Properties of Addition and Multiplication - Free Educational videos for Students in K-12

Properties of Addition and Multiplication - By Anywhere Math

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00:0-1	Welcome to anywhere . Math . I'm Jeff Jacobson .
00:01	And today we're going to talk about the properties of
00:04	addition and multiplication . Let's get started . All right
00:26	. Well today's lesson is all about equivalent expressions .
00:31	Well first let's talk about what exactly are equivalent expressions
00:35	. If you think about you might already know equivalent
00:39	fractions , right ? You know that one half and
00:43	two force are equivalent fractions because they have the exact
00:49	same value . That's exactly the same with equivalent expressions
00:56	. Equivalent expressions are expressions that have the same value
01:10	. Okay , expressions that have the same value ,
01:13	they might look a little bit different . The order
01:16	might be different but the value is the same .
01:20	Now let's get into the two types of properties we're
01:22	gonna talk about today . The first property we're going
01:25	to talk about is the community of property . Now
01:28	when you look at that word you might think commute
01:32	. And if you ask your parents about the word
01:34	community , they would probably think about commuting to work
01:37	. So they would go from their house to work
01:41	. And then when they're done with work they go
01:43	from work back to their house . Now the distance
01:47	would always be the same . It's not going to
01:48	change whether I go from the house to work or
01:51	work from the house . I could change the order
01:54	but the distance is still going to be the same
01:57	. That's the same thing with a community of property
02:01	. The order does not gonna put that big capital
02:09	letters does not change the value . The other thing
02:18	is that it only works with two types of operations
02:22	, addition and multiplication . Okay so make sure you
02:33	have that written down . So for the community of
02:36	property of addition We could have something like 3-plus 2
02:42	. Yeah . Well that expression is equivalent Right ?
02:48	It has the same value as 2-plus 3 . Okay
02:54	we change the order but the value does not change
02:58	. Three plus two is 52 plus three is five
03:00	. The value is still the same . It works
03:03	for addition . It can also work for multiplication .
03:06	Four times five is equivalent . Yeah , 25 times
03:13	four . They both have the same value for community
03:18	property . The order does not change the value order
03:21	does not matter . And it only works for addition
03:25	and multiplication . Right ? If I try to do
03:27	subtraction , 3 -2 is not equal to 2 .
03:35	-3 . -2 is one . Two minus three is
03:37	negative one . So that doesn't work . And same
03:40	thing with division 10 divided by two is not the
03:45	same as two divided by 10 . They don't have
03:50	the same value , They are not equivalent . Let's
03:53	check out the associative property . All right . Let's
03:56	talk about the second property . The associative property .
04:00	Well , just like we did with community of property
04:02	. We talked about the word commute , associative property
04:05	. Let's talk about the word . Associate Associate just
04:09	means . What do you identify with if I want
04:11	to give myself as an example ? Uh I like
04:15	to play soccer . So I associate myself with soccer
04:19	players or with my team . I also like to
04:22	snowboard in the winter . So in the winter I
04:24	might associate myself with other snowboarders , depending on what
04:30	group I'm in . It doesn't change who I am
04:32	. I'm still myself . I haven't changed . But
04:35	the grouping has changed . Okay , so the associative
04:39	property is changing the grouping . So whenever you think
04:46	of right ? Associate property , think of groups ,
04:51	right . Do I kind of associate myself with the
04:54	soccer group or the snowboarding group ? Right . Changing
04:58	the grouping does not , again big capitalize does not
05:06	change the value . Okay . And this is just
05:14	like the community of property . We only use this
05:17	with addition , addition and multiplication . If I had
05:32	three plus four plus seven . Well , right now
05:38	we're grouping 4-plus 7 together . But because this is
05:42	all addition , we're only adding here , that would
05:46	be equivalent to three plus four plus seven . I
05:52	could decide to group the three plus the four together
05:55	. Okay . Instead of the four plus the seven
05:57	. Okay , those are equivalent expressions . Right here
06:01	, we just demonstrated the associative property of addition .
06:06	Same thing with multiplication three times uh 10 times five
06:13	. Okay , That's equivalent to three times 10 Times
06:20	five . And I'll put the five out front .
06:24	Okay , those are equivalent expressions as well because this
06:30	is all being multiplied together . So changing the grouping
06:34	is not going to change the value . 10 times
06:37	five is 50 times five times 3 is 150 .
06:41	Three times 10 is 30 times five is 150 .
06:45	The value is the same . They are equivalent expressions
06:49	. Let's get into some examples . Alright , here
06:51	we go with the example one . Simplify the expression
06:54	and explain each step . So a We've got seven
06:59	plus in parentheses . 12 plus x . Um well
07:03	, I can't add 12 plus X . Because X
07:05	is a variable . I don't know what it actually
07:07	is , I don't know the value of it .
07:09	But I could do seven plus 12 . And if
07:13	I notice we're only using addition . So in that
07:17	case instead of having these group together , I could
07:20	change the grouping to this seven plus 12 and then
07:26	plus X . Okay , well we're simplifying . Let's
07:31	explain this step . What step do we just use
07:34	? We changed . We didn't change any of the
07:36	order . 7 , 12 X . The order didn't
07:39	change . So it's not community of property . The
07:43	grouping changed , right ? So that's associative property .
07:47	And if you think this is addition so it's associative
07:50	property of addition . I'm just gonna write a P
07:54	. A associative property of addition . Okay now let's
07:59	simplify . Well seven plus 12 is 19 plus X
08:04	. So now that is simplified . Let's go to
08:08	the next 16.1 plus X . Plus 8.4 . It's
08:14	all addition . So I know I'm gonna be using
08:16	one of the properties of addition . Um But I
08:20	want to do 8.4 plus 6.1 . Well first I
08:25	should change the order so I can group them together
08:27	after that . So let's change the order . So
08:31	let's make this x . 6.1 And then plus 8.4
08:37	. So all I did was change the order .
08:41	So we know that that one was community property .
08:44	Community property was changing the order and you keep the
08:46	same value . So community property of addition . I'm
08:50	gonna just going to say community property edition C .
08:53	P . A . Like a certified public accountant .
08:56	Uh Now we still have another step to do ,
08:59	we still haven't simplified yet again . Like I said
09:02	before , I want to group these together . So
09:05	let's change the grouping . Let's go X plus 6.1
09:09	plus 8.4 Were grouping those two decimals together . Change
09:15	the grouping . That's associative property of addition . Remember
09:20	explaining your steps as you go and now we can
09:23	just add those together . So I get X plus
09:26	. Uh What is that ? 14.5 14.5 . There's
09:33	my simplified expression Okay lets go the next one C
09:38	five times in parentheses . 11 y remember if you
09:44	have a number next to a parentheses ? That means
09:46	multiplication . If you have a number next to a
09:50	variable , that also means multiplication . And we call
09:53	that a coefficient . Remember coefficient . That means we're
09:57	multiplying it by that variable multiplication multiplication . Were only
10:02	multiplying here . So that allows us to do either
10:06	the community of property or associate property or both .
10:09	So I'm gonna have five times 11 . And then
10:14	times why ? Okay . Because I can do five
10:17	times 11 . So all I did was change the
10:20	grouping . That's associative property of this time multiplication .
10:28	Now . Five times 11 . That's simple . 55
10:33	times wide . So 55 Y . Last one X
10:38	plus five . Eight cm parenthesis plus 1/4 at the
10:40	end . Again , I want to change the grouping
10:44	uh here the order's fine . I can keep that
10:47	order and just change the grouping . So I go
10:49	X plus in parentheses . +58 plus 1/4 . I
10:55	just changed the grouping . That's associative property of addition
11:01	. Hey and now let's that well 5/8 plus 1/4
11:06	. I need a common denominator so that's going to
11:09	become eight and that's going to become with two .
11:13	So two eights instead of 14 so I can add
11:15	those X plus five eight plus +28 is +78 Here's
11:23	some to try on your own as always . Thank
11:32	you so much for watching and if you like this
11:34	video please subscribe .

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