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.
Multiplicative identity.
Additive inverse property. a + (–a) = 0. For example, 2 + (–2) = 0.
Multiplicative inverse property.
Distributive property.
Multiplicative property of zero.
Zero-product property.
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
![10(2 + 3) does not equal 23.](https://www.dummies.com/wp-content/uploads/369318.image8.png)
but that’s incorrect. The correct answer is
![10(2 + 3) = 50](https://www.dummies.com/wp-content/uploads/369319.image9.png)
Knowing what you can’t do is just as important as knowing what you can do.