These properties tell us the legal moves we can make when adding or multiplying numbers.
But why aren't there properties for subtraction or division?
Some mathematicians refuse to acknowledge that subtraction and division are even operations! Subtraction is the same thing as adding a negative and division is the same thing as multiplying by a fraction. a-b=a+(- b) and a/b=a* 1/b
Therefore, we can use the Properties of Real Numbers for subtraction and division, but we need to change our way of thinking.
