Multiplying and Dividing Integers - Free Educational videos for Students in K-12

Multiplying and Dividing Integers - By Anywhere Math

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00:0-1	Welcome to New or Math . I'm Jeff Jacobson .
00:01	And today we're gonna talk all about multiplying and dividing
00:05	integers . Let's get started . All right . Today
00:25	we're gonna talk about multiplying and dividing introduce first .
00:28	We're just going to talk about multiplying integers . And
00:31	with multiplying integers there's two situations we have to think
00:34	of what happens when you multiply introduce that have different
00:38	signs like a positive and negative . And what happens
00:41	when you multiply introduce that have the same sign either
00:45	positive times positive or negative times negative . The first
00:49	one we're going to talk about is multiplying injuries with
00:53	different signs . So let's think about well , what
00:56	if I had three times -2 ? Well , we
01:01	know multiplication is just a shortcut for repeated edition .
01:05	So you can think of this as three groups of
01:09	negative too . So if we think about that ,
01:12	that's equal to negative two plus negative two plus negative
01:18	two . Right ? Three times . If it was
01:21	just a three times to you be thinking , Okay
01:24	, two plus two plus two . Right . It's
01:26	just repeated addition . Well , we already know how
01:28	to do this adding introduce . We've done that before
01:32	. If I'm adding the same sign these are all
01:34	negative . It just gets more negative and I keep
01:37	the signs so negative two plus negative two plus negative
01:39	two is negative . Six . Okay . So notice
01:43	when I'm multiplying different signs , it's gonna be negative
01:48	. What if it was the other way around ?
01:50	Right ? If it was -3 times 2 ? Well
01:55	, again , with multiplication , the order doesn't matter
01:59	. I could rewrite that as two times negative three
02:03	. Which means I have two groups of negative three
02:06	which is negative three plus negative three . And that
02:10	gives me negative six again . So notice it doesn't
02:14	matter if the first integer is positive and the second
02:17	is negative or First is negative . 2nd is positive
02:22	. If you're multiplying two integers and they have different
02:25	signs , you're always going to get a negative for
02:30	your product . All right now let's talk about multiplying
02:33	integers with the same sign . So either a positive
02:35	times positive or negative times negative . Well , we
02:39	can skip positive times positive because you've been doing that
02:42	for a long time . Three times two is six
02:44	. Right ? You don't have to worry about that
02:46	. The one we do have to concentrate on is
02:49	what happens when we have a negative times a negative
02:52	to kind of illustrate what a negative times a negative
02:55	has to be . We're gonna see if we can
02:57	find a pattern here . So , first negative three
02:59	times to well , we just did that . That's
03:02	negative . six . Right ? Different signs . Same
03:05	thing here , negative three times one different signs .
03:08	So that's gonna be negative . Three negative three times
03:11	zero . Well , anything times zero is zero now
03:16	is where we get to the same signs and we
03:19	have to think well what what does that need to
03:21	be ? And when I say what does it need
03:23	to be multiplying with negative numbers , it doesn't really
03:29	make sense to think of it as repeated addition .
03:32	It doesn't really hold true like it did when we
03:35	had different signs . Um So that kind of explanation
03:39	doesn't really work instead . If we look at the
03:43	pattern here . Well from negative three to our ,
03:47	sorry , from negative 62 negative three . What happened
03:50	? Well we actually added three right negative six plus
03:56	three is negative three . From negative 3 to 0
04:00	. Same thing . We added three . So if
04:03	we continue that pattern and we add three what are
04:08	we gonna get ? Well zero plus three is three
04:12	. If we continue that pattern again 3-plus 3 is
04:17	six . So notice that negative three times negative one
04:24	, multiplying the same signs is going to give us
04:27	a positive just like a positive test positive gives us
04:29	a positive and that holds true here as well .
04:32	So that pattern hopefully we'll kind of show you what
04:36	a negative times negative has to be . There's really
04:40	not a great explanation of why it is . It
04:43	just has to be for kind of math to work
04:45	out . Um So I hope that kind of makes
04:48	sense now . It's kind of explain it all together
04:51	. All right . So here are the rules multiplying
04:53	in pictures with a different sign will always give you
04:56	a product that is negative , multiplied integers with the
05:01	same sign . We'll always give you a product that
05:04	is positive . Okay , make sure you write this
05:07	down and um let's get to some examples . All
05:11	right . Here's a couple examples . First negative five
05:13	times negative six . Well five times six is 30
05:17	and they're multiplying the same signs so it's going to
05:20	stay positive now be we've got three intruders were multiplying
05:27	. Don't worry about it . Just go the first
05:29	two And think about our rules . So if I
05:32	do nine times negative eight , that's a positive times
05:37	a negative different signs . So that's gonna be negative
05:40	72 and then multiply by that negative to now we've
05:45	got same signs multiplied . So that's going to give
05:48	us a positive . Um and 72 times two is
05:52	1 44 . Here we go . Here's something to
05:57	try on your own . An example to evaluate .
06:11	So the first one we have negative two squared .
06:15	Now , what this means is the negative two is
06:18	being squared . So that means negative two times negative
06:22	two same signs . So that's going to be a
06:26	positive for b negative five square it Now this one's
06:31	a little bit tricky . You'll notice there is no
06:34	parenthesis here . And if you think about it ,
06:37	you guys look well what's being squared because there's no
06:40	parentheses , it's actually just the five being square .
06:44	So what that means is we have a negative five
06:48	times five . Okay , So the way we do
06:52	that first is what we gotta do what's in parentheses
06:54	first . So five times five is 25 and then
06:58	we have the negative out front . So you gotta
07:01	be careful with that . Here's some more to find
07:03	your own . All right now , let's talk about
07:11	division . If we're dividing two integers that have different
07:15	signs , the quotient is negative . It's the exact
07:19	same as multiplication . If we divide two integers that
07:22	have the same signs , same thing , the question
07:26	is positive . So the rules for multiplication with integers
07:30	and division with integers is exactly the same . If
07:35	we're doing same signs it's going to be positive .
07:38	Different signs going to be negative . So let's try
07:41	a few examples . Alright example three negative 60 divided
07:45	by five . We're dividing different signs . So we
07:50	know our quotation is gonna be negative and 60 divided
07:53	by five is 12 . So negative 12 . Next
07:58	one be negative 24 divided by negative three same signs
08:03	. So we know our quotient will be positive And
08:06	that will give us eight . I could write 8/1
08:10	but I don't need it . Next one . divided
08:13	by -5 . Well , we know any number or
08:16	sorry , zero divided by any number is always zero
08:22	. Right ? But now here D What about -5
08:26	divided by zero . Mm . Well this one's a
08:30	little bit tricky . -5 divided by zero . We
08:34	don't have an answer for that . We call it
08:37	un defined . Mhm . And that's just something you
08:43	got to know . You got to memorize . Here's
08:45	something to try on your own . All right .
08:59	Here's the last example example for evaluate when X equals
09:03	eight and y equals negative four . So this is
09:06	the expression we're going to evaluate , we're kind of
09:08	bringing everything together . Uh Subtraction with integers , multiplication
09:14	and division . Um So my first step whenever I
09:17	evaluate is to substitute so eight I substitute in for
09:21	X . I have 10 minus . I don't need
09:24	parentheses around it because it's not negative . So I'm
09:27	just gonna write eight squared Divided by now for -4
09:33	. I do want parentheses around it . Just because
09:37	it looks confusing when you have a division symbol and
09:40	then a negative symbol right next to each other .
09:43	That looks weird . So we just put parentheses and
09:46	now we just use order of operations to simplify .
09:49	So first I'm going to do my exponents , this
09:52	is not negative eight squared , it's just the eight
09:55	square . So I'm gonna have 10 minus eight square
09:58	to 64 divided by negative four . So next step
10:04	I'm gonna do my division before my subtraction . So
10:07	I still have 10 minus 64 divided by negative four
10:12	. That's gonna be negative because it's different signs .
10:15	And 64 divided by four is 16 , so negative
10:19	16 and now subtracting uh and injuries the same thing
10:24	is adding its opposite . So I have 10 Plus
10:28	16 which is 26 . I don't know if I
10:31	have enough room , I'm gonna write it over there
10:35	. So 26 is my answer . Here's something to
10:38	try on your own . As always , thank you
10:46	so much for watching and if you like this video
10:49	, please subscribe .

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