Title Prealgebra Textbook English 2.2 MB 612
```                            1 The Whole Numbers
1.1 An Introduction to the Whole Numbers
Graphing numbers on the number line
Ordering the whole numbers
Expanded notation
Rounding whole numbers
Tables and graphs
Exercises
1.2 Adding and Subtracting Whole Numbers
The Commutative Property of Addition
Grouping Symbols
The Associative Property of Addition
Adding Larger Whole Numbers
Subtraction of Whole Numbers
Subtracting Larger Whole Numbers
Order of Operations
Applications — Geometry
Application — Alternative Fuels
Exercises
1.3 Multiplication and Division of Whole Numbers
The Multiplicative Identity
Multiplication by Zero
The Associative Property of Multiplication
Multiplying Larger Whole Numbers
Division of Whole Numbers
Division is not Commutative
Division is not Associative
Division by Zero is Undefined
Dividing Larger Whole Numbers
Application — Counting Rectangular Arrays
Application — Area
Exercises
1.4 Prime Factorization
Divisibility
Divisibility Tests
Prime Numbers
Factor Trees
Exponents
Application
Exercises
1.5 Order of Operations
Fraction Bars
The Distributive Property
Exercises
1.6 Solving Equations by Addition and Subtraction
Equivalent Equations
Operations that Produce Equivalent Equations
Wrap and Unwrap
Word Problems
Exercises
1.7 Solving Equations by Multiplication and Division
Word Problems
Exercises
2 The Integers
2.1 An Introduction to the Integers
The Integers
Ordering the Integers
Opposites of Opposites
Positive and Negative
Absolute Value
Applications
Exercises
Vectors on the Number Line
Magnitude and Absolute Value
Adding Integers with Like Signs
Adding Integers with Unlike Signs
Properties of Addition of Integers
Grouping for Efficiency
Exercises
2.3 Subtracting Integers
Order of Operations
Change as a Difference
Exercises
2.4 Multiplication and Division of Integers
The Product of a Positive Integer and a Negative Integer
The Distributive Property
The Multiplicative Property of Zero
Multiplying by Minus One
The Product of Two Negative Integers
Memory Device
Division of Integers
Exercises
2.5 Order of Operations with Integers
Evaluating Fractions
Absolute Value
Exercises
2.6 Solving Equations Involving Integers
Adding or Subtracting the Same Amount
Multiplying or Dividing by the Same Amount
Combining Operations
Applications
Exercises
3 The Fundamentals of Algebra
3.1 Mathematical Expressions
Translating Words into Mathematical Expressions
Combinations
Exercises
3.2 Evaluating Algebraic Expressions
Exercises
3.3 Simplifying Algebraic Expressions
Speeding Things Up
The Distributive Property
Moving a Bit Quicker
Extending the Distributive Property
Distributing a Negative
Exercises
3.4 Combining Like Terms
Like Terms
Combining Like Terms
Speeding Things Up a Bit
Simplify
Applications
Exercises
3.5 Solving Equations Involving Integers II
Variables on Both Sides
Exercises
3.6 Applications
Consecutive Integers
Consecutive Odd Integers
Tables
Exercises
4 Fractions
4.1 Equivalent Fractions
The Greatest Common Divisor
Reducing a Fraction to Lowest Terms
Reducing Fractions with Variables
A Word on Mathematical Notation.
Equivalent Fractions in Higher Terms
Negative Fractions
Exercises
4.2 Multiplying Fractions
Multiplication Rule
Multiply and Reduce
Multiply and Cancel or Cancel and Multiply
Parallelograms
Triangles
Exercises
4.3 Dividing Fractions
Reciprocals
Division
Exercises
4.4 Adding and Subtracting Fractions
Adding Fractions with Different Denominators
Least Common Multiple
Least Common Multiple Using Prime Factorization
Comparing Fractions
Exercises
4.5 Multiplying and Dividing Mixed Fractions
Changing Mixed Fractions to Improper Fractions
Changing Improper Fractions to Mixed Fractions
Multiplying and Dividing Mixed Fractions
Exercises
4.6 Adding and Subtracting Mixed Fractions
Working in Vertical Format
Subtracting Mixed Fractions
Working in Vertical Format
Borrowing in Vertical Format
Exercises
4.7 Order of Operations with Fractions
Order of Operations
Complex Fractions
Application — Trapezoid
Exercises
4.8 Solving Equations with Fractions
Undoing Subtraction
Undoing Multiplication
Clearing Fractions from the Equation
Applications
Exercises
5 Decimals
5.1 Introduction to Decimals
Decimal Notation
Pronouncing Decimal Numbers
Decimals to Fractions
Rounding
Comparing Decimals
Exercises
5.2 Adding and Subtracting Decimals
Subtracting Decimals
Adding and Subtracting Signed Decimal Numbers
Exercises
5.3 Multiplying Decimals
Multiplying Signed Decimal Numbers
Order of Operations
Powers of Ten
Multiplying Decimal Numbers by Powers of Ten
The Circle
Exercises
5.4 Dividing Decimals
Decimal Divisors
Dividing Signed Decimal Numbers
Rounding
Dividing by Powers of Ten
Order of Operations
Exercises
5.5 Fractions and Decimals
Terminating Decimals
Repeating Decimals
Expressions Containing Both Decimals and Fractions
Exercises
5.6 Equations With Decimals
Combining Operations
Combining Like Terms
Using the Distributive Property
Rounding Solutions
Applications
Exercises
5.7 Introduction to Square Roots
Square Roots
Order of Operations
Fractions and Decimals
Estimating Square Roots
Exercises
5.8 The Pythagorean Theorem
Exercises
6 Ratio and Proportion
6.1 Introduction to Ratios and Rates
Rates
Unit Rates
Exercises
6.2 Introduction to Proportion
Solving Proportions
Applications
Exercises
6.3 Unit Conversion: American System
Units of Length
Units of Weight
Units of Volume
Units of Time
Converting Units of Speed
Exercises
6.4 Unit Conversion: Metric System
Units of Length
Units of Mass
Units of Volume
Exercises
6.5 American Units to Metric Units and Vice-Versa
Converting Units of Length
Converting Units of Weight and Mass
Converting Units of Volume
Converting Units of Speed
Exercises
7 Percent
7.1 Percent, Decimals, Fractions
Changing a Percent to a Fraction
Changing a Percent to a Decimal
Changing a Decimal to a Percent
Changing a Fraction to a Percent
Exercises
7.2 Solving Basic Percent Problems
Find a Given Percent of a Given Number
Find a Percent Given Two Numbers
Find a Number that is a Given Percent of Another Number
Exercises
7.3 General Applications of Percent
Exercises
7.4 Percent Increase or Decrease
Percent Increase
Percent Decrease
Discount
Exercises
7.5 Interest
Extending the Simple Interest Formula
Exercises
7.6 Pie Charts
Pie Charts
Exercises
8 Graphing
8.1 The Cartesian Coordinate System
Allowing for Negative Numbers
Exercises
8.2 Graphing Linear Equations
The Graph of an Equation
Linear Equations
Exercises
Index
```
Document Text Contents
Page 1

Prealgebra Textbook

Second Edition

Department of Mathematics
College of the Redwoods

2012-2013

Page 2

ii

All parts of this prealgebra textbook are copyrighted c© 2009 in the
name of the Department of Mathematics, College of the Redwoods. They
are not in the public domain. However, they are being made available
free for use in educational institutions. This offer does not extend to any
application that is made for profit. Users who have such applications
in mind should contact David Arnold at [email protected] or
Bruce Wagner at [email protected]

NonCommercial-ShareAlike 3.0 Unported License, and is copyrighted
c© 2009, Department of Mathematics, College of the Redwoods. To view
a copy of this license, visit

or send a letter to Creative Commons, 543 Howard Street, 5th Floor,
San Francisco, California, 94105, USA.

mailto:[email protected]
mailto:[email protected]

Page 306

296 CHAPTER 4. FRACTIONS

This is a perfectly good answer, but if you want a mixed fraction answer, 35
divided by 6 is 5, with a remainder of 5. Hence,

−2 1
12
· 24

5
= −55

6
.

You Try It!

EXAMPLE 8. Simplify: −4 4
5
÷ 5 3

5
.Simplify:

−24
9
· 32

3

Solution. Change to improper fractions, invert and multiply, factor, cancel,
and simplify.

−44
5
÷ 53

5
= −24

5
÷ 28

5
Change to improper fractions.

= −24
5
· 5
28

Invert and multiply.

= −2 · 2 · 2 · 3
5

· 5
2 · 2 · 7 Prime factor.

= −�2 · �2 · 2 · 3
�5

· �5
�2 · �2 · 7

Cancel common factors.

= −6
7

Multiply numerators and denominators.

Page 307

4.5. MULTIPLYING AND DIVIDING MIXED FRACTIONS 297

❧ ❧ ❧ Exercises ❧ ❧ ❧

In Exercises 1-12, convert the mixed fraction to an improper fraction.

1. 2
1

3

2. 1
8

11

3. 1
1

19

4. −11
5

5. −13
7

6. 1
3

17

7. 1
1

9

8. 1
5

11

9. −11
2

10. −15
8

11. 1
1

3

12. −15
7

In Exercises 13-24, convert the improper fraction to a mixed fraction.

13.
13

7

14. −17
9

15. −13
5

16. −10
3

17. −16
5

18.
16

13

19.
9

8

20.
16

5

21. −6
5

22. −17
10

23. −3
2

24. −7
4

In Exercises 25-48, multiply the numbers and express your answer as a mixed fraction.

25. 1
1

7
· 21

2

26. 1
1

8
· 11

6

27. 4 · 11
6

28. 1
7

10
· 4

Page 611

INDEX 601

right triangles
hypotenuse, 438
pythagorean theorem, 437

rounding, 6
digit, 6
percent, 507
rounding digit, 349
test digit, 349

Rules Guiding Order of Operations,
312, 374, 393

set, 2
simplify

definition, 201
simplifying

algebraic expressions, 187
solution, 156
solution of an equation

ordered pair, 581, 582, 584–586
point, 581, 582, 584–586

solving equations, 156, 208, 326
by clearing fractions, 329
combining like terms, 208
using reciprocals, 327

square, 22
of a number, 425
perimeter, 22, 203

square root, 425, 425
decimals, 430
estimating, 430
fractions, 430

square unit, 42
subscripts, 318
substitution

using parentheses, 313
subtraction

adding the opposite, 128
decimals, 361
signed, 362

integers, 128
whole numbers, 15

symbols
multiplication, 33

tables, 8

graphing, 8
term, 197
tips for evaluating algebraic expres-

sions, 179
trapezoid

altitude, 318
area, 318
base, 318

triangle
altitude, 257
area, 257, 334
base, 257
perimeter, 217
vertex, 257

undo, 89, 160
Units

american system, 467
american units to metric units,

490
length, 467
length conversion, 469
metric system, 479
metric units to american units,

490
time, 472
volume conversion, 472
volumes, 471
weight, 470
weight conversion, 471

unlike signs
division, 143
multiplication, 141

unlike terms, 198
unwrap, 160

variable, 156
dictionary, 163, 216
whole numbers, 75

variable part, 197–200
vectors, 113

as negative integers, 114
as positive integers, 114
direction, 113
magnitude, 113, 114

whole number

Page 612

602 INDEX

negative, 98
opposite, 98

whole numbers
dividing, 33
multiplication, 33
solving equations, 75
subtraction, 15
variable, 75

word problems
requirements, 163, 216, 332
using tables, 219

writing mathematics, 191

zero
additive identity, 17, 120
dividing by, 40, 144
multiplication, 35, 139