Order of Operations - Free Educational videos for Students in K-12

Order of Operations - By Anywhere Math

Transcript


00:0-1	with a new school , you're just getting started .
00:02	Some of you may have done a little back to
00:03	school shopping . So let's say you bought Five t
00:07	shirts that were $12 each and three pairs of pants
00:12	that were $40 each . How much did you spend
00:16	? Oh sorry I forgot uh the T shirts were
00:19	on sale . There were $3 off each one .
00:23	And your dear Aunt Sally , I gave you a
00:28	gift certificate for your birthday worth $50 . Now .
00:32	How much did you spend ? Welcome to anywhere .
00:53	Math . I'm Jeff Jacobson . And today you may
00:55	have guessed we're talking about order of operations . Now
01:00	let's talk about that back to school shopping . Uh
01:02	Let's start with the t shirts . The t shirts
01:04	if you remember we're $12 Each to begin with .
01:09	But then they were on sale there were $3 off
01:11	each of them . So if we subtract three that
01:15	would give us $9 for each t shirt . Right
01:19	uh you bought five of them . So the t
01:22	shirts Cost $45 , mm . Okay that's the t
01:28	shirts . Well how about the pants ? The pants
01:33	were $40 . We bought three of those . No
01:39	sale unfortunately . So those were $120 . Yeah if
01:44	we had those two up that's pants If we add
01:50	those two up we get $165 . But your dear
01:56	aunt sally gave you a gift certificate on your birthday
01:59	worth $50 . So we're gonna subtract 50 which gives
02:04	us a grand total of 115 dollars . Now we
02:12	could solve the same problem using a numerical expression and
02:16	the order of operations . But first let's talk about
02:20	what these order of operations are . As the name
02:23	suggests , it's basically an order that you do the
02:27	operations and that's all it is . It's a set
02:30	of rules that we use so that when we get
02:32	a problem a an expression uh everybody will get the
02:36	same answer if they do it correctly , people won't
02:39	do it two different ways and get two different answers
02:42	. Um So the operation that we do first is
02:46	anything in parenthesis ? Mhm . What this is after
02:57	you do anything in parentheses ? Next if you have
03:01	any exponents mm you take care of those after that
03:08	. The next operation is multiply or divide . Now
03:12	notice I say or Multiplying doesn't always come before the
03:19	division . It's whichever one multiply or divide comes first
03:24	going left to right , multiply or divide left two
03:30	right . And finally uh we either add or subtract
03:38	again or see or add or subtract going from left
03:46	to right . Mhm . So these are the order
03:53	of operations and this is what where you are going
03:56	to use uh to evaluate numerical expressions . Okay ,
04:01	for our first example let's evaluate a numerical expression .
04:05	Let's do the exact problem about the back to school
04:09	clothes . So first let's write the actual expression .
04:13	uh if you remember we talked about T shirts were
04:16	$12 but then there were $3 off , so 12
04:20	minus three . That's going to represent the cost of
04:24	the t shirts . Uh We bought five of those
04:28	, so we're gonna multiply that by five . Okay
04:31	then we also Have to add the cost of the
04:35	pants . We bought pants . Uh that were what
04:39	were they ? $40 each And we bought three of
04:42	them , so three times 40 each . But then
04:46	at the end we had our gift certificate from Old
04:48	Deer and sally . Um And so we're gonna subtract
04:53	$50 , that's how much we had worth of a
04:55	gift certificate . Here is our numerical expression . If
04:59	you look at the instructions , evaluate the following numerical
05:03	expression . If you remember from the last video evaluate
05:06	just means to find the value . All we do
05:10	is this is kind of complicated . We're gonna break
05:12	it down until we get one value . Um A
05:16	numerical expression . Well numerical oh just means it has
05:21	numbers . And an expression is just like a phrase
05:25	a mathematical phrase in this case a numerical expression .
05:29	Uh More specifically has numbers and operations . It has
05:34	to have operations . So you see we've got multiplication
05:37	, subtraction addition . Uh Those are the operations .
05:40	So that's what a numerical expression is . So what
05:46	are we going to do first ? Well hopefully you
05:48	remember we need to use those order of operations .
05:52	And a quick and easy way to remember is please
05:56	excuse my dear aunt sally see if you got that
05:59	joke from earlier . Um Pen does . For sure
06:04	. Parentheses . Mhm . Exponents multiply or divide now
06:09	. Multiplication doesn't always come before division . So I'm
06:12	gonna write it like this because we don't know which
06:16	ones coming first we have to go left to right
06:18	and then finally . Mhm . Addition or subtraction .
06:22	So some people remember penda . Some people remember please
06:26	excuse my dear aunt Sally who gave us that gift
06:30	certificate . So let's do it . First up parentheses
06:34	. Do we have any parentheses ? Yes We do
06:37	right here . So that's what we got to take
06:39	care of first . So 12 -3 . It's not
06:43	the key when solving order of operations problems are evaluating
06:48	numerical expressions Is to do one step at a time
06:53	. The most common mistake I see students do is
06:56	they try to do too many things at once and
06:59	that gets them in trouble . So try to just
07:01	do one step at a time . So I'm only
07:03	doing the parenthesis . So the five is still there
07:07	, plus the three times 40 -50 . Okay ,
07:13	parentheses are done . So now we're gonna go to
07:15	exponents . Well if we look there are no exponents
07:18	, so we're done with that . Now multiply or
07:21	divide , whichever comes first left to right . So
07:25	if I'm going left to right , Here's multiplication ,
07:28	five times 9 Is 45 . I still have the
07:32	plus three times 40 -50 . Am I done with
07:38	multiplication or division ? No , I have another multiplication
07:42	here . So now 45 stays the same plus three
07:47	times 40 , which is 120 minus 50 . We're
07:52	done with multiplication division . So now our last step
07:55	is addition or subtraction . Whichever comes first left to
07:59	right . So notice we have both . But this
08:02	edition comes first going left to right . So I'm
08:04	gonna add 45 and 120 , which is 165 -50
08:11	. So our final uh Uh the difference here is
08:16	115 , which is exactly what we got when we
08:22	did it the first time . Let's try another example
08:26	. All right , here's example to we got to
08:28	evaluate this numerical expression and feel free to pause the
08:32	video if you want to try this on your own
08:34	first . Well to do this , we got to
08:37	remember the order of operations obviously and we know that
08:40	parentheses come first . Well if you look we have
08:44	two things that we could possibly do inside the parentheses
08:48	, we have addition . We have an exponent when
08:51	you have parentheses and you have more than one operation
08:54	inside the parentheses , you use the order of operations
08:58	inside the parentheses to figure that out . So we
09:02	know that exponents would come before addition . So that's
09:06	what we're gonna do again . I'm gonna do one
09:09	step at a time and I'm always going down to
09:11	help stay organized . So 30 divided by seven plus
09:17	well to cube . Hopefully from the last video .
09:20	Remember to cube means two times two times two .
09:23	Which is hey , I still have that time six
09:27	at the end . My parentheses aren't done . I
09:30	still got to do this edition . So I still
09:32	have that . 30 divided by seven plus . eight
09:35	is 15 times six . Now parentheses are done .
09:40	There's no exponents here . We already did at the
09:43	beginning . Uh now were to multiply or divide going
09:47	left to right . We had division and multiplication but
09:51	left to right . This division comes first . So
09:55	30 divided by 15 is too and two Times six
10:01	is 12 . Here's something to try on your own
10:11	. Okay , let's do another example . So evaluate
10:13	this numerical expression , uh , same thing or of
10:16	operations . We're gonna do parentheses first and again if
10:19	you want to pause it and do it on your
10:21	own , go for it . So parentheses I'm gonna
10:24	do six plus one which is seven . I'm gonna
10:30	keep those parentheses there because I have a number right
10:32	next to the parentheses and we haven't talked about that
10:36	yet but we'll get to it . Uh So now
10:39	after parentheses there's nothing I can do inside the parentheses
10:43	. So I'm going to leave it alone and next
10:45	would be exponents . So to square it is just
10:48	two times two which is four . So 15 minus
10:51	47 divided by four . Now this is new when
10:58	you have a number next to parentheses . That's just
11:01	a way of showing multiplication . Uh It's kind of
11:04	just a shortcut . Instead of drawing uh an ex
11:09	for multiplication or a dot , we can just put
11:11	it next to the parentheses . Um And you'll see
11:14	that a lot when you when you get into algebra
11:16	, Pre algebra and algebra . So that means multiplication
11:20	and now we have multiplication division going left to right
11:25	. That multiplication comes first . So I've got 15-4
11:29	times seven Is 28 divided by four . I'm not
11:34	going to do this attraction because I have division which
11:37	comes before . So 28 divided by four is 7
11:43	And 15 -7 . Is they ? Okay ? Thanks
11:53	for watching . And if you like this video please
11:55	subscribe .

Summarizer

DESCRIPTION:

OVERVIEW:

Order of Operations is a free educational video by Anywhere Math.

This page not only allows students and teachers view Order of Operations videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.