Math Antics - Order Of Operations - Free Educational videos for Students in K-12

Math Antics - Order Of Operations - By mathantics

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00:03	Uh huh Hi , welcome to Math Antics . Today
00:08	we're going to talk about an important math concept called
00:11	order of operations . Order of operations is just a
00:15	set of math rules that tell you which math operations
00:18	, like addition or multiplication to do first . Now
00:21	you might be wondering especially if you're a teenager ,
00:24	why do I need rules to tell me which operations
00:27	to do first ? Can't I just do them in
00:29	any order I want ? Well , that's a really
00:31	good question . And to answer it , we're going
00:33	to give two totally different people the same math problem
00:36	to solve the problem is two plus five times four
00:41	. Mm I like addition better than multiplication . So
00:45	I'm going to do that first . Let's see .
00:47	Two plus five gives us seven and then I just
00:49	multiply that seven by the four and I get 28
00:53	. That was easy . But you'd better not copy
00:55	my answer . Don't worry . I'm not going to
00:58	copy your answer because I want the right answer and
01:01	I prefer multiplying . So I'm going to do that
01:04	first . Let's see . Four times five equals 20
01:07	. And then I'll add the two which gives me
01:10	22 for a final answer . What makes you think
01:13	that's the right answer ? All my calculations were correct
01:16	. I even checked it with a calculator . The
01:19	only calculator I need is right up here And the
01:22	correct answer is 22 . Okay , so which one
01:28	of these guys do you think is right ? Neither
01:31	one made any mistakes with the calculations . They just
01:34	did the operations in a different order and got different
01:37	answers . Well , since there were no mistakes in
01:40	a way they were both right . But math would
01:42	be a very confusing subject if there were different answers
01:45	to the same problem . And that's where order of
01:48	operations can help us out the order of operations .
01:51	Rules are a way for us all to agree on
01:53	the order that you should do math operations in and
01:56	if we always do operations in the same order then
01:59	we'll always get the same answer . So now that
02:01	you know why we need order of operations rules ,
02:04	let's find out what those rules are . They're basically
02:07	four of them and they go something like this .
02:09	First do operations in parentheses and brackets . Next do
02:14	exponents , then do multiplication and division , last ,
02:18	do addition and subtraction . Let's take a closer look
02:22	at each of these rules and see some examples where
02:24	they help us . First on the list was do
02:27	operations and parentheses and brackets . Now , in case
02:30	you haven't seen parentheses or brackets using math before let
02:33	me briefly explain how they work . Parentheses are just
02:37	these symbols that curve forwards and backwards and they're used
02:40	in pairs like this . And when we put numbers
02:43	and operators in between them , it forms a group
02:46	. It's almost like the parentheses form a package to
02:48	hold whatever math stuff we put inside them and brackets
02:52	work exactly the same way as parentheses . They just
02:55	have a different shape that looks a little more boxy
02:57	, but they mean exactly the same thing . So
03:00	parentheses and brackets are used to group things together and
03:04	our rules tell us to do any operations inside these
03:07	groups first , for example , have a look at
03:10	this problem 10 times four Plus 5 . It has
03:13	three numbers and two operations , multiplication and addition .
03:18	But two of the numbers and the addition symbol are
03:20	inside parentheses . That means that they form a group
03:23	and we need to do that part of the problem
03:25	. First four plus five equals nine . So the
03:28	part inside the parentheses can just be replaced with a
03:31	simplified value nine oh and once you do the math
03:35	, that's inside parentheses and get a single number like
03:37	this , you usually don't need to show the parentheses
03:39	anymore . Now that the parentheses are gone , we
03:43	just have one operation left to do . We multiply
03:45	10 times nine and that gives us 90 as our
03:48	final answer . So parentheses can really help you know
03:52	what part of a problem you're supposed to do first
03:54	. But what if you get a problem that has
03:56	more than one set of parentheses like this ? Five
03:59	minus three plus six times to fortunately it doesn't matter
04:03	which set of parentheses you do first . You just
04:06	need to do everything that's inside the parentheses before you
04:09	do anything that's not inside parentheses . In other words
04:13	we need to simplify both of our parentheses groups before
04:16	we can do the addition in between them . The
04:19	first group five minus three simplifies to two . And
04:22	the second group six times to simplifies to 12 .
04:26	Now we can do the last operation and add the
04:28	values that we got from . Simplifying two plus 12
04:32	equals 14 . Okay , now that we know that
04:35	we always do operations and parentheses or brackets first ,
04:38	let's take a closer look at the second rule that
04:40	says the next thing we do is exponents . Now
04:44	if you haven't seen exponents before , they're just a
04:46	way of writing repeated multiplication . For example , the
04:50	repeated multiplication four times four can be written in a
04:53	shorter form as four multiplied twice and four times four
04:57	times four can be written as four multiplied three times
05:00	and four times four times four times four can be
05:03	written as four multiplied four times , get the idea
05:07	. This small number is called an exponent or power
05:10	. It just tells you how many times to multiply
05:12	the bigger number together . So after we take care
05:15	of any parentheses , simplifying any exponents becomes the next
05:19	highest priority . For example in this problem we have
05:22	to simplify the exponents before we can do the other
05:25	multiplication . The exponent is telling us to multiply five
05:28	together twice . So five times 5 is 25 .
05:32	And after we do that , then we multiply the
05:35	result by three . So 25 times three is 75
05:39	. Oh and one thing I should point out sometimes
05:42	you'll get a problem that has exponents inside of parentheses
05:45	like this problem . And you may wonder how can
05:48	I get rid of the parentheses ? Before I do
05:50	the exponents , you might think that if you simplify
05:53	the exponent first , you're breaking the rules . But
05:55	the truth is that by doing whatever operations are inside
05:58	the parentheses , you are doing the parentheses first ,
06:02	the parentheses really just tell you where to start .
06:04	So in this problem first we do three to the
06:07	power of to which means three times three which is
06:10	nine . Then the part inside the parentheses is nine
06:13	times four which equals 36 . And once the parentheses
06:17	are gone we add 36 plus six and get 42
06:20	as our final answer . All right now we're gonna
06:23	look at the last two rules together . These two
06:26	rules are really important because they deal with the most
06:29	common math operations , addition , subtraction , multiplication and
06:33	division . And the rules tell us that we need
06:36	to do multiplication and division before we do addition and
06:40	subtraction . To see how these rules work . Let's
06:42	look at a few quick examples that use those basic
06:45	operations first . Let's try this 12 plus five times
06:49	four . Ha ha Does this look familiar , yep
06:52	, It's the one we gave to my two friends
06:54	earlier and now that we have our rules , we
06:57	see that we have to do the multiplication before the
06:59	edition Five times four equals 20 . And then we
07:03	had the two which gives us 22 . So the
07:06	second guy was right . What a surprise . Now
07:12	let's try this one . Three times 5 -1 .
07:16	Our rules tell us that multiplication is higher on the
07:19	list than subtraction . So we do three times five
07:22	first and that gives us 15 . And then we
07:25	subtract the one which leaves 14 as our final answer
07:29	. Here's one with division and subtraction . 20 minus
07:33	10 divided by five . And since division has a
07:36	higher priority , we do the 10 divided by five
07:38	first which equals two . And then we subtract two
07:41	from 20 and get 18 as our final answer .
07:45	And here's another problem . 12 divided by 6-plus 5
07:49	. Again . Our rules say to do the division
07:51	before addition . So 12 divided by six equals two
07:55	. And then we add the five to get seven
07:58	. And here's one last problem . 40 divided by
08:01	four times 5 . Which do we do first ?
08:04	The multiplication or division are rules . Don't tell us
08:08	. Well , that's because multiplication and division are tied
08:12	for priority or importance . So our addition and subtraction
08:16	and that's the reason we need an extra part at
08:18	the end of each of these rules that says from
08:21	left to right , if you have a problem that
08:24	has both multiplication and division , then you're supposed to
08:27	work it from left to right . That's because in
08:30	some cases you can get a different answer . If
08:33	you go from right to left . For example ,
08:35	in this problem , if you work from right to
08:37	left the wrong way , you do the four times
08:40	five first and get 20 and then 40 divided by
08:43	20 equals two . But if you go from left
08:46	to right , you would do 40 divided by four
08:49	first , which is 10 and then 10 times five
08:52	equals 50 . Wow . The direction we went made
08:55	a big difference . So whenever you have a problem
08:58	that has a mixture of multiplication and division or a
09:01	mixture of addition and subtraction , you know to do
09:03	the operations in order from left to right . All
09:07	right , we're just about done . But let's have
09:09	one more . Look at all four of our rules
09:11	before you start practicing with the exercise is the order
09:14	of operations . Rules say first do operations and parentheses
09:18	and brackets . Next new exponents , then do multiplication
09:23	and division from left to right , last do addition
09:27	and subtraction from left to right . All right ,
09:31	That does it for this video . Good luck with
09:33	the exercises . And I'll see you next time .
09:35	Learn more at math Antics dot com .

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