Question

what is the difference between closure associative commutative and distributive property of numbers? and how to recognize which property should be used while solving a certain example.

Answer 1

Associative:

An operation is associative if we can group numbers in any way without changing the answer.
For addition: (a + b) + c = a + (b + c)
For multiplication: (ab)c = a(bc)

Cummutative:

An operation is cummutative if we can change the order of numbers involved without changing the result.

For addition: a + b = b + a
For multiplication: ab = ba

Distributive:

It says that when a number is multiplied by the sum of two other numbers, the first number can be handed out or distributed to both of those two numbers and multiplied by each of them separately

a * (b + c) = ab + ac