Question

May someone please define and give an example of closure, commutative, associative, identity, inverse, and distributive property?

I'm not asking you to do my homework, ha ha. This is for a test and I'm trying to study. Unfortunately, I can't understand the textbook's definition. So, if you can use simple words for a teenager to understand, I'd appreciate it.

Thank you! :)

PLEASE use your own words.

Answer 1

You think you can help, @hartnn ?

Answer 2

is this related to groups, rings and fields ??

Answer 3

No, this is properties of addition and multiplication.

Answer 4

Commutative Property. Think: "change places". Works for addition 5+3=3+5 , but not for subtraction 5-3=3-5

Answer 5

Elaborate on "change places"

Answer 6

please, explain the other ones, too.!

Answer 7

Change places NOTE that the order of the numbers was changed on the right hand side of the equation that I wrote.

Answer 8

You're still writing?

Answer 9

Associative: Think "associates are people I associate with" In maths (2 x 3) x 4 can be worked out by using the rules of maths that tell you to do the bracket first and then times by 4. It would work just as easily as 2 x (3 x 4) , bracket first. Because multiplication is associative.

Answer 10

Please, just explain. Ha ha @1on1 I feel like you're under the impression that you need a reply from me to explain these properties. :P

Answer 11

Go on, go on. :P

Answer 12

one answer at a time.

Identity
For addition the identity is zero because when zero is added nothing changes
For multiplication the identity is......., because when you multiply by it nothing changes.

Answer 13

Next :)

Answer 14

what was missing in the previous answer i gave?

Answer 15

please... keep going.

Answer 16

an example. x +0= x

Answer 17

please... please.. i do not have time for you doing that. you are unaware f the situation that is going on at this household.

Answer 18

One is the identity for multiplication

Answer 19

The inverse for addition is what you add to something to end up with zero, called the additive inverse (or opposite)
the inverse for multiplication (multiplicative inverse) is what you multiply by to end up with one . Sometimes called the reciprocal.
END

Answer 20

Please explain closure.

Answer 21

Closure means the answer is contained in the same set of numbers as the numbers in the question.
For Example the counting numbers are not closed under division because 4 divided by 3 gives a result that is not a counting number