p. 7‐10: #9, 13, 17, 21, 23, 37, 47‐51 odd
Mr. Gallo
Algebra 2
1‐2: PROPERTIES OF REAL NUMBERS
Real Number Review
 Has special subsets related in several ways
 Algebra involves operations on this set
 Also imaginary numbers (will learn about later)
 Can graph every real number on the number line
4
‐6
‐4
1.5 0
‐2
0
4
5
2
4
6
1
Subsets of the Real Numbers
Irrational Numbers
Real Numbers
Natural Numbers
Whole Numbers
2
1, 2,3, 4,...

0,1, 2,3, 4,...
Integers
3, 2  1, 0,1, 2,3,...
Rational Numbers
1
2
 , 0.222,1, 2, ,...
2
3
Classifying Variables
 Limit value of variable to a specific set of numbers
 Done for specific circumstances
Example 1: What set of numbers would best describe the number of participants in a race? Whole Numbers
Example 2: What if each participant made a donation d
of $15.50 to a local charity, which subset of real numbers best describes the amount of money raised?
Rational Numbers
Graphing Real Numbers
 What is the graph of the numbers  5 2 , 2, 2.6 : 5
1
  2
2
2
5
 is between ‐3 and ‐2
2
‐6
‐4
‐2
2.6 is between 2 and 3
0
2
4
6
2  1.4
2 is between 1 and 2
2
Ordering Real Numbers
 How do 17 & 3.8 compare?
 What perfect square(s) is close to ?
17
16  17  25
4  17  5
3.8  4
 3.8  17
Properties of Real Numbers
Relationships that are true for all real numbers
Additive Identity
Multiplicative Identity
Opposite
 The ________________ or Reciprocal
 The________________ or Additive Inverse
_______________________
of any number is a or –a
Multiplicative Inverse
_______________________
of any nonzero number a
1
is:
a
 The product of a number and its reciprocal equals 1
1
 1
8    1 5     1
8
 5
 Sum of number and additive inverse equals zero
12   12   0
7  7  0
Properties of Real Numbers
Properties of Real Numbers
Let a, b and c represent real numbers
Property
Addition
Closure
a  b is a real number
ab is a real number
a  b=b+a
ab =ba
Commutative
Associative
Identity
Inverse
Distributive
Multiplication
 a  b  +c=a+  b  c 
 ab  c=a  bc 
a  0  a, 0  a  a
a1  a,1a  a
0 is the additive identity
1 is the multiplicative identity
a   a   0
1
a  1, a  0
a
a  b  c   ab  ac
3
Examples: Which property does the equation illustrate?
 2  3 
A.   3    2   1
B.  34 5   435
Inverse Property of Multiplication
Commutative Property of Multiplication
C. 3  g  h   2 g   3 g  3h   2 g
Distributive Property
Homework: p. 15‐17 #10‐12, 14‐22 even, 30‐34 even, 35‐40, 58, 75‐83 odd
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