Download Real Numbers Chapter 1 Chapter 1-1

Chapter 1
Real
Numbers
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 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
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-2
Addition of Real
Numbers
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-3
Number Lines
Evaluate 3 + (- 4) using a number line
1. Always begin with 0.
2. Since the first number is positive, the first arrow
starts at 0 and is drawn 3 units to the right.
3
-5
-4
-3
-2
-1
0
1
2
3
4
5
3. The second arrow starts at 3 and is drawn 4 units
to the left , since the second addend is negative.
-4
3
-5
-4
-3
-2
-1
0
1
3 + (– 4) = -1
2
3
4
5
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-4
Add Fractions







2
7
Add  
16 3







The LCD is 48. Rewriting the first fraction with the LCD
gives the following.







7  3  2
16 3 3
21   32
48
48





















 16 
16
  11
48
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-5
Identify Opposites
Any two numbers whose sum is 0 are said to
be opposites, or additive inverses, of each
other.
The opposite of a is –a.
The opposite of –a is a.
a + (– a) = 0
Example:
The opposite of –5 is 5, since –5 + 5 = 0
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-6
Add Using Absolute Values
To add real numbers with the same sign,
add their absolute values. The sum has the
same sign as the numbers being added.
Example:
–6 + (–9) = –15
4 + 8 = 12
The sum of two positive numbers will
always be positive and the sum of two
negative numbers will always be negative.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-7
Add Using Absolute Values
To add two signed numbers with different
signs, subtract the smaller absolute value from the
larger absolute value. The answer has the sign of
the number with the larger absolute value.
Example:
13 + (–4) = 9
–35 + 15 = -20
The sum of two numbers with different
signs may be positive or negative. The sign
of the sum will be the same as the sign of the
number with the larger absolute value.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-8