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

Writing simple algebric expressions - By tecmath

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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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