Download Real Numbers Chapter 1 Chapter 1-1

Chapter 1
Real
Numbers
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Chapter
Chapter1-1
1-1
1
Chapter Sections
1.1 – Study Skills for Success in Mathematics
1.2 – Problem Solving
1.3 – Fractions
1.4 – The Real Number System
1.5 – Inequalities and Absolute Value
1.6 – Addition of Real Numbers
1.7 – Subtraction of Real Numbers
1.8 – Multiplication and Division of Real Numbers
1.9 – Exponents, Parentheses and Order of Operations
1.10 – Properties of the Real Number System
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© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
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Education,
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Chapter
Chapter1-2
1-2
2
Exponents,
Parentheses and
Order of Operations
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2011,Pearson
2007 Pearson
Education,
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Chapter
Chapter1-3
1-3
3
Learn the Meaning of Exponents
In the expression 42, the 4 is called the base,
and the 2 is called the exponent.
42
exponent
base
43 is read “4 to the third power” and means
4·4·4 = 43
3 factors of 4
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© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
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© 2015,
Education,
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Chapter
Chapter1-4
1-4
4
– vs.
2
x
2
(-x)
An exponent refers only to the number or
variable that directly precedes it unless
parentheses are used to indicate otherwise.
–
x2 = -(x)(x)
(– x)2 = (–x)(–x) = x2
Example: – 32 = – (3)(3) = – 9
(– 3)2 = (–3)(–3) = 9
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© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
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© 2015,
Education,
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Chapter
Chapter1-5
1-5
5
Learn the Order of Operations
To evaluate mathematical expressions, use the
following order:
1. First, evaluate the information within parentheses ( ),
brackets  , or braces  .These are grouping
symbols, for they group information together. A
fraction bar, —, also serves as a grouping symbol. If
the expression contains nested grouping symbols (one
pair of grouping symbols within another pair),
evaluate the information in the innermost grouping
symbols first.
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2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
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Chapter
Chapter1-6
1-6
6
Learn the Order of Operations
2. Next, evaluate all exponents.
3. Next, evaluate all the multiplications and
divisions in the order in which they occur,
working from left to right.
4. Finally, evaluate all additions or subtractions in
the order in which they occur, working from left
to right.
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2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
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Education,
Inc. Inc.
Chapter
Chapter1-7
1-7
7
Order of Operations
Evaluate:
Steps Taken
6 + 3 • 52 – 4 =
Exponent
6 + 3 • 25 – 4 =
Multiply
6 + 75 - 4=
Add
81 – 4 =
77
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2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
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Education,
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Chapter
Chapter1-8
1-8
8
Order of Operations
Evaluate:
Steps Taken
-7 + 2 [-6 + (36 / 32 )] =
Exponent
-7 + 2 [-6 + (36 / 9 )] =
Divide
-7 + 2 [-6 + 4] =
Add
-7 + 2 [-2] =
-7 - 4 =
Multiply
-11
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2015, 2007
2011,Pearson
2007 Pearson
Education,
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Education,
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Chapter
Chapter1-9
1-9
9
Expressions Containing Variables
Evaluate:
-7x + 9 when x = 3
This means to substitute 3 for x.
-7(3) + 9 = -21 + 9 = -12
Evaluate:
x2 when x = 3
32 = (3)(3) = 9
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-10
1-10
10