Math Antics - Adding & Subtracting Integers - Free Educational videos for Students in K-12

Math Antics - Adding & Subtracting Integers - By Mathantics

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00:03	Uh huh . Hi , welcome to Math Antics .
00:08	And our last video we learned what negative numbers are
00:10	and we learned that they're part of a special set
00:12	of numbers called *** . Next we need to learn
00:16	how to do arithmetic with those integers . In this
00:19	video we're going to learn how to add and subtract
00:21	integers in the next video we'll learn how to multiply
00:24	and divide imagers , adding and subtracting whole numbers is
00:28	pretty easy because there's really only two possibilities . You're
00:32	either adding to positive numbers or subtracting two positive numbers
00:36	. But adding and subtracting integers is more complicated because
00:39	with negative numbers in the mix there's a lot more
00:42	possibilities . Fortunately you don't need to memorize all these
00:46	possibilities . Instead , we're going to learn some simple
00:49	rules and strategies that will make the process a lot
00:52	easier . Let's start by learning to key rules that
00:56	are really helpful to know when working with negative numbers
00:59	. The first rule is this adding a negative is
01:03	the same as subtracting imposter to visualize what that means
01:08	. Suppose I give you positive two cupcakes . You'd
01:11	be pretty happy , right ? But what if I
01:14	give you negative two cupcakes instead ? That's the same
01:18	as taking two cupcakes away from you . Would you
01:21	still be happy when it comes to math ? This
01:25	rule means that if you have a problem like this
01:28	five plus negative one where you're adding a negative number
01:33	, you can just change it to subtraction Instead of
01:35	five plus -1 . You can just write 5 -1
01:40	. There are different ways of writing the same thing
01:43	. Okay so rule number one is adding a negative
01:47	is the same as subtracting a positive . Now .
01:50	What about Rule # 2 ? Well the second rule
01:53	is this subtracting a negative is the same as adding
01:57	a positive . Let's say you have negative two cupcakes
02:02	. Like if you have a debt you owe me
02:05	two cupcakes , you wouldn't be too happy having that
02:07	negative , would you ? But what if I subtract
02:11	that negative from you ? Taking away the -2 made
02:14	you more positive . Right ? Subtracting the negative gives
02:18	you less debt when it comes to math . This
02:22	rule means that if you have a problem like five
02:24	minus negative one , where you're subtracting a negative number
02:28	, you can just change it to addition instead of
02:31	five minus negative one . You can just write five
02:35	plus one . And that's a problem . You already
02:37	know how to solve . All right now that you
02:40	know our two rules . I want to show you
02:42	that there's really only four different types of problems .
02:45	Or for cases when adding or subtracting integers In case
02:50	one you start with a positive number and you make
02:53	it more positive . In case to you start with
02:56	a positive number and you make it more negative In
03:00	case three , you start with a negative number and
03:03	you make it more negative . And in case four
03:06	you start with a negative number and you make it
03:09	more positive . The key to getting the right answer
03:12	to the problem is to figure out which of these
03:14	cases you're dealing with . So let's look at each
03:17	case in more detail in case one you start with
03:21	a positive number and you make it more positive .
03:24	The good news is that you already know how to
03:26	do that ? That's just what regular edition is .
03:30	For example , when you have the problem seven plus
03:33	three , you're starting with positive seven and you're making
03:36	it more positive by adding positive three to it to
03:40	get the answer of positive 10 . But what if
03:43	instead of seven plus three , you're giving the problem
03:46	seven minus negative three . That seems a lot harder
03:49	. Right ? Well if you remember rule number two
03:52	, it's not harder at all . In fact it's
03:55	exactly the same problem Because rule number two says subtracting
03:59	a negative is the same as adding a positive .
04:03	We can change the minus minus three into plus three
04:07	and we get the same answer positive 10 . So
04:11	case one is just addition like you're used to doing
04:15	but now that we have negative numbers , there's a
04:17	new way that it could be written that you need
04:19	to be on the lookout for O . And in
04:22	this case starting with a positive and making it more
04:25	positive . You know your answer will always be positive
04:28	because you stay on that side of the number line
04:31	In case to you start with a positive number but
04:34	you make it more negative . That is you do
04:36	something to it that makes its value smaller or moves
04:39	it to the left on the number line . But
04:41	that's just like regular subtraction . Like you already know
04:44	how to do . For example here we have the
04:47	problem 8 -5 . We start with positive eight but
04:51	we make it more negative by subtracting five from it
04:55	. Subtracting five , moves it to the left on
04:57	the number line down to three . As our answer
05:01	, our answer is still a positive number but it's
05:03	less positive than it was before . And that raises
05:07	an interesting question . What if we subtract even more
05:10	to move it further in the negative direction ? Like
05:13	what if we subtract eight instead of 5 ? That
05:16	would take us all the way back down to zero
05:18	on the number line . And before you knew about
05:21	negative numbers . Back when you thought the number line
05:23	just stopped at zero , you probably thought that's all
05:26	we could take away but watch this . Let's start
05:30	with positive eight . But then subtract 10 from it
05:33	. Can we do that ? Can we subtract a
05:35	bigger number from a smaller one ? Now we can
05:39	it just means that the answer we get will be
05:41	a negative number . Starting with positive aid and subtracting
05:45	10 takes us past zero and down to negative two
05:50	on the number line . So our answer is -2
05:54	. As you can see case two is a little
05:56	more complicated because the answer can be positive , negative
06:00	or even zero depending on the numbers you're subtracting And
06:04	it's even more complicated than that . Because there's also
06:07	another way this type of problem can be written .
06:09	Thanks to rule number one . Rule # one says
06:13	that adding a negative is really the same as subtracting
06:16	a positive And that means our original subtraction problem 8
06:21	-5 . Could have been written like this instead .
06:24	eight Plus Negant Fire . But either way it's written
06:28	you're starting with a positive and making it more negative
06:32	. Now on to case three in case three you
06:35	start with a negative number and you make it more
06:37	negative . That's really just the opposite of case one
06:41	where we started on the positive side of the number
06:43	line and made it more positive . For example ,
06:47	let's say that you're giving the problem negative seven plus
06:50	negative three . That means that you start with negative
06:53	seven and then you make it even more negative by
06:56	adding negative three which gives you negative 10 as the
07:00	answer . And as you might have guessed by now
07:03	, thanks to our rules , there's another way we
07:05	could write this type of problem because of rule number
07:08	one , we know that adding a negative three is
07:12	the same as subtracting three . So this problem could
07:15	also be written like this -7 -3 . But either
07:20	way it's written in this case you're starting with a
07:23	negative number and making it even more negative . And
07:26	because of that you know that your answer will always
07:28	be negative for case three since you stay on the
07:31	negative side of the number line . And finally in
07:35	case for you also start with a negative number .
07:37	But this time you're going to make it more positive
07:41	. Here's an example of a problem like that -8
07:44	Plus five . This problem starts with negative eight but
07:48	then we add positive five which makes it more positive
07:51	or moves us to the right on the number line
07:54	up to negative three which is our answer . Our
07:57	answer is still negative but it's less negative than what
08:00	we started with . Ah But this looks similar to
08:04	case too right ? Imagine what would happen if you
08:07	made it even more positive ? You could add eight
08:10	instead of five and that would move you all the
08:13	way up to zero . And if you add it
08:15	even more like negative eight plus 10 that would take
08:18	you to the positive side of the number line and
08:21	give you the answer of positive too . So just
08:25	like in case to the answer here can be positive
08:28	, negative or even zero depending on the numbers you're
08:31	at him . And just like before there's another way
08:34	this type of problem can be written Remember Rule #
08:37	two that subtracting a negative is the same as adding
08:41	a positive because of that . Rule negative eight plus
08:45	five could also be written as negative eight minus negative
08:50	five . That's a lot of negatives . But thanks
08:54	to rule number two we can write our minus minus
08:57	as a plus . But either way it's written in
09:00	this case we start negative and move in the positive
09:03	direction . Okay , now that we've learned our two
09:07	rules and we've seen that there's really just four types
09:10	of problems or four different cases that you'll need to
09:12	solve . I want to give you a basic strategy
09:15	that will help when you're adding or subtracting integers .
09:18	The strategy involves asking three simple questions . The first
09:22	question is , am I starting with a positive or
09:25	a negative number ? This question is easy to answer
09:28	because all you have to do is look at the
09:30	sign in front of the first number of the problem
09:33	. If there's no sign then you're starting with a
09:35	positive number . But if there's a minus sign then
09:38	you're starting with a negative number . Once you know
09:41	what you're starting with . The next question to ask
09:44	is am I making it bigger or smaller ? In
09:48	other words , is what you're adding or subtracting ?
09:50	Going to make the value move in the positive direction
09:53	of the number line or the negative direction . If
09:56	you're subtracting a positive or adding a negative rule number
09:59	one , then you're making the value smaller which is
10:03	moving to the left on the number line . If
10:06	you're adding a positive or subtracting a negative rule number
10:10	two , then you're making the value bigger , which
10:13	is moving to the right on the number line .
10:16	And the last question that you need to ask is
10:18	will my answer be positive , negative or zero ?
10:22	The answer to this will depend on which case you
10:24	have and what values you're working with . If it's
10:28	a case one problem , you know , the answer
10:30	will always be positive and if it's case three problems
10:34	then , you know , the answer will always be
10:35	negative . But you'll remember that in cases two and
10:39	four , the answer could change between positive , negative
10:42	or zero depending on the difference between the two numbers
10:45	that you're working with . So asking these three questions
10:49	will help you visualize what's happening in the problem that
10:51	you're trying to solve and it will help you get
10:53	the right answer . But the most important thing that
10:55	you can do to get good at integer arithmetic is
10:58	to practice . It's important that you try a lot
11:01	of problems that you have an answer key for so
11:03	that you know , if you're doing it right and
11:05	don't get discouraged if it's confusing at first you'll get
11:08	it if you practice and you might want to re
11:11	watch this video a few times since there's so much
11:13	that it covers . As always . Thanks for watching
11:16	Math Antics and I'll see you next time learn more
11:20	at Math Antics dot com

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