Download Operations with Radical Expressions

1-1
Properties of Real Numbers
Big Idea:
-Graph, order, identify, and use
properties of real numbers.
Subsets of Real Numbers:
Natural numbers: Positive, whole numbers
1, 2 , 3 , ….
Whole Numbers: whole numbers including 0
0, 1 , 2 , 3 ….
Integers: Natural numbers , their opposites,
and 0.
…-3, -2, -1, 0, 1, 2 , 3 …
Rational Numbers: numbers that can be
written as fractions, can be terminating
decimals, or repeating decimals
2
9
0.75, 
,0.4,15,0
3, 10
Irrational Numbers: numbers that cannot
be written as a fraction and decimals
that have no pattern
2, 7 ,0.125489340, pi
Ex 1:
A) Graph the numbers on a number
line.
3

4
,
7 ,3.6
 Ex
2: Compare each.
A) -10 -8
B) 0.5
C) 5
7
D) 0.4
0.01
1
3
More Properties
Opposite or additive inverse.
The sum of opposites is 0.
Reciprocal or multiplicative inverse.
The product of reciprocals is 1.
Ex 3: Find the opposite and reciprocal
of each number.
4
A) 4
B) 3

5
1
C) 
2
D) 5.6
Properties of Addition and
Multiplication
Closure 5 +x is a real number.
xy is a real number.
Commutative 6 + 3 = 3 + 6
2y = y2
Associative
(5 + 6) + 7 = 5 + (6 +7)
(8·9)10 = 8(9·10)
Identity
4+0=4
8·1 = 8
Inverse
x + (-x) = 0
2·½ = 1
Distributive
5(x + y)= 5x + 5y
Ex 4:
Which property is illustrated?
a. (-7)(2 · 5) = (-7)(5 · 2)
b. 3 · (8 + 0) = 3 · 8
Absolute Value
The absolute value of a number is the
distance from zero on the number
line.
4 
4 
Ex 5: Find the absolute value.
1
A) 4

3
C)
38 
B)
D)
 9.2 
3  7 
Essential Question:
What are the similarities and differences of
the subsets of Real Numbers?
Write down this question at the end of
your notes and answer it in complete
sentences. Your answer must be in
your own words and must be at least 3
sentences long. This is a part of your
Notes grade.