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

Math Antics - Absolute Value - By mathantics

Transcript


00:03	Uh huh . Hi this is rob . Welcome to
00:07	Math antics . In this lesson , we're going to
00:09	learn about a math concept called absolute value . That
00:13	sounds pretty intense doesn't it ? But don't worry it's
00:15	actually pretty simple . So simple . In fact that
00:19	it might seem kind of boring at least . That's
00:21	the way I remember when I was in school .
00:23	Okay class . This is an absolute value science .
00:30	And it's like magic . If I put in a
00:35	positive number it comes out unchanged . Okay but if
00:51	I put in a negative number yeah then just like
00:58	magic it comes out positive . Any questions ? Well
01:12	maybe it wasn't quite that bad but absolute value sure
01:16	seemed a lot less exciting than the name suggested .
01:18	It seemed like just a way to turn a negative
01:21	number into a positive one . For example the absolute
01:24	value of two is two but the absolute value of
01:27	negative two is also to the absolute value of five
01:31	is five . But the absolute value of negative five
01:34	is also five . See those vertical lines on either
01:37	side of the numbers . That's assemble use for absolute
01:40	value . So when you see something in between those
01:42	vertical lines it means to find the absolute value of
01:45	it . But what does absolute value even mean from
01:49	these examples ? It seems like it's just the positive
01:51	version of any number . Well sort of but it's
01:55	a little more involved than that absolute value is a
01:58	more general concept in math that actually has more to
02:01	do with the idea of distance than it does with
02:02	the idea of positive or negative numbers . It's usually
02:06	introduced in basic math right after you learn about negative
02:09	numbers . But absolute value is a concept that's even
02:12	more useful and more interesting and advanced math because of
02:15	that , I'm gonna teach you about absolute value using
02:18	an idea that you usually don't encounter until a little
02:21	later on in your math journey . And that idea
02:23	is vectors . The term vector might sound kind of
02:27	technical but they're actually really simple vectors are basically just
02:31	arrows in real life . And arrow can have all
02:34	sorts of different properties . For example , this arrow
02:36	is made of wood and has feathers while this arrow
02:39	is red plastic with around thinking at the end .
02:42	But in math the arrows , we call vectors only
02:45	have two properties . They have a direction and a
02:48	magnitude . What do those two properties mean ? Well
02:51	, direction is pretty obvious . It's just which way
02:54	the arrow or vector is pointing . It could be
02:57	up down , left , right or just about any
03:00	direction you can think of . But what does magnitude
03:03	mean ? Well that word might make you think of
03:05	an earthquake . Who actually magnitude is just a fancy
03:15	word for the amount extent or strength of something like
03:19	how strong an earthquake is or how bright a star
03:22	is , or how heavy an object is . In
03:25	the case of a vector , you can think of
03:27	magnitude as being the length of the arrow to see
03:29	what I mean . Let's use the number line to
03:31	measure some vectors . This factor has a magnitude or
03:35	length of two because it starts at zero and ends
03:38	at two and this specter has a magnitude or length
03:41	of five because it starts at zero and goes to
03:44	five . Okay , so we know the magnitudes of
03:47	these vectors . But what about their directions ? Well
03:49	, they're both pointing to the right on your screen
03:51	. And since we're using the number line as a
03:53	reference there , pointing in the positive direction . Right
03:57	. But what about this factor here ? It starts
03:59	at zero like our other vectors do , but it
04:02	ends at -2 . And the arrow indicates that it's
04:05	pointing in the exact opposite direction from the other two
04:07	vectors . It's pointing to the left or in the
04:10	negative direction of the number line . So what do
04:12	you think its magnitude is for those of you that
04:15	said to your right , even though the vector is
04:18	pointing in the negative direction , its length is still
04:21	a positive number . Its length is to just like
04:24	this factor that's pointing in the positive direction . They're
04:27	pointing in opposite directions . But if you rotate one
04:30	vector around you can see that they really do have
04:32	the same length or magnitude . And another way to
04:35	say that is that they have the same absolute value
04:38	. Ah See why I said that absolute value has
04:41	more to do with distance . In fact when it
04:44	comes to any number that you'd find on the number
04:46	line you can think of its absolute value as its
04:49	distance from zero . That explains why absolute value is
04:53	a little bit boring when you first learned about it
04:55	because the number line is a one dimensional space ,
04:58	There are only two possible directions positive or negative .
05:02	If you ask for the absolute value of any positive
05:05	number along that line , you're asking for the distance
05:08	that number is from zero , which is just the
05:10	number itself . And since the negative numbers are a
05:14	mirror image of their positive counterparts , when you ask
05:17	for the absolute value of any negative number along the
05:19	line , the only difference is the direction or sign
05:23	of that number and that's why the absolute value of
05:26	a negative number is just it's positive counterpart . Hopefully
05:30	that seems a little more interesting than just thinking about
05:32	absolute value as a way to turn negative numbers into
05:36	positive ones . In advanced math , absolute value gets
05:39	even more interesting and it actually gets kind of complex
05:42	vectors can point in all sorts of directions besides just
05:45	positive or negative . But hopefully thinking about absolute value
05:49	as the magnitude or length of a vector makes it
05:52	a little more interesting . And it shows you that
05:55	absolute value isn't just some silly rule that someone made
05:58	up to make math even harder and now that you
06:01	know that absolute value is related to distance it will
06:03	help you understand a useful application of absolute value in
06:06	the realm of basic math to see what I mean
06:09	suppose that you and your best friend each have a
06:12	certain amount of money in your pockets and one of
06:14	you has more than the other . Now it doesn't
06:17	really matter to you who has more money but you
06:20	want to know the difference between the amounts . How
06:23	do you find the difference between two amounts , yep
06:25	you subtract them and the answer you get from subtracting
06:29	depends on the order of the numbers because subtracting doesn't
06:32	have the community of property , right ? If we
06:34	subtract the amounts in this order seven minus four we'll
06:39	get the answer three . But if we subtract the
06:41	amounts in this order four minus seven we'll get the
06:45	answer negative . Three . Do you notice something about
06:48	these answers , yep , Even though the sign or
06:51	direction is different , the magnitudes are the same .
06:54	They're both three . That means that the absolute values
06:56	of the answers would be the same and like I
06:59	said we don't really care who has more money .
07:02	We just want to know how much that differences .
07:04	So in this problem we only need the magnitude or
07:07	absolute value of the difference . No matter which way
07:10	we do the subtraction , we just take the absolute
07:13	value of the answer to get what we want .
07:15	And this idea can be really helpful when you're entering
07:17	numbers into your calculator to solve math problems like this
07:20	one , let's say an airplane , we'll call it
07:23	plain A . Is flying at an altitude of 7328
07:27	m . And another plane plane B Is flying at
07:31	an altitude of 9150 m . And the problem asks
07:35	you to find the difference in their altitudes . You
07:38	know that means you need to subtract . So you
07:40	quickly get out your calculator and start typing in the
07:43	first number . But as soon as you get the
07:45	7328 entered and hit the subtract button , you realize
07:49	the second altitude is bigger . That means you'll have
07:52	a negative number as your answer . Should you start
07:55	over and type the bigger number first . Thanks to
07:57	absolute value . You don't have to no matter which
08:01	order . You subtract the numbers in the magnitude of
08:03	the answer will be the same . Just the direction
08:06	or sign of the answer will be different . So
08:09	if you continue on and enter 9150 and then hit
08:13	the equal sign the answer you get is negative 1,822
08:19	. Now all you have to do is mentally think
08:21	of that number as an absolute value and ignore the
08:23	minus sign . The difference in the altitudes of the
08:26	two planes is 1,822 m . If you're not quite
08:31	convinced of that , try the problem for yourself ,
08:33	subtracting both ways and see what answers you get .
08:36	In one case you'll get 1,822 and then the other
08:40	you'll get negative 1,822 . So now you know that
08:45	in its most basic form , absolute value is just
08:48	the distance between a number and zero on the number
08:51	line . And you've also seen how it can be
08:53	helpful when you want to find the difference between two
08:55	different numbers regardless of which is greater . In that
08:59	case the absolute value represents the distance between those two
09:03	numbers . The last thing I want to show you
09:05	in this video is how to handle a couple situations
09:08	involving absolute value that you might encounter on tests when
09:11	evaluating mathematical expressions . For example what if you're asked
09:15	to evaluate this expression involving absolute values ? We learned
09:18	how to multiply integers in the last video but now
09:21	these integers are inside absolute value science . So what
09:24	do we do ? Well , when it comes to
09:26	order of operations , absolute value science are similar to
09:30	parentheses , which means that you need to take care
09:32	of them first before you start working on the other
09:34	arithmetic operations . So in this problem before we can
09:38	multiply the integers we need to take the absolute value
09:41	of the numbers . 1st the absolute value of negative
09:44	three is three and the absolute value of five is
09:47	five . So the problem simplifies 23 times five which
09:51	is 15 . That example was pretty easy . But
09:54	what about this one ? Negative Absolute Value of -8
09:59	. Why is there an extra negative sign outside of
10:01	the absolute value signs ? Well whenever you see a
10:04	negative sign immediately outside and to the left of a
10:08	group like parentheses braces or the absolute value signs ,
10:12	it means that you need to negate that group .
10:15	That means you need to multiply that group by -1
10:18	. So if it helps you can think of this
10:20	problem like this negative one times the absolute value of
10:24	negative eight . And since absolute value signs are groups
10:27	like parentheses . To simplify it , we would first
10:30	need to do the absolute value , The absolute value
10:33	of -8 is eight and then we multiply that by
10:36	negative one and we get the answer negative eight .
10:39	That seems pretty simple to . But I want to
10:42	use this example to point out an important difference between
10:45	parentheses and absolute value science . It's a difference that
10:48	can trick you want to test if you're not careful
10:50	. Let's see the expression we just simplified side by
10:53	side with a similar expression that has parentheses instead of
10:56	absolute value science . In both of these cases the
10:59	negative sign outside the group is telling us to negate
11:02	the group . That means multiplying it by -1 .
11:06	But there's a very important difference between the two expressions
11:09	. The order of operations rules tells us to do
11:12	things that are inside of groups first . Right ?
11:14	But there's nothing to do inside the parentheses . It's
11:18	just a negative eight hanging out inside of them .
11:20	And the parentheses themselves don't tell us to do anything
11:23	. So this expression is just asking us to multiply
11:26	negative one times negative eight , which is positive eight
11:30	. But in the case of the absolute value science
11:32	, while they do function like groups , they aren't
11:34	just for grouping like the parentheses are they're also telling
11:37	us to do something to whatever is inside of them
11:40	. What are they telling us to do ? They
11:42	tell us to use the magnitude of the number in
11:45	sight which would be positive eight . So in this
11:48	expression we multiply negative one times positive eight . Which
11:51	simplifies to negative eight . Do you see how it
11:54	would be easy to confuse these examples on a test
11:58	they look similar at first glance but they simplified two
12:00	different answers . The key is to always remember that
12:04	absolute value signs are not just there to group things
12:07	, they're also asking you to find the absolute value
12:10	of whatever number or expression is inside the group .
12:13	All right . As you can see , absolute value
12:16	is a lot more than just a way to turn
12:18	negative numbers and the positive ones . Although that's basically
12:21	what it does when you're just dealing with numbers on
12:23	the number line . But it has lots of other
12:26	applications in math too . And look this student has
12:30	a negative attitude about math class but not to worry
12:37	, I put him in an absolute value sign and
12:41	presto wow he comes out with a positive attitude about
12:49	math class . Any questions remember ? You can't get
12:57	good at math just by watching videos about it ,
12:59	You actually have to do practice problems . So the
13:01	idea is you're learning really sink in so be sure
13:04	to do some absolute value problems on your own .
13:06	As always . Thanks for watching Math Antics and I'll
13:08	see you next time learn more at Math Antics dot
13:12	com .

Summarizer

DESCRIPTION:

OVERVIEW:

Math Antics - Absolute Value is a free educational video by mathantics.

This page not only allows students and teachers view Math Antics - Absolute Value videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.