Writing Expressions - Free Educational videos for Students in K-12

Writing Expressions - By Anywhere Math

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00:0-1	Welcome to anywhere . Math . I'm Jeff Jacobson .
00:02	And today we're gonna talk about writing expressions . Let's
00:06	get started . Yeah . Alright if you're like most
00:26	people you might think simplifying expressions is no big deal
00:30	. But when it comes to writing them from a
00:32	word problem or a phrase then you start to get
00:35	a little nervous . So let's break it down with
00:39	writing expressions is all about finding those keywords . So
00:43	if you look right here copy this chart down ,
00:48	these are the keywords and the corresponding operations that you
00:52	should be looking for . Okay , keep an eye
00:55	out for these words . So positive video write this
00:58	down and these are words you really have to memorize
01:02	and what they correspond with what operation some of them
01:04	you should already know . Okay let's get started with
01:07	example one . So write the phrase as an expression
01:10	. We've got some phrases , we're going to turn
01:12	them into expression . So again we're looking for those
01:15	keywords or phrases . So eight . Less than 21
01:19	. Hopefully you recognize less than from that chart .
01:23	And you remember that less than we're talking about subtraction
01:27	, but less than is really an important one to
01:30	know because the order Uh , for these , for
01:34	these numbers is going to be switched . But here
01:36	less than it's actually not going to be 8 -21
01:40	, it's gonna be 21 -8 . Okay . We're
01:44	saying eight less than 21 . So we're starting with
01:48	21 and subtracting ate from it . This is my
01:52	answer . That's my expression . Remember we're riding expressions
01:56	. I'm not actually asking you to simplify that .
01:59	I don't want you to actually do 21 might say
02:01	we stop right there and that's your expression . So
02:05	in the chart less than and more than I would
02:09	put a big star next to dolls . More than
02:15	and less than put a big star next to those
02:19	and maybe right , you know , pay attention to
02:22	the order or something . Okay , because that's a
02:29	really common mistake . I see a lot of students
02:32	make is that if they were doing this , they
02:35	would write 8 -21 instead of 21 -8 . So
02:39	more than in less than really pay attention to those
02:41	orders because it's switched . Okay , let's see the
02:44	next one be the product of 30 and nine .
02:48	Okay , well , let's look for the key word
02:51	here . Its product . I also want to say
02:55	something about these terms , some difference , product and
02:59	quotient . They're all related . They're all kind of
03:03	the same type of term . We know product is
03:06	talking about multiplication when you see those words , some
03:11	differs . Product promotion . They come in pairs always
03:15	also look for and because that is where the operation
03:21	goes . So we know product means multiplication and is
03:28	where we put it . So the product of 30
03:31	and nine mean 30 times nine . Okay . And
03:37	we know when we write it next to the parentheses
03:39	. That means multiplication . You can also write 30
03:41	, right ? You can you can do that as
03:45	well . So make another note in that chart ,
03:49	some difference . Uh , product and quotient . Pay
04:03	attention to the end . Right ? Uh look for
04:10	and that's where the operation will go . Okay ,
04:17	let's try another example . Okay . Example to write
04:20	the phrase as an expression . So we're doing the
04:22	same thing from example one . We're looking for those
04:25	keywords . Let's start with a 14 more than a
04:28	number X . Well , hopefully the key phrase that
04:33	you see here is more than Okay . And we
04:37	remember more than means addition . So what are we
04:39	adding ? We've got 14 and we've got a number
04:42	X . Right now , we're no longer writing numerical
04:47	expressions . Were writing algebraic expressions . And if you
04:51	remember from the video before it's going to be an
04:54	algebraic expression because we have an unknown , we've got
04:58	a variable this X . So let's write it .
05:02	We know we're dealing with addition . If you remember
05:05	from example one more than you got to remember ,
05:08	the order is changed . So instead of 14 plus
05:12	X , it's going to be X plus 14 .
05:18	Let's go to be the question of three and a
05:20	number W Let's look for that keyword . So hopefully
05:24	you recognize quotient and if you remember some difference product
05:31	quotient , all four of those also look for and
05:36	they come in pairs quotient and that and is where
05:42	the operation goes , Quote . It means division .
05:45	So I'm doing three divided by W . So I'm
05:51	gonna write that three divided by W . Or three
05:55	over W . Just like that . Okay , last
05:58	one . See the difference of two and three times
06:02	the number . So this one's a little more complicated
06:05	. Let's look for those keywords difference . Hopefully should
06:08	stick out . You also look for and remember just
06:13	like here , quotation and difference . And uh and
06:17	then also you should see height . Okay . Times
06:22	so Difference means subtraction . Well , what are we
06:25	subtracting ? We're gonna subtract two . And is where
06:29	that subtraction goes ? So I'm gonna start with 2
06:33	-3 times . Well , times means multiplication . What
06:37	am I multiplying ? I'm sorry . I should have
06:41	let's go with P . I forgot to read my
06:46	variable there . So three times P . And we
06:51	can write that as three P . So there's my
06:56	algebraic expression for this phrase . Okay , here's something
07:02	to try on your own . All right , here's
07:14	our last example . You plant a tree that is
07:16	10" tall . The height increases by 15" each year
07:22	. So part a write an expression to represent the
07:25	height of the tree in t years . All right
07:29	. So now this is where it really gets a
07:30	little bit more complicated , but the process is the
07:33	same . We have a word problem . We're still
07:36	looking for those keywords or phrases . So if you
07:39	look here , hopefully one word jumps out at you
07:44	and that would be or phrase increases by . Okay
07:49	, well we know that means addition . Okay ,
07:52	so when we're writing our expression , uh we got
07:56	to know that we're going to be using addition .
07:58	So that helps we also know that they want us
08:01	to write an expression to represent the height of the
08:04	tree in T years . T is gonna be our
08:08	variable . So we're going to have an algebraic expression
08:12	. Okay , well let's think about it . How
08:16	tall is a treat when we start before even one
08:19	year , when we just have the tree ? How
08:21	tall is it ? Well we know It starts out
08:24	at 10" , so I'm gonna start with 10 ,
08:28	that's where we're starting . Um It increases by five
08:33	inches each year . Sorry 15 inches . Each year
08:36	increases means I'm going to be adding And if you
08:40	think about it , if it was one year I
08:42	would be adding 15" . If it was two years
08:45	I'd be adding 30 Three years , I'd be adding
08:49	45 . What am I doing each time ? Right
08:52	well Each year 15" each year , that means I'm
08:56	gonna be multiplying those . So I'm gonna write that
08:59	as 15 times the number of years . Remember if
09:04	it was one year , 15 times one is 15
09:07	, So I'm adding 15 . If it was 2
09:09	, 15 times two is 30 , I'm adding 30
09:12	and I'm , the variable I'm using is T .
09:15	Okay . Now when you have your expression always just
09:20	double check . See if it makes sense . Okay
09:22	? Because if it doesn't then you might have a
09:25	problem . Uh Well , let's see If this expression
09:29	represents the height of the tree after 30 years .
09:33	What if it was zero years ? Well , We
09:36	would substitute zero and year and 15 times zero is
09:39	zero Plus 10 is 10 . So after zero years
09:43	is the height of this tree ? 10 in .
09:45	Yeah , that's what it started at after one year
09:49	. 15 times one is 15 , add that .
09:51	It would be 25 inches tall . Which makes sense
09:54	because every year it grows 15 inches . So that
09:58	is my expression . Okay , I'm happy with that
10:01	. It's an algebraic expression because it has a variable
10:05	. Let's look at the next one . Be used
10:07	. This expression to find the height after nine years
10:12	. Well we know T . Is the variable that
10:15	represents years . So I'm gonna substitute nine in for
10:19	tea . So it becomes 15 so high . 10
10:23	plus 15 times nine . Always use your parentheses when
10:28	you're substituting . Uh So 10 plus my order of
10:33	operations . Said I gotta do this multiplication 1st .
10:36	15 times nine . Well nine times 10 is 99
10:40	times five is 45 90 plus 45 is 100 and
10:45	35 . If I add those together I get 145
10:51	. Remember your units we're talking about inches . So
10:56	after nine years I would expect the tree to be
10:59	145" tall . Here's one more to try on your
11:03	own . As always . Thank you so much for
11:10	watching . And if you like this video , please
11:12	subscribe .

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