What is the difference between commutative and associative properties?

What is the difference between commutative and associative properties?

The commutative property states that the order of numbers does not change the result, like in addition: a + b = b + a. The associative property states that the way numbers are grouped does not change the result, like in addition: (a + b) + c = a + (b + c).

Can you give me examples of each?

Sure! For the commutative property, an example is 3 + 5 = 5 + 3. For the associative property, an example is (2 + 3) + 4 = 2 + (3 + 4).

Are there any operations where these properties don't apply?

Yes, for example, subtraction and division do not follow the commutative property. For instance, 5 - 3 is not the same as 3 - 5.

What about multiplication? Does it follow these properties?

Yes, multiplication also follows both the commutative and associative properties. For example, a × b = b × a and (a × b) × c = a × (b × c).