classifying numbers properties. number sets natural numbers: 1, 2, 3, … whole numbers: 0, 1, 2, 3,...
TRANSCRIPT
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