An operation for which the commutative property holds is one that allows the operands to be in any order.

The commutative property holds for addition of real numbers: 5+2 = 2+5.

The commutative property does not hold for exponentiation: 5^2 ≠ 2^5.

(5

An operation exhibits the identity property if performing the operation causes no change. Multiplication by 1 is an identity operation. 6*1 = 6

Addition of 0 is an identity operation. 5 + 0 = 5

A "binary" operation exhibits the associative property if a sequence of such operations can be performed on any pairs of operands. For example, "+" is a binary operator: One that has two operands. It has a "left" operand and a "right" operand. If we want to do 1+3+5, we can do it as (1+3)+5 or as 1+(3+5). Because of the commutative property, we can also rearrange the operands so we can do 3+(1+5).

The distributive property of multiplication over addition lets us write a(b+c) = ab + ac.

The commutative property holds for addition of real numbers: 5+2 = 2+5.

The commutative property does not hold for exponentiation: 5^2 ≠ 2^5.

(5

^{2}is 25, 2^{5}is 32.)An operation exhibits the identity property if performing the operation causes no change. Multiplication by 1 is an identity operation. 6*1 = 6

Addition of 0 is an identity operation. 5 + 0 = 5

A "binary" operation exhibits the associative property if a sequence of such operations can be performed on any pairs of operands. For example, "+" is a binary operator: One that has two operands. It has a "left" operand and a "right" operand. If we want to do 1+3+5, we can do it as (1+3)+5 or as 1+(3+5). Because of the commutative property, we can also rearrange the operands so we can do 3+(1+5).

The distributive property of multiplication over addition lets us write a(b+c) = ab + ac.