Explanation You are interchanging 2 elements. Therefore, it is the commutative property of addition.

Explanation You are taking the elements of addition inside the parenthesis and multiplying each by the element in front of the parenthesis. Therefore, it is the distributive property.

Explanation You are interchanging only the 2 elements inside the parenthesis.  Therefore, it is the commutative property of addition.

Explanation An expression times the number one brings you back to the epression. This is the multiplicative identity property.

Explanation Since you are regrouping the elements, it is the associative property of multiplication.

Explanation You are taking the first expression times each component of the second expression. This is an example of the distributive property.

Explanation An expression plus its negation give the identity element (0).  This is an example of the additive inverse property.

Explanation An expression times its reciprocal gives the multiplicative identity (1) as the answer. This is an example of the multiplicative inverse property.