Question

2 + (x + y) = (2 + x) + y is an example of which algebraic property?

Answer 1

What are the options.

Answer 2

Distributive Property

Associative Property of Addition

Commutative Property of Addition

Symmetric Property

Answer 3

It is the communicative property.

Answer 4

This is the commutative property of addition. This basically says that the order in which you add numbers does not change the answer.

Answer 5

it's not that

Answer 6

commutative property is

x+y = y+x

or

x*y = y*x

Answer 7

And how is that different than what we have here @jim_thompson5910 ?

Answer 8

It is not the associative property because it is not x +(y+c)= y+(x+c)

Answer 9

It is the associative propety. o-O

Answer 10

it is the associative property because you're re-associating parenthesis

Answer 11

I AM TELLING YOUU IT IS @magbak

Answer 12

Yes. Your example fit the question's example, magbak. :)

Answer 13

No it does not.

Answer 14

"In mathematics, a binary operation is commutative if changing the order of the operands does not change the result" Isn't that all we're doing here, changing the order in which we add things?

Answer 15

the associative property of addition is

x+(y+z) = (x+y)+z

Answer 16

OH YES IT DOES FIT THE EXAMPLE.

Answer 17

Wait nevermind. Your example doesn't fit. But Associative property is the answer.

Answer 18

Yes it is the associative property of addition.

Answer 19

thank you!!!!!

Answer 20

You are welcome.

Answer 21

vinnv226, because addition is commutative, this explains why associativity works

but the two are different ideas

Answer 22

Isn't the Associative Property just applied Commutative Property?

Answer 23

Yes @jim_thompson5910 is correct and should be given full credit.

Answer 24

I'm still hung up on this and why the commutative property does not imply the exact same thing.

Answer 25

Commutative Property = Switching the numbers and variable
Associative Property = Switching the parenthesis only; the numbers and variable stays in the same place.

Answer 26

But isn't the result the same? By switching the parenthesis, you're just switching the order in which you add things, which is the same as just switching the numbers around.

Answer 27

if you're familiar with matrices and matrix multiplication you might recall that matrix multiplication is NOT commutative but it is associative

ie

A*B = B*A is false in general

but

A*(B*C) = (A*B)*C is true


A,B,C are matrices

Answer 28

so that's one example of how the two are different

Answer 29

Yes but computer wise and by checking by a automatically graded test it will be marked wrong unlike if it was a teacher graded assignment that a teacher can give half credit.

Answer 30

But it seems to me that, if the Associative Property didn't exist, I could just as easily prove this statement by using the Commutative Property a few times.

Answer 31

that's the thing: if an operation is commutative, then you can prove it's associative (not the other way around though)

Answer 32

yes you can use the commutative property to say

x+(y+z) = (x+y)+z

is true, but the associative property is much quicker

Answer 33

I see, that seems a little misleading then, to have both options as the answer on a test when both answers can be used to prove it. Seems equivalent to asking "which of these is a rectangle" and then having both a rectangle and a square as answer choices.

Answer 34

Or rather, putting a picture of a square, asking "what shape is this" and having "square" and "rectangle" as answer choices

Answer 35

if it's a square, then you would go with square since it's the most descriptive and closest to what it really is

sure it's also a rectangle, but it's also a polygon too, but we don't go with "polygon" when we can say "square" since that's the most descriptive and to the point

Answer 36

I see your point, but it strikes me as misleading. I guess thats why I don't write test questions.

Answer 37

it is a bit misleading but it's just one of those questions where the best answer is chosen (more or less)

Answer 38

Well, honestly it's uncommon I get to learn things about math while answering math questions on here, and even less common for me to learn something about a topic as basic as algebraic properties. Thanks for that Jim

Answer 39

I'm glad I was of help

Answer 40

I was glade I was of no help and I just clarified so things.