Understanding the Properties of Numbers
Remembering the properties of numbers is important because you use them consistently in pre-calculus. The properties aren’t often used by name in pre-calculus, but you’re supposed to know when you need to utilize them. The following list presents the properties of numbers:
Reflexive property. a = a. For example, 10 = 10.
Symmetric property. If a = b, then b = a. For example, if 5 + 3 = 8, then 8 = 5 + 3.
Transitive property. If a = b and b = c, then a = c. For example, if 5 + 3 = 8 and
Commutative property of addition. a + b = b + a. For example, 2 + 3 = 3 + 2.
Commutative property of multiplication.
Associative property of addition. (a + b) + c = a + (b + c). For example, (2 + 3) + 4 = 2 + (3 + 4).
Associative property of multiplication.
Additive identity. a + 0 = a. For example, –3 + 0 = –3.
Additive inverse property. a + (–a) = 0. For example, 2 + (–2) = 0.
Multiplicative inverse property.
Multiplicative property of zero.
For example, if x(x + 2) = 0, then x = 0 or x + 2 = 0.
If you’re trying to perform an operation that isn’t on the previous list, then the operation probably isn’t correct. After all, algebra has been around since 1600 BC, and if a property exists, someone has probably already discovered it. For example, it may look inviting to say that
but that’s incorrect. The correct answer is
Knowing what you can’t do is just as important as knowing what you can do.