sides , we
07:42 got one side here and one side here that exactly
07:45 the same . And that's going to be 10 plus
07:48 10 beside . And this side we also have what
07:52 ? This side here and this side here which is
07:56 over the At this 4-plus 6 and four plus six
08:07 . Okay . So how we're going here now ,
08:11 we can actually group all of our life terms here
08:14 . So we can group our just our normal numbers
08:17 as well as our X numbers here . So let's
08:18 do that . We have 10 20 24 28 .
08:26 So right that in 28 And we also have one
08:31 x 2 x 28 plus two eggs . And that's
08:37 the perimeter of this rectangle I'd say it's a bit
08:39 strange , doesn't it ? But that's the way you
08:41 can write . And even if you want to be
08:43 you know the way I tend to like to write
08:45 . And I might put this to XIA first so
08:46 it could even equal to two X Plus 28 .
08:51 Again , it's exactly the same amount . It's just
08:54 written a bit different . I like to put the
08:55 ones with the pro numerals first . Okay . So
09:01 how'd you go with it ? Okay . And again
09:03 you can substitute values if you're not too sure you
09:05 could actually substitute values in and we can say for
09:08 instance that what about we make this X here one
09:11 . So 10 plus five plus 10 plus five .
09:17 It would be 30 years . So does this work
09:20 here 28 plus two X . Two times X is
09:23 too because X is one . So two times one
09:25 is +22 plus 28 is 30 . Okay , so
09:29 this expression works again , substitute a few values in
09:33 . Check it out for yourself . Okay , what
09:35 about the area of this rectangle ? All right ,
09:39 this is a bit more difficult now and we work
09:41 an area we go to leave times a week .
09:46 Okay , So let's do this the length which is
09:49 10 times the width , which group it together for
09:55 the minute , which is for plus six . There's
10:01 a reason I'm grouping it up because if I just
10:03 do this 10 times four plus X . And I
10:06 don't put the brackets around and that makes it a
10:08 little bit different . Okay , So if we were
10:11 to do this , We can actually leave this for
10:13 the start and I might even uh actually I'll take
10:17 the next week . But the next video is gonna
10:18 be looking at , hey , can actually expand this
10:20 a bit further . So we could actually end up
10:22 with a value that we've got this 10 Just without
10:26 putting the times that we can put them strangers to
10:27 each other 4-6 . But what we can also do
10:31 is we can actually expand this out further . This
10:32 is what we're gonna have a look at this next
10:34 video , The way of actually expanding these sorts of
10:37 expressions . We end up with 10 times four ,
10:40 Which is 40 and 10 times X , Which is
10:44 10 x . So we end up with 40 plus
10:48 10 X . You might even then change this around
10:50 and get the answer being 10 X Plus 40 .
10:54 Now that last step through you a little bit .
10:57 Don't get too worried about that . Okay , we're
10:59 going to have a look at that in the next
11:00 video title of , that video is going to be
11:03 expanding two factors . Okay , so anyway , hopefully
11:08 that's fine with you . If you're not sure this
11:11 and you wanna you wanna double yourself and make sure
11:14 you're getting the right answer the moment . What about
11:15 with substitutes and values in here ? So , so
11:17 we actually said xia once , let's make it too
11:20 now , 10 times four plus 2 , 10 times
11:23 six , We have an area of 60 cm squared
11:27 . Does this work here ? 10 times two is
11:30 20 Plus , 40 is 60 . So you can
11:33 really check your answers by substituting in values anyway .
11:37 Hopefully that was just some help . So the next
11:39 video , we're gonna actually look at this time of
11:41 our expanding these types of brackets . Okay , So
11:44 if you get a little bit stuck on that ,
11:45 don't be too despondent . Have a look at this
11:47 next video . I hope to see that , but
00:0-1 .
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