Transcript 1.1 1. 2. 3. 4. 5. Number Sets and the Structure of Algebra Understand the structure of algebra. Classify number sets. Graph rational numbers on a number line. Determine the absolute.

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Number Sets and the Structure of
Algebra
Understand the structure of algebra.
Classify number sets.
Graph rational numbers on a number line.
Determine the absolute value of a number.
Compare numbers.
Definitions
Variable
A symbol that can vary in value.
Constant
A symbol that does not vary in
value.
A mathematical relationship that
does not contain an equal sign
Expression
Equation
A mathematical relationship that
contains an equal sign.
Inequality
A mathematical relationship that
contains an inequality symbol (, <,
>, , or ).
Absolute Value
A given number’s distance from 0
on a number line. Notation = | |.
Fractions
Radicals
Set
Set Notation
Natural
numbers
Whole
Numbers
Integers
A collection of objects.
{ }
Counting numbers {1,2,3, …}
Natural numbers and 0.
{0,1,2,3, …}
Positive and negative natural numbers
and zero. {… -2, -1, 0, 1, 2, 3, …}
A real number that can be expressed
as a ratio of integers (fraction)
Any real number that is not rational.
 2 , 
Rational
Number
Irrational
Number
Real Numbers All numbers associated with
the number line.
|3|=
Absolute Value
3
| 2.5 | =
2.5
|0|= 0
|-7 |=
7
| - 4.8 | =
4.8
True or False?
>0
The absolute value of a number is always positive.
False
The absolute value of a number is either positive or 0.
≥0
The absolute value of every real number is non-negative.
To which set(s) of numbers does 6
belong?
a) Natural Numbers
b) Whole numbers
c) Integers
d) Rational numbers
e) Irrational numbers
f) Real numbers
Copyright © 2011 Pearson Education, Inc.
Slide 1- 7
To which set of numbers does 6
belong?
a) Natural Numbers
b) Whole numbers
c) Integers
d) Rational numbers
e) Irrational numbers
f) Real numbers
Copyright © 2011 Pearson Education, Inc.
Slide 1- 8
Simplify |7|.
a) 7
b) 7
c) 0
d) 1/7
Copyright © 2011 Pearson Education, Inc.
Slide 1- 9
Simplify |7|.
a) 7
b) 7
c) 0
d) 1/7
Copyright © 2011 Pearson Education, Inc.
Slide 1- 10
Which statement is false?
a) 7 > 4
b) 2.4 > 1.4
c) 10 < 22
d) 3.6 > 6.4
Copyright © 2011 Pearson Education, Inc.
Slide 1- 11
Which statement is false?
a) 7 > 4
b) 2.4 > 1.4
c) 10 < 22
d) 3.6 > 6.4
Copyright © 2011 Pearson Education, Inc.
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