Irrational Numbers

​An Irrational Number is a real number that cannot be written as a fraction of two integers.

Irrational Number Examples

​π=3.1415..., e=2.71828...., √3=1.732..., -√7=2.6457...

Irrational numbers have never ending decimals that do not repeat.

Real Numbers

​Real numbers are the set of numbers made up of the union of rational numbers and irrational numbers.

Real Numbers

Commutative Properties for Real Numbers

Commutative Property of Multiplication
ab=ba
Commutative Property of Addition
a+b=b+a

Commutative Properties for Real Numbers

​Think Commuting to work--you travel to a different place.

Associative Properties for Real Numbers

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

Associative Properties for Real Numbers

Think of who a person associates with in a group of people. The place doesn't change but who they associate with does.
(a+b)+c=a+(b+c)

Distributive Property of Multiplication over Addition

​a*(b+c)=a*b+a*c

for any real numbers a, b, and c.