Math Antics - Negative Numbers - Free Educational videos for Students in K-12

Math Antics - Negative Numbers - By Mathantics

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00:03	Uh huh Hi , welcome to Math Antics . In
00:08	this lesson , we're going to learn about negative numbers
00:11	. Negative numbers can be a little confusing at first
00:13	so don't get discouraged if it takes you a while
00:15	to get it to learn what negative numbers are We
00:18	first need to start with whole numbers . You remember
00:21	what whole numbers are right there . The set of
00:23	numbers on the number line starting with zero and then
00:26	counting up one at a time , 1234 all the
00:30	way to infinity . That's a lot of numbers but
00:34	it's only half the story and that's because the number
00:37	line really goes in both directions . You're used to
00:40	seeing the number line starting at zero and just going
00:43	to the right but the number line also goes to
00:46	the left and what numbers are on that part of
00:48	the number line , yep , you guessed it ,
00:51	negative numbers . The negative numbers are just like a
00:55	mirror image of the numbers on the right side of
00:57	the number line that we call the positive numbers .
01:00	And zero is the special number that separates the positive
01:03	numbers from the negative numbers . By the way ,
01:06	when you combine all these numbers 123 and so on
01:10	up to infinity and negative one negative two negative three
01:13	and so on down to negative infinity . And the
01:15	number zero . That entire set of numbers gets a
01:18	special name in math . They're called the integers .
01:22	As you can see the negative numbers look just like
01:25	the positive numbers . The only difference is that they
01:28	have a negative sign in front of them . The
01:30	negative sign looks just like the minus sign . In
01:33	fact if we wanted to we could write a positive
01:36	sign A plus in front of all the positive numbers
01:39	. But to save time we just assume that if
01:42	the number doesn't have any sign in front of it
01:44	then it's positive . Positive is the default sign .
01:48	Okay . Now that you know what negative numbers are
01:50	? We need to learn how to compare them to
01:52	other integers . Remember that in math comparing just means
01:56	saying which of two numbers is bigger or smaller than
01:59	the other or saying that they're equal . And to
02:01	do that we use the greater than less than or
02:04	equal science . You're probably already pretty good at comparing
02:08	positive imagers . Like if I ask which is bigger
02:11	two or three . You know that three is bigger
02:13	than two . But what if I ask you to
02:15	compare to negative imagers which is bigger negative two or
02:19	negative three ? Uh This is where negative numbers can
02:23	be a little tricky . Especially if this is your
02:25	first time learning about them . That's because you're so
02:28	used to three being bigger than to that when you
02:32	see negative two and negative three , it's really tempting
02:35	to think that negative three must be bigger than negative
02:38	two , but it's not negative three is actually smaller
02:43	or less than negative two . And to help you
02:46	understand why let's look at our number line again .
02:49	Have you noticed that if you start at zero on
02:51	the number line and then you move to the right
02:54	, the numbers keep getting bigger and bigger as you
02:56	go along , one is greater than 02 is greater
03:00	than one and three is greater than two and so
03:03	on . But what if we go in the opposite
03:05	direction instead to the left as we go to the
03:08	left , the numbers get smaller and smaller two is
03:11	less than 31 is less than two and zero is
03:15	less than one . Well , those same exact rules
03:19	apply to the negative side of the number line .
03:21	Also the numbers get bigger as you go to the
03:24	right and they get smaller as you go to the
03:26	left . So since -3 is on the left side
03:30	of -2 , it's actually smaller than -2 . I
03:34	like to think of it like this . On the
03:36	positive side of the number line three is more positive
03:39	than two . So it's bigger . But on the
03:42	negative side of the number line , -3 is more
03:45	negative than -2 . So it's smaller and you can
03:49	use that idea no matter what the numbers are On
03:52	the positive side , 500 is more positive than 200
03:56	. So it's bigger . But on the negative side
03:59	-500 is more negative than -200 . So it's smaller
04:05	. Keep that in mind if anyone ever offers to
04:07	give you negative $500 , The 500 part sounds pretty
04:11	good , but the negative part . Not so much
04:16	. All right . So the positive integers are on
04:18	the right side of zero on the number line ,
04:20	which means they're all greater than zero . And the
04:22	negative integers are all on the left side of zero
04:25	on the number line , which means they're all less
04:27	than zero . Hold on a second , less than
04:31	zero . How can any number be less than zero
04:34	? I mean doesn't zero mean nothing . That's a
04:37	good question at first . It can be hard to
04:40	see how there could be numbers that are less than
04:42	zero . But here's an example that will help you
04:44	understand . Let's say we want to use integers to
04:47	measure how many meters above sea level small islands are
04:51	. This island is 10 m above sea level .
04:54	This island is only five m above sea level .
04:58	This island here happens to be exactly the same height
05:01	a sea level . So we can use the integer
05:03	zero to show how its height compares to sea level
05:07	. But what about this island ? It's not even
05:09	above sea level at all . It's five m below
05:12	the surface . But our measurement is supposed to tell
05:14	us how many meters above sea level it is fortunately
05:18	with negative numbers . That's no problem . We can
05:21	just say that it's height compared to sea level is
05:24	negative five m . Or what about an example with
05:28	money ? Suppose there's three brothers who each have a
05:31	different amount of money . The first brother has $20
05:35	. The next brother has $0 and the last brother
05:39	actually owes his dad $20 . What number do we
05:42	use to represent how much money he has . Yep
05:46	, negative $20 and temperatures . Another great example .
05:51	We use 0°C to describe the temperature for water to
05:55	freeze , but it can be warmer or colder than
05:57	that . The temperature could be negative like negative 20°.
06:02	. So negative numbers are very useful in the real
06:05	world to help describe things that can be above or
06:09	below zero . Okay now that you know how negative
06:13	numbers work , let's see how we can compare any
06:15	two integers . If we don't include zero for a
06:18	moment basically there's just three situations you'll either need to
06:22	compare two positive integers or two negative integers or one
06:27	positive and one negative integer . And you already know
06:31	how to compare two positive integers . The further right
06:33	on the number line you go bigger than numbers get
06:36	seven is greater than 4 50 is greater than 20
06:40	and 1000 is greater than 100 . It's also really
06:43	easy to compare a positive integer and a negative integer
06:47	because a positive number is always bigger than a negative
06:50	number . All of the positive numbers are on the
06:53	right side of the number line , and all of
06:55	the negative numbers are on the left , So negative
06:58	five is less than five and -40 is less than
07:03	three And -100 is less than one . The only
07:09	tricky situation is when you have to compare to negative
07:12	imagers , then you have to think about which one
07:14	is further to the left on the number line .
07:17	Again , a great way to do that is to
07:19	identify the number that would normally be more positive on
07:23	the positive side of the number line and realize that
07:25	it's more negative on the negative side . -8 is
07:30	more negative than -4 . So it's smaller . -15
07:35	is more negative than -10 . So it's smaller And
07:40	-100 is more negative than -25 . So it's smaller
07:45	. All right . So in this video , we
07:47	learned what negative numbers are and how they can be
07:50	used to describe things in the real world . They're
07:53	just like positive numbers . But on the other side
07:55	of zero on the number line , Yeah . And
07:58	we learned that the whole numbers , along with their
08:00	negative counterparts form the set of numbers we call integers
08:04	. We also learned how to compare . It injures
08:07	. As you go to the right on the number
08:08	line , the integers get bigger and as you go
08:11	to the left they get smaller comparing integers . Can
08:14	be confusing at first . So be sure to practice
08:16	until you've really got it as always . Thanks for
08:19	watching Math Antics and I'll see you next time .
08:22	Learn more at Math Antics dot com .

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