Real numbers can be described as being the set of all x, such that x is the

coordinate of a point on a number line. The real numbers include the rational and

irrational numbers. Rational numbers include integers and quotients of integers.

Integers are whole numbers. Positive integers, such as 1, 2, 3, and so forth, are also

called natural numbers. An operation is a method of combining two elements of the set

of real numbers to form a third element (not exclusive). The properties of real numbers

depend upon two basic operations, addition and multiplication. This section is designed

to give you the concepts and skills necessary for the content and course work to follow.

For any real numbers a, b, c, and d, the additive and multiplicative properties are

as follows:

a. **Commutative Properties**.

a+b=b+a

ab = ba

Examples:

3+5=5+3

2X4=4X2

b. **Associative Properties**.

(a + b) + c = a + (b + c)

(ab)c = a(bc)

Examples:

(2 + 1) + 4 = 2 + (1 + 4)

(4 X 3) X 2 = 4 X (3 X 2)

c. **Identity Properties**.

a+0=a

aX1=a

Examples:

3+0=3

7X1=7

MD0837

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