The order in which three or more real numbers are added or multiplied can be grouped in any fashion giving the same result.

(a+b)+c = a+(b+c) or (ab)c= a(bc)

When multiplying a term by a quantity containing a sum of two or more terms, each item in the sum must be multiplied by the outside term.

a(b+c) = ab+ac

In addition, adding zero yields the identity of the original number. In multiplication, multiplying by 1 yields the identity of the original number

a+0 = a     or     a(1) = a

A number with the same distance from zero. Opposites are considered additive inverses.

a and -a are opposites and additive inverses

two numbers who have a sum of zero. Additive inverses are opposites.

a+ (-a) = 0

two numbers that when multiplied yield a result of 1. These are also called reciprocals.

(a/b)(b/a) = 1        or        a(1/a) = 1

two numbers whose product is 1.

a/b and b/a ; a and 1/a are reciprocals

The order in which two real numbers are added or multiplied gives the same result.

a+b=b+a       or        a(b) = b(a)

The distance a number is away from zero.

|-a|= a or |a| = a

A mathematical statement that two quantities are greater, less, greater than or equal to, or less than than or equal to each other.

a > 5 or a < -3

A mathematical statement in which two quantities are expressed as equals.

a + 4 = 3