Properties of Addition and Multiplication - By Anywhere Math
Transcript
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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