7/28/2019 College Algebra Lectures

1/2

College Algebra Lectures:

Chapter R:Real Numbers

Rational Numbers- they are numbers which can be expressed in the form p/q where p and q are

integers and q0.Examples: a.) 0

b.) -7

c.) 5

Real Numbers

Rational Numbers

,, 3 , 7 Irrational Numbers

3,,1,,1,,Integers

3 ,

45 ,

195 ,

Rational numbers that

are not integers.

,1,,3,

Whole

Numbers

1,,3,

Negative

Numbers

1,,3,

Natural Numbers

(positive numbers)

Zero

7/28/2019 College Algebra Lectures

2/2

d.) 4545454545

Irrational Numbers- they are munbers that are not rational numbers.

Examples: a.) 3141596535 b.) 14141356

c.)61111 , Real Numbers- It is the set of all rational numbers combined with all irrational numbers. It can be

modeled by using a number line.

Properties of Real Number:

For any real numbers a, b, and c.

a+b=b+a and ab=ba Commutative Properties of Addition and Multiplication

a+ (b+c)=(a+b)+c and a(bc)=(ab)c Associative Properties of Addition and Multiplication

a+0=0+a=a Additive Identity Property

-a+a=a+(-a)=0 Additive Inverse Property

a(1)=1(a)=a Multiplicative Identity Property

1 1 1 ( )

a( b+c)= ab+ac Distributive Property

Absolute value- It is the distance of a number in the number line.

For any real number a,

|| { , ,

Distance between two numbers a and b=| | | |