Section P1 Algebra Expressions and Real Numbers

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Section P1Algebra Expressions and Real Numbers
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Algebraic Expressions
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Algebraic Expressions are combinations of
variables and numbers using the operations of
addition, subtraction, multiplication, or
division as well as powers or roots.
Example
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Evaluating Algebraic Expressions
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Example
Evaluate an Algebraic Expression
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Formulas and Mathematical Models
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Mathematical Modeling the process of finding
formulas to describe real-world phenomena.
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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.
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Sets
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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
.
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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
.
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Example
For the following sets of numbers find the Union
and the Intersection.
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The Set of Real Numbers
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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.
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Numbers Examples





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Example
Consider the following set of numbers.
List the numbers in the set that are

1. Natural Numbers
2. Whole Numbers
3. Integers
4. Rational Numbers
5. Irrational Numbers
6. Real numbers

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Ordering the Real Numbers
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The Absolute Value - Distance
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Example
Evaluate the following Absolute Value problems.
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Example
Find the distance between -7 and 3 on the number
line.
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Simplifying Algebraic Expressions
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The terms of an algebraic expression are those
parts that are separated by addition. There are
four terms in the expression below.
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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.
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Example
Simplify this Algebraic Expression
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Properties of Negatives
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Evaluate an Algebraic Expression
(a) 4 (b) 10 (c) 12 (d) 8
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Find the distance between -8 and 4 on the number
line.
(a) -4 (b) 12 (c) 10 (d) 8
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List the numbers in the set below that belong to
the set of rational numbers.
(a) (b) (c) (d)