Master the Order of Operations (PEMDAS) in Math - [5-7-5] - Free Educational videos for Students in K-12

Master the Order of Operations (PEMDAS) in Math - [5-7-5] - By Math and Science

Transcript


00:0-1	Hello . Welcome back . The title here is called
00:02	Order of operations . This is part One . I
00:05	am not exaggerating when I tell you that what we're
00:07	going to learn in this lesson is really one of
00:09	the most important things that you'll ever learn in math
00:12	. It's called order of operations . And it's all
00:14	about how to do the calculations in the correct order
00:18	. That's why it's called order of operations . The
00:20	reason why it's important is because we use it in
00:22	Math , we use it in algebra , we use
00:24	it in geometry , we use it in all of
00:26	science and engineering . It really is one of the
00:28	core things that you will ever learn . So order
00:31	of operations means when we calculate we have to do
00:33	it in certain order . That's what it means to
00:35	say . Order of operations . The order is very
00:38	simple here . I'm gonna write it on the board
00:39	but I want you to keep in mind that we're
00:41	not going to be dealing with exponents in this lesson
00:44	. We're going to introduce exponents and talk about what
00:46	to do with exponents in a later lesson . But
00:49	for now we're doing everything but exponents . So when
00:52	you're doing operations and calculations you do them in a
00:55	certain order . The very first thing that you do
00:58	step number one . The first thing that you do
01:00	is always what we just said in the last lesson
01:02	. We do the parentheses . That's what this means
01:04	, parentheses . So whatever is inside of parentheses ,
01:07	you always do it first . And that is why
01:09	we did the last lessons on dealing with parentheses in
01:13	math . Now after you've conquered that , the very
01:15	next thing that you do , setting aside exponents for
01:19	now is you do multiplication and you do division .
01:23	All right , multiplication and division . And then the
01:25	third thing you do and this is the end of
01:28	our list that you do after you do the multiplication
01:30	and division part is you do addition and subtraction .
01:33	So I'm gonna leave this on the board throughout this
01:36	lesson because we will refer back to it . But
01:38	it's a very simple list . Basically the first thing
01:41	you do is you always conquer parentheses first . Whatever
01:44	is inside of those princes . That's what you do
01:46	first . After you conquer that . The next thing
01:48	you do is you do multiplication and division , right
01:51	? And you also then after that do addition and
01:53	subtraction . When you do the multiplication division . Notice
01:57	how these are in the same step . Multiplication and
01:59	division are at the same level , right ? Addition
02:02	and subtraction are below that . But they are also
02:05	at the same level . So let's see how to
02:07	conquer this . Let's take a look at a problem
02:09	for instance , seven times three plus two . So
02:14	we want to calculate this . The first thing we
02:16	do is we say do we have any parentheses ?
02:18	No , we don't . So we don't actually have
02:19	to deal with any parentheses . But you see until
02:22	you learn this , you don't really know what to
02:24	do first . Do you take the seven times three
02:27	and then add the two ? Or do you do
02:30	the three plus two and then multiply by seven .
02:33	And that is why we have to have these lists
02:36	of the way in which you do it because there's
02:38	only one right answer . And the way that we
02:40	do the answer is we look at the order of
02:42	operations . No parentheses . Okay . Do addition .
02:45	Do multiplication and division first . Now we do have
02:48	multiplication going on . So the addition here comes last
02:52	. So we have to calculate late this by saying
02:55	seven times three . We do that 1st 21 .
02:57	Now this edition is still going to happen but it
03:00	comes later . It comes last because it's in the
03:02	last priority . All right . What is 21 plus
03:06	two ? That's the only thing left 23 . So
03:08	the answer to this problem is 23 . So what
03:12	we did is we did the multiplication first and then
03:14	after we did that , we then completed the calculation
03:18	by doing edition . Let's do it in the wrong
03:20	order and see what happens . Instead of doing this
03:22	first , let's do the edition . First three plus
03:25	two is five . So we get that five .
03:27	Now we take the five and we multiply by 77
03:30	times five is 35 . 35 is definitely not the
03:34	right answer . If you take these uh this and
03:37	dump it into a calculator or computer , you will
03:39	not get 35 . You will get 23 you go
03:43	in the wrong order , You get a five here
03:45	five times 735 . That's wrong . So we have
03:47	to do it in the correct order . Otherwise the
03:49	answer is wrong . Alright , next problem . Now
03:53	that we have the introduction out of the way to
03:55	conquer the problems is actually pretty fun and easy .
03:58	Let's take a look at 12 . We'll divide it
04:01	by three and then we'll multiply by five . First
04:05	step . The first thing we always try to do
04:07	is parentheses but we don't have any parentheses . Next
04:10	we go to multiplication and division . But here's the
04:13	thing , we have a division here and then we
04:15	also have a multiplication . So both of these division
04:19	and multiplication are on the same level . They're the
04:21	same priority level . So what do you do ?
04:23	Do you do this first or do you do this
04:25	first ? Here's the thing . When you have multiplication
04:28	and division on the same level , you just do
04:31	it like reading a book left to right , You
04:33	always perform the same level calculations . These are at
04:36	the same level by going left to right . So
04:39	because you just do it like a book going left
04:41	to right , we do the 12 divided by three
04:43	, first 12 , divided by three is four ,
04:46	but then we still have to multiply by five .
04:48	Now the only thing left is four times five which
04:51	is 20 and this is the final answer . All
04:54	right . What would happen if we go in the
04:57	wrong order ? So here we did left to right
04:59	and we got an answer of 20 . Let's say
05:01	we do it in the wrong order . Let's do
05:03	the three times five . First , three times five
05:04	is 15 . So this gives us a 15 ,
05:07	12 divided by 15 , 12 divided by 15 .
05:11	I don't know what it is , but it's definitely
05:12	not 20 . So that would be the wrong thing
05:14	to do . So , we do the order of
05:16	operation in order . But when we have the same
05:20	level operation and the same uh kind of in the
05:23	same , you know ? And at the same level
05:25	here and we have to choose what to do .
05:26	We just do the same level operations as reading a
05:29	book . And the same exact thing will happen with
05:31	addition and subtraction . When we have adding and subtracting
05:34	happening at the same level . We just read it
05:36	like a book left to right . All right .
05:39	Let's get some more practice . I promise you ,
05:40	it will get easier as we do more of these
05:43	. Next problem . 5 -3 . Close Princes Plus
05:48	two . First thing we check parentheses . Very first
05:52	thing . So we look inside the Princes . We
05:54	have to do that first . We have 5 -3
05:57	. There's only one thing happening in here . So
05:59	we have to do the 5 -3 . But notice
06:01	you say , well , wait a minute . You
06:02	already told me that the adding and subtracting comes last
06:06	here . You're trying to do it first . Well
06:08	, I'm telling you that you have to do it
06:10	in the order of operations . The order of operations
06:13	says we must do parentheses first inside the Princes .
06:17	Even though it's kind of a last priority things .
06:20	Since it's inside the Prince season immediately kicks it up
06:23	. You have to do it first . So we
06:25	do follow this order . But you still must do
06:28	what's inside of this first . And you must follow
06:30	the order of operations inside of the parentheses . So
06:33	we have to do the five minus three first to
06:35	get it to . We still must then add this
06:37	to two plus two as you know , is four
06:39	. And so four is the right answer . If
06:42	you do this calculation in any other order , you
06:45	will get the wrong answer . For instance , if
06:46	you ignore the princes and say three plus 255 minus
06:51	50 that's wrong . So the answer is four .
06:54	You have to do it in the order that we're
06:56	doing it here . All right . Really important .
07:00	I cannot stress how important this is . So we're
07:02	gonna do a lot of practice . Let's take a
07:04	look at three plus five , multiplied by three plus
07:09	one . Now this looks weird . We have not
07:11	one set of parentheses but we have to parentheses .
07:13	It doesn't tell us what to do if we have
07:15	two parentheses , but it does say we must do
07:17	parentheses first . So what this means is we must
07:20	do this first and then this first . And whenever
07:23	we get as the answers . Lastly , we multiply
07:26	because multiplication comes after parentheses Now , I know we
07:30	are adding inside of here . And so you think
07:32	adding is last . But because it's inside of the
07:34	parentheses , we must do them first . So what
07:37	do we have ? Three plus five is eight and
07:41	three plus one is four . We can do them
07:43	kind of at the same time because you can do
07:46	one and then the other . But you still have
07:48	to do the princes first , both of them .
07:50	So here gives you an eight . Here gives you
07:52	a four . Now we're done with parentheses . We
07:54	can drop the princes eight times four because they don't
07:57	serve any purpose anymore . And now we have of
07:59	course multiplication . That's the only thing left anyway .
08:02	Eight times four is 32 . So the answer is
08:05	32 . If you do this in other order ,
08:09	you're not gonna get the same cancer . Or if
08:11	you do it'll be a coincidence . Next problem .
08:14	This one does not have any princes . 15 divided
08:18	by three Plus 16 . Divided by four . Now
08:23	. Here we go . We first look at the
08:25	order of operations . Do parentheses first , but we
08:27	do not have any parentheses . What is the next
08:30	level ? We do multiplication and division . We have
08:33	a division here in the division here . And in
08:35	addition here , we know that we're not going to
08:37	add first because that comes later . Multiplying and dividing
08:40	come first . So we see that we have this
08:44	division here and then we have this division here .
08:46	So we have to kind of do both of them
08:48	first . Before we ever do any adding What is
08:51	15 divided by three . That's going to be what
08:54	? 5 ? Right . We still have the plus
08:57	sign . What is 16 divided by 4 ? 16
09:01	? Five by four is four because four times four
09:02	is 16 . You see we did this one to
09:04	get this , we did this one to get this
09:05	. They're kind of at the same place . We
09:07	do them both . And then finally at the end
09:09	we add and get a night . If you do
09:12	this in the wrong order , you will get the
09:13	wrong answer . For instance , let's say we just
09:15	read it left to right . 15 divided by three
09:18	is 5 . So this is five , five plus
09:21	16 . If we just did this next , which
09:23	is wrong ? Five plus 16 , that's 21 then
09:27	21 divided by four is not nine . So that
09:30	would be the wrong answer . So we do the
09:32	order of operations . We didn't have any parentheses .
09:34	We see the multiplying and dividing comes first . So
09:37	we do the division's first . Both of them separately
09:39	. The addition comes last And we get an answer
09:42	of nine . Alright , next problem . Let's say
09:50	we have 20 -4 times three . All right .
09:56	First thing as we have already said is we do
09:59	parentheses first , but we don't have any parentheses here
10:01	at all . What comes next ? Try to remember
10:03	the list . Don't look at the list , think
10:05	about it . It's just parentheses . Multiply , divide
10:07	comes next , then adds attract very simple list .
10:10	So we add subtract . I'm sorry we multiply or
10:13	divide . Next we have this This is going to
10:15	come last . Multiply always comes first , So four
10:19	times three is 12 and then this minus with the
10:22	20 has to be done last . So we kind
10:24	of go to the end of the problem and do
10:25	this first . We never ever do subtraction first .
10:29	Next 20 minus 12 . You can count on your
10:32	fingers , you can go off to the side is
10:34	going to give you an eight and so the answer
10:36	to that is eight . If you do it in
10:38	the wrong order you won't get the right answer .
10:40	If you go left to right , 20 minus four
10:42	is 16 . 16 times three is definitely not eight
10:47	. This is the right answer . So you have
10:50	to do it in the right order . What ?
10:52	about 84 divided by parentheses ? Eight plus four plus
10:59	one . How do we do that ? Very first
11:02	thing we check parentheses always first . No matter what
11:06	else happens , parentheses has to happen first . We
11:09	have a set of parentheses , so it must happen
11:11	first . Yes . What's inside of it Is addition
11:13	. But because it's in the parentheses it has has
11:16	to happen first . Eight plus 48 plus four is
11:19	what ? 12 ? Now I can drop the parentheses
11:22	. After I've done the calculation , I still have
11:24	this division symbol with the 84 I still have this
11:27	plus one . All I've done is this first .
11:30	Now I must do this calculation and I asked myself
11:33	, what do I do ? I have divide and
11:35	I have add Multiply , divide . Always happens before
11:40	addition and subtraction . So the next thing I have
11:42	to do , you ignore this ? I must do
11:44	the 84 divided by 12 . So what I have
11:47	to do is figure out what is 84 divide by
11:51	12 . So I have to go through my multiplication
11:53	tables 12 times 5 . 12 times six . Eventually
11:57	you realize 12 times seven is 84 . Right from
12:01	your multiplication tables 12 times seven is 84 . So
12:05	what I'm going to get here is I'm going to
12:07	get for the division here . Which is going to
12:08	happen first is going to be a seven and then
12:10	this plus one is the very last thing . What's
12:12	not plus seven , seven plus the one finally ,
12:16	once that's the only thing left . Of course ,
12:18	it's got to be +88 is the final answer .
12:21	As the problems get harder or longer , I should
12:24	say we have to do a little better job .
12:27	Just making sure that we're doing everything in the right
12:29	order . Let's take a look at four times five
12:33	plus three . The very first thing we do is
12:37	always parentheses . Here's your parentheses . So , we
12:39	have to do it first . All right . The
12:42	four times is going to be done later , but
12:45	I have to do this . First five plus three
12:47	. Is what ? Eight ? All right . So
12:49	now I have to do what ? The only thing
12:50	left is multiplication four times eight is 32 And this
12:55	is the final answer . 32 . All right .
12:58	How many more do we have here ? Only a
12:59	couple more problems . Yeah , they're a little bit
13:03	longer . Not too bad . Let's take a look
13:05	at four times three . And this is going to
13:08	be plus four times three . What is the very
13:12	first thing we do first ? We always do parentheses
13:16	next . We always do a multiply divide next .
13:19	We always do addition , subtraction . Of course .
13:22	Whatever is inside the Princes must be done first ,
13:24	no matter what . So , I have two sets
13:27	of parentheses here . This 14 times three is gonna
13:29	give me 12 . This 14 times three is also
13:32	going to give me 12 . And this plus sign
13:34	must then happen last . I have to do what's
13:36	inside of your first . What's inside of your 1st
13:39	12 plus 12 . If you go over here And
13:42	just do it , get a four and a two
13:45	. And so the answer is 24 . And so
13:48	the answer to this problem is 24 . All right
13:52	. Now , here is our last problem . Let's
13:55	take a look at two plus six times five minus
14:01	parentheses . Five times four . All right . So
14:05	, we have again . What is our order first
14:07	? We do parenthesis . Then we do multiply divide
14:09	. Then we do add subtract . We see .
14:11	We have one parenthesis set here and another one here
14:14	. So , we have to do those first .
14:16	So , uh we can do them at the same
14:18	time . But let's just do it . Maybe a
14:20	little more . Break it out . We have to
14:21	do this one . First , two plus six is
14:22	eight . We can drop the princes after . You
14:25	calculate times five -5 times four . So , we
14:29	could have done this one in Paris at the same
14:32	time as this one . But let's just take it
14:34	one step at a time . Do this one first
14:36	. But now we have this stuff . All we
14:38	did was leave the rest of the problem that we
14:40	must do this one First before anything else . So
14:43	we have eight times five . That will do that
14:45	later . And then here five times four is 20
14:49	. So now we have eight times 5 -20 .
14:53	What do we do first ? We do uh multiply
14:56	divide before add subtract . Here . We have multiply
14:59	here , we have subtract . So we have to
15:01	do the multiply first , eight times five is 40
15:04	. And then the last thing we do is the
15:06	-20 , which is 20 . The answer is 20
15:09	. So in this one I did it the same
15:10	way . But I'm just saying you could do this
15:12	and do this at the same time , but I
15:13	chose to do this one first , rewrite the problem
15:16	, then do this one , next , rewrite the
15:17	problem , then go down from there . So again
15:20	, incredibly important , very important . In fact we
15:23	have several lessons on this . You always do parentheses
15:26	first , whatever's inside of these parentheses first , then
15:29	you do uh multiply divide which are at the same
15:32	level , they're multiplies not higher than divide there at
15:35	the same level than you do ads of track ,
15:37	which are also at the same level . Practice every
15:40	one of these problems , follow me onto part two
15:42	, we're gonna get a little more practice with order
15:43	of operations . Again , it is really one of
15:45	the most central things that we're gonna learn . So
15:47	take your time , make sure you understand what I'm
15:49	doing . Follow me to part two , we'll continue
15:51	building your skills .

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