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
2
Properties of the
Real Number System
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-3
3
Commutative Property
Commutative Property of Addition
If a and b represent any two real numbers, then
a+b=b+a
4+3=3+4
7
=
7
Commutative Property of Multiplication
If a and b represent any real numbers, then
a·b=b·a 6·3=3·6
18
=
18
Commutative (commute) changes the order.
*Note that the commutative property does not hold for
subtraction and division
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-4
4
Associative Property
Associative Property of Addition
If a, b, and c represent three real numbers, then
(a + b) + c = a + (b + c) (3 + 4) + 5 = 3 + (4 + 5)
7
+
5 =
12 =
3 +
12
9
Associative Property of Multiplication
If a, b, and c represent any three real numbers, then
(a · b) · c = a ·(b · c)
(6 · 2) · 4 = 6 · (2 · 4)
12 · 4 = 6 ·
48 = 48
8
Associative (associate) changes the grouping.
*Note that the associative property does not hold for
subtraction and division
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-5
5
Distributive Property
If a, b, and c represent three real numbers, then
a(b + c) = ab + ac
2(3 + 4) = 2(3) + 2(4)
2(7) = 6 + 8
14 = 14
Distributive involves two operations (usually
multiplication and division).
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-6
6
Identity Properties
If a represents any real number, then
a + 0 = a and 0 + a = a
Identity Property of Addition
4+0=4
0+4=4
a · 1 = a and 1 · a = a
Identity Property of Multiplication
13 · 1 = 13
1 · 13 = 13
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-7
7
Inverse Properties
If a represents any real number, then
a + (-a)= 0 and (-a) + a = 0
Inverse Property of Addition
7 + (-7) = 0
a
1
·a
= 1 and
(-7) + 7 = 0
1
a
· a = a (a  0)
Inverse Property of Multiplication
1
12 ·12 = 1
1
12
· 12 = 1
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 1-8
8