Classifying Numbers

Properties

Number Sets

Natural Numbers: 1, 2, 3, … Whole Numbers: 0, 1, 2, 3, … Integers: …-3, -2, -1, 0, 1, 2, 3, … Rational Numbers: where p and q are

integers and q≠0 Irrational Numbers: non-terminating and

non-repeating Real Numbers: all rational and irrational

pq

These are rational:

5

-3.45 2.333…

45

49

These are irrational

3.46446444644446…

11

The number sets do overlap….

Real Numbers

Rational Irrational

Integer

Whole

Natural

Classify each number in as many ways as possible.

0.12122122212222…

56

-7

23

Classify each number in as many ways as possible.

0 23.0 -2.2

4.77

100

19

Activity

You are to place the numbers in your bag in the appropriate place on the Venn Diagram.

Properties of Addition & Multiplication:For all real #’s, a, b, c…

Closure: then a+b is a real number ab is a real number

Commutative: a + b = b + aab = ba

Associative: (a+b)+c = a+(b+c) (ab)c = a(bc)

Identity: a + 0 = 0 + a = aa*1 = 1*a = a

Inverse: a + (-a) = 0 11a

a

Distributive Property

For all real numbers a, b, and c:

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

State a property to justify the following statements…

6 +(-3) = (-3) + 6 2(4 – 5) = (4- 5)2 3(4a+5) = 12a + 15 -5 + (x + 2) = (-5 + x) + 2 (x+3) + 6 = 6 + (x+ 3) 4 ( 1) = 4 -5 + 5 = 0

What type of number do I get when I perform the following operation?

What type of number do I get when I perform the following operation?

What type of number do I get when I perform the following operation?

What type of number do I get when I perform the following operation?

What type of number do I get when I perform the following operation?

What type of number do I get when I perform the following operation?

What type of number do I get when I perform the following operation?

What type of number do I get when I perform the following operation?

What type of number do I get when I perform the following operation?

Homework

Worksheet