Download P.1 - Nutley Public Schools

P.1 Real Numbers and Algebraic Expressions
A _______ is a collection of objects whose contents can be clearly
determined. The objects in a set are called ___________ of the set. They
are written in ___________ { }.
Real Numbers
Rational Numbers
Irrational Numbers
Integers
Whole Numbers
Natural Numbers
The set of _________________________ is formed by combining the
rational numbers and irrational numbers. The ______________________
is a graph used to represent the set of real numbers.
ab
ba
Definition of Absolute Value
x 
Example 1: Rewrite each expression without absolute value bars:
x
a)
b) 2  
c)
if x < 0
d) 1 2
3 1
x
Properties of Absolute Value
For all real numbers a and b,
1) a  0
2)  a  a
5)
a
a
b0

b
b
3) a  a
4) ab  a b
6) a  b  a  b (called the triangle inequality)
Distance between Two Points on the Real Number Line
If a and b are any two points on a real number line, then the distance
between a and b is given by
a  b or b  a
Example 2: Find the distance between -5 and 3 on the real number line.
Algebra uses letters, such as x and y, to represent real numbers called
________________. A combination of variables and numbers using the
operations of addition, subtraction, multiplication, and division, as well as
powers or roots, is called an _____________________________.
Order of Operations (in order from left to right)
1) Parentheses
2) Exponents (powers)
3) Multiplication and division
4) Addition and subtraction
Example 3: Evaluate the following
7( x  3)
when x = 9
2 x  16
Name
Commutative property of
addition/multiplication
Associative property of
addition/multiplication
Distributive Property of
multiplication over addition
Identity property of
addition/multiplication
Inverse property of
addition/multiplication
Meaning
a+b=b+a
ab = ba
(a+b) + c = a + (b+c)
(ab)c = a(bc)
a(b + c) = ab + ac
Examples
a+0=a;0+a=a
a(1) = a ; 1(a) = a
a + (-a) = 0; (-a) + a = 0
1
1
a   1;  a  1 a 0
a
a
1
the __________________________ or __________ of b.
b
a
The quotient of a and b, a  b , can be written in the form
where a is the
b
__________________ and b is the ________________ of the fraction.
We call
Simplifying Algebraic Expressions
5x – 6y + 2
Example 4: Simplify 6(2x – 4y) + 10(4x + 3y)
Properties of Negatives:
1) (-1)a = -a
2) -(-a) = a
3) (-a)b = -ab
5) -(a + b) = -a – b
6) -(a – b) = -a + b
4) a(-b) = -ab