Absolute Value - Free Educational videos for Students in K-12

Absolute Value - By Anywhere Math

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00:0-1	Welcome anywhere . Math . I'm Jeff Jacobson . And
00:01	today we're gonna talk about absolute value . Let's get
00:05	started . Which animal can travel farther away from sea
00:27	level . A bald eagle or a whale . Alright
00:31	, let's try to figure this out now . First
00:33	Bald Eagles have been seen gliding at heights of up
00:37	to 4500m above sea level . Now , what about
00:44	the whale ? Well , it all depends on the
00:46	type of whale . And the way we're going to
00:49	talk about today is called the Q beer beat whale
01:00	. And right there now this funny looking whale is
01:05	really , really special . I just saw that it
01:07	was able to dive 3000 m below sea level .
01:14	This mammal holds the record for the deepest dive and
01:19	the longest dive . It was underwater for over two
01:23	hours . Let's draw a quick little number line because
01:27	I'm talking about sea level . Instead of a horizontal
01:30	number line , I'm gonna draw a vertical number line
01:35	and zero is going to represent sea level . Okay
01:42	, well above sea level is obviously gonna be my
01:45	bald eagle . Below sea level is going to be
01:48	this whale 3000 m below sea level . Now below
01:54	. I'm gonna write that as negative negative 3000 .
01:59	So the question is which one is farther away from
02:03	sea level . Okay . Hopefully with the number line
02:07	you can see that . Oh definitely the bald eagle
02:09	is farther away because this distance is greater than this
02:14	distance . Now when we're talking about distances away from
02:18	zero , we're talking about absolute value . So let's
02:22	get into absolute value . And some examples , absolute
02:25	value of a number is just the distance . A
02:33	number is from zero on a number line . Okay
02:48	, It's the distance that number is from zero on
02:52	a number line . Now , distance is really important
02:55	because when you think about it , we'd never have
02:58	negative distances . Right . If someone asks you ,
03:01	how far did you run yesterday ? You're never gonna
03:04	say oh I ran negative five miles . That makes
03:06	no sense . So the same thing here , when
03:09	you take the absolute value of a number , you're
03:11	going to get something that's positive , A distance is
03:14	positive . So the way we write absolute value is
03:19	with two vertical lines . So for example . Uh
03:23	huh . Mm . Okay . This I would read
03:26	as the absolute These two lines means the absolute value
03:32	of three . Okay , the absolute value of three
03:36	is three . Right ? And you can think about
03:40	it , how far away from zero is three on
03:44	a number line ? Well it's three away . Okay
03:47	, that's why that's three . Let's get into our
03:49	first example . Okay , example , number one a
03:52	find the absolute value of seven . So we're talking
03:56	about how far away is seven from zero on a
03:59	number line . So I'm going to draw a number
04:01	line . We're here at seven . The question is
04:07	, what is this distance from 07 ? How far
04:12	away is that ? Seven from zero ? Well I
04:15	can count . Right . 1234567 . Right ? But
04:19	it's pretty obvious that it is seven . Okay ,
04:23	seven away . So that means the absolute value .
04:28	Right ? We read it like that and one quick
04:30	tip . Make sure that these vertical lines are longer
04:34	than your numbers . If not If you're not kind
04:39	of careful it can really quickly look like 171 .
04:44	Okay , so again make sure that when you write
04:47	absolute value , those numbers are those vertical lines are
04:51	longer than your numbers . So the absolute value of
04:54	seven is seven . Okay . Let's look at b
04:58	find the absolute value of negative 2.5 . Same thing
05:01	. I'm gonna draw a quick number line . So
05:04	negative two and one half would be halfway between negative
05:07	two and negative three . So it's going to be
05:09	right about there negative two and one half again .
05:15	What is the distance from ? Negative 2.5 to 0
05:19	? So from here to hear . Okay again you
05:25	could count but hopefully you notice that that distance is
05:29	2.5 . It's 2.5 away in the absolute value of
05:33	negative 2.5 is 2.5 positive 2.5 . Right ? These
05:41	are distances . It's going to be positive . Okay
05:44	? So hopefully you notice here something , the absolute
05:47	value of a positive number . Stay positive . It's
05:51	a positive distance . But then when we took the
05:53	absolute value of a negative number , it became positive
05:57	, right ? Because distance need to be positive .
06:00	Okay , here's some to try on your own .
06:11	Okay . example to compare to and absolute value of
06:16	-5 . Uh Well first we need to figure out
06:22	what the absolute value of negative five is . Now
06:24	we could draw a number line again and find our
06:27	distance but hopefully you're starting to get it . How
06:30	far away is negative five from zero ? Well the
06:34	absolute value of negative five is five . So my
06:38	answer is two is less than the absolute value of
06:43	-5 . Let's look at b compare the absolute value
06:49	of -4 and the absolute value of four . Well
06:54	the absolute value of negative four is going to be
06:57	four right ? Negative force four away from zero ,
07:00	that's four . uh and the absolute value of four
07:04	is also for which means The absolute value of -4
07:10	is equal to the absolute value of four . Okay
07:18	yeah here's some more to try on your own .
07:28	Alright example three order the values from least to greatest
07:32	. Uh So we have a lot of absolute values
07:35	here and we've got a couple of new things we
07:38	haven't talked about yet . So in order to order
07:41	these , I first need to know what the value
07:43	is so I need to figure out these absolute values
07:46	. So first what is the absolute value of negative
07:49	five ? Well that's going to be five right ,
07:52	it's five away from 03 is still three . The
07:57	absolute value of two , that's two away from zero
08:00	. So that is to now here notice where the
08:05	negative sign is . Okay it's not inside the absolute
08:09	value , it's on the outside . So we would
08:11	read this as the negative absolute value of three .
08:16	So first what you need to do is just find
08:18	the absolute value of three and then you add your
08:22	negative after that . So the absolute value of three
08:26	is 3 . Then we put the negative sign in
08:29	front so we get -3 . Last one here The
08:35	negative absolute value of -4 . So again ignore this
08:41	negative for a second and let's concentrate on the absolute
08:44	value . The absolute value of negative for is four
08:48	. Right ? Negative four is far away from zero
08:52	but then we put a negative in front so this
08:54	becomes negative four . Okay ? So now if we're
09:00	gonna order these obviously my negative four is the least
09:05	which means this Is the least . So the negative
09:08	absolute value of -4 . His first then they get
09:13	three here so that's Negative Absolute Value of three .
09:18	Then we've got to which was absolute value of two
09:22	. Then we've got three which is just three .
09:26	And finally the greatest is gonna be the absolute value
09:30	of negative five . So there is my order from
09:37	least to greatest . Okay , here's some more to
09:40	try on your own as always , thank you so
09:47	much for watching and if you like this video ,
09:49	please subscribe .

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