What is the difference between commutative property and associative property?

Question

they seem like the same thing to me!

Answer 1

Commutative property changes the order.

Example: 1+2+3=6 or 2+3+1=6

Associative property keeps the same order but changes parentheses.

1 x (2 x 3) = 6 or (1 x 2) x 3 = 6

Answer 2

Addition is commutative and associate.

Addition is commutative because

(a + b) = (b + a)

Addition is associative because

a + (b + c) = (a + b) + c

Commutation has to do with the order of the operators performed, and association has to do with the order of evaluations.

Subtraction is not associative; take a = 1, b = 2, c = 3.

a - (b - c) = 1 - (2 - 3) = 1 - (-1) = 2

(a - b) - c = (1 - 2) - 3 = (-1) - 3 = -4

So, as you can see, not equal.

Division is not commutative; take a = 1, b = 3.

a / b = 1/3

b/a = 3/1 = 3

As you can see, a/b is not equal to b/a.

Answer 3

commutative means:

x operation y = y operation x

A bad example:

Stopping a car and getting out is not the same as getting out and the stopping the car: this operation is NOT commutative.

associative means:

(x operation y) operation z = x operation (y operation z)

When you have 3 variables you can do 1,2 and then 3 or

2,3 and then 1, it the same.