Final answer:
The equations a + b = b + a, and ab = ba, represent the Commutative Property, which states that the order of addition or multiplication does not affect the result.
Step-by-step explanation:
The equation Mr. Hampton writes on the board, a + b = b + a, and ab = ba, represent the Commutative Property of addition and multiplication, respectively. According to this property, the order in which two numbers are added or multiplied does not change the result.
For instance, the addition of ordinary numbers follows this property—you get the same result when adding 2 + 3 as when adding 3 + 2. Same goes for multiplication, as multiplying 2 * 3 will give the same result as 3 * 2.