Subtracting Integers - Free Educational videos for Students in K-12

Subtracting Integers - By Anywhere Math

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00:0-1	the L . S . Ice bucket challenges all over
00:02	facebook and Youtube . At the moment . People are
00:06	pouring buckets of ice cold water over their heads to
00:09	raise money for a less research . If you were
00:11	going to do the challenge and you were worried that
00:14	your water was too cold , How could you raise
00:18	the temperature ? Welcome to anywhere . Math . I'm
00:38	Jeff , Jacobson . And today we are going to
00:41	talk about subtracting integers . If the ice water was
00:45	too cold . One way you could raise the temperature
00:47	would be to add warmer water that's going to raise
00:51	the temperature . The second way would be to remove
00:54	all the ice If you did that , the temperature
00:57	should the temperature of the water should raise up a
01:00	little bit . Uh Now if you remove all the
01:02	ice technically is no longer ice water is just water
01:05	. But removing in math we think of that as
01:09	subtraction . And the ice in the ice water we
01:13	could think of as a negative integer . So you'd
01:16	be subtracting negative integers . Let's look at some more
01:21	problems with subtracting negative and positive integers . Alright before
01:26	we start talking too much about subtracting integers . Uh
01:29	I've got a problem for us Compare 5 - to
01:33	compare that to 5-plus -2 . Well 5 -2 .
01:37	You guys have done that since probably kindergarten ? That's
01:39	just three . We know that five plus a negative
01:43	two . We just practiced in the last video adding
01:46	integers . Five plus . A negative two would give
01:49	me three as well . Mm Yeah let's try another
01:54	one . If we did negative six -4 and compare
01:59	that to negative six plus a negative four . Well
02:07	-6 -4 . It's a little more difficult than this
02:10	. You can think of it . Uh using a
02:13	number line . He's black . So I'm starting at
02:19	negative six here . 0 Maybe there's -6 . I'm
02:24	starting there and I'm subtracting for which means I'm going
02:28	to the left when we subtract going to the left
02:31	four , that would put me at negative 10 .
02:37	Yeah . So -6 -4 would be negative 10 .
02:43	And here -6 plus a negative for they're both negatives
02:47	. When we add them together , my answer is
02:49	gonna be negative . So that's also gonna be negative
02:52	10 . Okay . Yeah . If I look at
02:57	this , hopefully you noticed that what changed from this
03:02	left column to the right ? Is that the subtraction
03:06	became addition . This was a positive to this is
03:12	five , positive 5 -3 positive too . The subtraction
03:17	changed to addition . The positive too became a negative
03:21	too . Okay . And notice we got the same
03:24	result . We got the same answer . Same thing
03:28	here . This subtraction became addition . Notice in both
03:35	the the energy at the beginning didn't change at all
03:39	. That five stayed the same is negative . Six
03:41	stays the same . This positive four became a negative
03:47	. So let's see if we can uh with this
03:50	information if we can make a rule and hopefully you
03:54	might if you want to pause and see if you
03:56	can come up with your own rule go for it
03:58	. Um But our rule for this when you're subtracting
04:02	integers . So tracking an integer is the same as
04:07	adding its opposite . So tracking an integer is the
04:12	same thing as adding its opposite positive two . And
04:16	negative two are opposites positive for and negative for our
04:20	opposites . So let's make sure you write that down
04:24	. Subtracting . Mhm . An integer . Mhm is
04:34	the same . Mhm As adding its opposite . Okay
04:51	so we're going to use that information and that rule
04:54	to help us solve problems with subtracting integers . Let's
04:58	try an example . Here's our first example . As
05:01	always if you want to try this on your own
05:03	positive video and see if you get them right 1st
05:07	. A 3 -12 . If we're using that rule
05:11	, notice we're subtracting an integer . Uh Subtracting an
05:15	integer is the same as adding its opposite . You
05:17	just got to have that memorized . You got to
05:19	remember it . So I'm subtracting an integer . It's
05:23	the same as adding its opposite . That three doesn't
05:26	change . The subtraction changes to addition . Same as
05:30	adding its opposite . Well that's a positive 12 .
05:34	The opposite of positive 12 is negative 12 . So
05:38	three plus negative 12 . Hopefully you're comfortable with adding
05:42	integers . And if not watched the previous video .
05:45	Three plus negative 12 is eight of nine . The
05:50	next one negative eight minus a negative 13 . Again
05:54	, I'm subtracting integers . Uh It's the same thing
05:57	as adding its opposite , negative eight stays the same
06:01	subtraction becomes addition And the opposite is 13 . Sorry
06:06	the opposite of -13 is 13 . So really I
06:10	don't even need my parentheses there because it's a positive
06:14	13 . So negative eight plus 13 is gonna give
06:18	me five . Yeah The last one C 5 -
06:24	and -4 five stays the same . Same thing is
06:29	adding its opposite . So that changes to plus .
06:33	The opposite of -4 is 4 . 5 plus .
06:37	four is 9 . Right ? And if you also
06:42	notice sometimes you'll be able to get a lot quicker
06:46	with these . If you notice when you have a
06:48	negative next to another negative I'm sorry I should say
06:51	subtraction next to a negative . That's just going to
06:54	become a plus right ? You can think of those
06:58	two kind of coming together and creating the plus The
07:02	13 is just the 13 . Right same thing here
07:05	. Those that minus and the negative become the plus
07:08	Plus four . So that when you get more comfortable
07:11	with it , you're going to be able to do
07:12	those a lot quicker . Here's some to try on
07:15	your own example to notice we've got three into Jersey
07:29	this time instead of just two . Um remember we're
07:33	subtracting , I can't just rearrange , I can't put
07:37	the negative seven over here and combine it with a
07:39	negative 14 because it's not uh an addition problem or
07:44	a multiplication problem . The community property doesn't apply at
07:48	this point . Um So I'm just gonna go left
07:51	to right . So negative 7 -20 subtracting an injured
07:56	, I'm going to change it to in addition .
07:58	So negative seven stays the same , It's attracting and
08:01	it is the same as adding its opposite . The
08:04	opposite of -12 is 12 . Still gonna have that
08:09	-14 there . So this is simple , negative seven
08:13	plus 12 . That's gonna give me five . And
08:16	then I have 5 -14 . Again here subtracting an
08:21	injury , I can change it to an addition .
08:24	It's the same thing is adding its opposite . That's
08:27	a positive 14 . So I'm gonna change it to
08:31	negative 14 . I'm adding its opposite five plus negative
08:35	14 is negative nine . So after simplifying that we're
08:42	gonna get to negative nine . Here's some more to
08:45	try on your own . Here's our last example problem
08:55	. We got a word problem . Uh Which continent
08:58	has the greater range in elevation . So from the
09:02	very tip top to the very lowest point . So
09:06	we've got North America and Africa . The highest elevation
09:09	in North America is 6,198 ft . That's Mount McKinley
09:13	in Alaska . The lowest elevation is death valley in
09:17	California , at -86 m . It's negative because it's
09:21	actually below sea level . Um in Africa the highest
09:26	elevation , 5,895 m and the lowest negative 155 m
09:33	. Hopefully you remember the word range I should look
09:38	familiar for from statistics when you're finding the mean ,
09:42	media mode and range . And if you do remember
09:45	that , you would remember ranges . Uh the distance
09:50	from the greatest number two the least . So all
09:54	you did was subtract , you found the difference ,
09:56	right ? That's what difference means we're gonna do the
09:59	same thing . So the range of elevations , we're
10:02	going to take the highest and subtract the lowest and
10:05	that's going to give us the range in elevation .
10:07	So for north America , let's start with that .
10:12	We're gonna do 6198 negative 86 . Okay . Subtracting
10:22	and order the same thing is adding its opposite .
10:25	So we're going to change this to 6198 plus 86
10:31	. Which would give me , let's see if I
10:33	take two away , that will make it 6200 .
10:36	So then I'll have 84 left . So 6284 meters
10:44	. That's the range in elevation . For north America
10:48	. Let's do the same for Africa . So for
10:52	Africa , we've got the highest , which is 5,895
10:58	m minus Negative . same thing . I'm gonna change
11:05	it to an addition problem . 5895 plus its opposite
11:12	, which is positive . 155 . And if I
11:17	add those two together to some , let's take five
11:19	a way that would make 5900 plus another 100 Would
11:25	be 6000 even . And then I'd have 50 left
11:27	, so 6050 m . So the question which continent
11:37	has the greater range in elevation North America . Here's
11:42	one more problem to try on your own . Thanks
11:55	for watching . And if you like this video ,
11:57	please subscribe .

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