1.1 & 1.2: Properties of Real Numbers &
Algebraic Expressions
Natural Numbers
1, 2, 3, 4, …
The numbers we use for counting.
Whole Numbers
0, 1, 2, 3,…
The natural numbers AND zero.
Integers
-3, -2, -1, 0, 1, 2, 3,…
The natural numbers (aka positive integers), their negatives
(aka negative integers), and zero.
Rational Numbers
3
4 ,
8
 0.074 ,  13 , 0.6
•Numbers that can be written as fractions
• REMEMBER-THE DENOMINATOR CAN’T BE
 
ZERO!
•Terminating decimals; Ex: 0.25  1
4
1
•Repeating decimals; Ex: . 3 
3
Irrational Numbers
5,

, 2,
0.395011294...
Irrational Numbers are…
•Can’t write as fractions
•Non-repeating and non-terminating decimals
•Square roots of numbers that aren’t perfect squares
The Real Numbers:
Ordering and Graphing on a Number Line
2

3
-5
-4
-3
6
1.5
 3.3
-2
-1
 11
0
1
2
3
4
5
Opposite and Reciprocal
The opposite of a
is –a.
Ex: the opposite of
2 is -2
The reciprocal of a is 1 .
a
1
Ex: the reciprocal of 5 is
5
1
Ex: the reciprocal of
is 2
2
Properties of Real Numbers:
Let a, b, and c represent real numbers
Property
Closure
Commutati
ve
Addition
a + b is a real
number
a+b=b+a
(a + b) + c = a + (b
Associative
+ c)
Multiplication
ab is a real number
ab = ba
(ab)c = a(bc)
Identity
a+0=a
a·1 = a
Inverse
a + (-a) = 0
a·(1/a) = 1, a≠ 0
Properties of Real Numbers:
8 + (-8) = 0
Inverse Property of
Addition
(2·5) ·(-8) = 2·(5·-8)
Associative Property of
Multiplication
(4+1) ·3 = (1+4) ·3
Commutative Property
of Addition
Absolute Value
A number’s distance from zero. REMEMBER: DISTANCE IS
ALWAYS POSITIVE!
9 
23 
(1)( 4) 
0 
 2 
Algebraic Expressions
15x2 + 6y
•Variable: a symbol that represents one or more numbers
•Algebraic Expression: an expression that contains one or more
variables
•Term: a number, variable, or the product of a number and one or
more variables
•Coefficient: The numerical factor in a term
•Evaluate: Substituting numbers for variables in an expression
and following order of operations
Combining Like Terms
Examples
3k + 6 – 5k - 2
a2 + 2b – 4b + 6a2
Challenge
What is the perimeter of the figure?
Evaluate
Hint: Simplify first!
x + 4y
when x = 3 and y = -2
5 z 2  10 z  8 z 2  z when z  2
Homework:
1.1: 1, 2-6 EVEN, 12-16 EVEN, 25-33 ODD, 34, 36 ,37,
48-54 EVEN
1.2: 1-11 odd, 22, 27, 31, 33, 36, 41, 43, 44
1.1 & 1.2: Properties of Real Numbers &
Algebraic Expressions