Answer:
see below
Step-by-step explanation:
Even if you don't memorize the names of these properties, it is a good idea to understand what they mean.
Identity properties of addition and multiplication mean there are values you can add (0) or multiply by (1) that do not change the original value. Multiplication by an identity is useful for adding or reducing fractions, changing units, rationalizing denominators, and a host of other simplifications.
Commutative properties mean you can change the order of operands without changing the result of the operation.
Associative properties mean you can perform sequences of operations on different pairs of operands and still get the same result: a +(b+c) = (a+b) +c; a(bc) = (ab)c. This does not mean you can group operands without regard to the operation: a+(bc) ≠ (a+b)c.
Inverse properties mean there are ways to undo operations. Addition or multiplication by the inverse results in the identity element.
Closure properties mean that the result of an operation is still in the set of possible operands: addition of integers results in an integer; multiplication of integer results in an integer because the set of integers is closed for multiplication and addition.
The distributive property lets you factor, eliminate parentheses, and collect terms. It is very handy for grouping things in convenient ways.
