# 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.**For example, 10 = 10.*a*=*a*.**Symmetric property. If**For example, if 5 + 3 = 8, then 8 = 5 + 3.*a*=*b,*then*b*=*a*.**Transitive property. If**For example, if 5 + 3 = 8 and*a*=*b*and*b*=*c,*then*a*= c.**Commutative property of addition.**For example, 2 + 3 = 3 + 2.*a*+*b*=*b*+*a*.**Commutative property of multiplication.****Associative property of addition. (**For example, (2 + 3) + 4 = 2 + (3 + 4).*a*+*b*) +*c*=*a*+ (*b*+*c*).**Associative property of multiplication.****Additive identity.**For example, –3 + 0 = –3.*a*+ 0 =*a*.**Multiplicative identity.****Additive inverse property.**For example, 2 + (–2) = 0.*a*+ (–*a*) = 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

but that’s incorrect. The correct answer is

Knowing what you *can’t* do is just as important as knowing what you *can* do.