Classifying Numbers and Properties of Operations

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

These are rational: • 5 • -3.45 • 2.333…

These are irrational • 3.46446444644446…

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

Classify each number in as many ways as possible. • 0 • 23.0 • -2.2

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 + a ab = ba • Associative: (a+b)+c = a+(b+c) (ab)c = a(bc) • Identity: a + 0 = 0 + a = a a*1 = 1*a = a • Inverse: a + (-a) = 0

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?

Homework • Worksheet

Classifying Numbers and Properties of Operations