**Properties of Real Numbers**

**Distributive Property**

** **

For any real numbers *a*, *b*, and *c*,

*a*(*b *+ *c*) = *ab *+ *ac *and (*b *+ *c*)*a *= *ba *+ *ca*.

**Inverse Properties**

For any real number *a*, there is a single real number – *a *such that

a + (-a) = 0 and –a + a = 0.

The inverse “undoes” addition with the result 0.

For any nonzero real number a , there is a single real number such that

a. = 1 and .a = 1.

The inverse “undoes” multiplication with the result 1.

**Identity Properties**

For any real number a , a + 0 = 0 + a = a.

Start with a number a; add 0. The answer is “identical” to a.

Also, a. 1 = 1. a = a.

Start with a number a; multiply by 1. The answer is “identical ” to a.

**Commutative and Associative Properties**

For any real numbers *a*, *b*, and *c*,

*a + b = b + a*

*and ab = ba.*

**Commutative properties**

Interchange the order of the two terms or factors.

Also, *a *+ (*b *+ *c*) = (*a *+ *b*) + *c*

and *a*(*bc*) = (*ab*)*c*.

**Associative properties**

Shift parentheses among the three terms or factors; order stays the same.