Properties of Real Numbers
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Properties of Real Numbers

Prentice Hall's Online Lesson Quiz   Enter Web Code: aga–0101

Real Numbers

Every real number can be classified as either rational or irrational.   

Rational

Irrational


  A rational number can be expressed as a    
  ratio , where m and n are integers and n 
  is not zero.

  Any real number that is not rational is 
  irrational.


  The decimal form of a rational number is    either a terminating or repeating decimal.

  The decimal form of an irrational number is 
  non-repeating and non-terminating.

Integers

{...–3, –2, –1, 0, 1, 2, 3, ...}

Whole Numbers

 { 0, 1, 2, 3, ...}

Natural Numbers

 { 1, 2, 3, ...}
 
Name the sets of numbers to which each value belongs.

 Real, Rational, Integer, Whole Number, Natural Number

4.131131113...

 Real, Irrational

8.75 + 2.437 = 11.187

 Real, Rational

– 45 ÷ 5 =  – 9

 Real, Rational, Integer

Properties of Real Numbers

For any real numbers a, b, and c:
 

Addition

Multiplication

  Commutative

a + b = b + a

(a)(b) = (b)(a)

  Associative

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

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

  Identity

a + 0 = 0 + a = a

a(1) = 1(a)= a

  Inverse

a + (–a) = (–a) + a = 0

             

  Distributive

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