Download Algebra Expressions and Real Numbers

Section P1
Algebra Expressions
and
Real Numbers
Algebraic Expressions
Algebraic Expressions are combinations of
variables and numbers using the operations of
addition, subtraction, multiplication, or division
as well as powers or roots.
Example:
7  777
3
Evaluating Algebraic Expressions
Example
Evaluate an Algebraic Expression
2  3( x  1)  4 for x =3
2
Formulas and Mathematical Models
Mathematical Modeling – the process of
finding formulas to describe real-world
phenomena.
Example
It takes you 30 minutes to get to your first
period class. This includes driving at a rate of
.8 miles per minute, and walking from the
parking lot to your class at a rate of .07 miles
per minute. The total distance of both walking
and driving is given by the algebraic
expression. Find the distance if it takes you 5
minutes to walk to class.
D  0.07t  .8(30  t )
Sets
A set is a collection of objects, whose elements
can be clearly determined.
The Roster Method- lists the elements of the
set, with commas in between. The three dots
(ellipsis) indicate that the listing continues for
ever.
If a set has no elements then it is called the null set or empty
set, represented by the symbol  .
Set Builder Notation – the elements are
described, not listed.
If a set has no elements then it is called the null set or empty
set, represented by the symbol  .
Example
For the following sets of numbers find the
Union and the Intersection.
2,4,6,8,10 3,4,5,6,7
2,4,6,8,10 3,4,5,6,7
The Set of Real Numbers
Every Real Number is either rational or irrational. We
refer to these sets as subsets of the real numbers,
meaning that all elements in each subset are also
elements in the set of real numbers.
x | x is rational or x is irrational
Numbers
Examples
Natural Numbers
Whole Numbers
2,3,4,17
0,2,3,4,17
Integers
-5,-2,0,2,5
Rational Numbers
Irrational Numbers
1 5
1
2
,  ,.4  ,0,.6 
2 1
5
3
2,  ,  3
25 is a rational number because 25  5.
Example
Consider the following set of numbers.
1

3, 0, , .95,  , 8,
2

List the numbers in the set that are:
a. Natural Numbers
b. Whole Numbers
c. Integers
d. Rational Numbers
e. Irrational Numbers
f. Real numbers

16 

Ordering the Real Numbers
The Absolute Value - Distance
Example
Evaluate the following Absolute Value
problems.
14  
  14
Example
Find the distance between -7 and 3 on
the number line.
Simplifying Algebraic Expressions
The terms of an algebraic expression are those
parts that are separated by addition. There are
four terms in the expression below.
An Algebraic Expression is simplified when
parentheses have been removed and like terms
have been combined. Like terms are terms that
have exactly the same variable factors. For
example 5x and 7x are like terms.
5x  7 x  12x
Example
Simplify this Algebraic Expression
2( x  3x)  (5x  4)  9 x
2
2
Properties of Negatives
Evaluate an Algebraic Expression
9  2  x  4   1 for x=-3
3
(a) 4
(b) 10
(c) 12
(d) 8
Find the distance between -8 and 4
on the number line.
(a) -4
(b) 12
(c) 10
(d) 8
List the numbers in the set below that
belong to the set of rational numbers.
1

5,  , .3, .8,
2

(a)
1

5,  , .3, .8,
2

9,  ,

9, 

(b)
1



5,

, .8,  

2


(c)
1


5,

, .3, .8,

2

(d)
1



5,

,
.3,
.8,



2


9,

13 


13 
