Download Classifying Numbers

Classifying Numbers
Properties
Number Sets
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Natural Numbers: 1, 2, 3, …
Whole Numbers: 0, 1, 2, 3, …
Integers: …-3, -2, -1, 0, 1, 2, 3, …
Rational Numbers: p q 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:
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5
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4
5
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-3.45
2.333…
49
These are irrational
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3.46446444644446…
11
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The number sets do overlap….
Real Numbers
Rational
Integer
Whole
Natural
Irrational
Classify each number in as
many ways as possible.
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0.12122122212222…
56
-7
2
3
Classify each number in as
many ways as possible.
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4.77
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0
23.0
-2.2
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19
100
Activity
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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…
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Closure: then a+b is a real number
ab is a real number
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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
1
Inverse: a + (-a) = 0
a 1
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…
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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?
+
5
0
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?
X
5
0
5
0
Homework
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Worksheet