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TitlePrealgebra Textbook
LanguageEnglish
File Size2.2 MB
Total Pages612
Table of Contents
                            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
		Answers
	1.2 Adding and Subtracting Whole Numbers
		The Commutative Property of Addition
		Grouping Symbols
		The Associative Property of Addition
		The Additive Identity
		Adding Larger Whole Numbers
		Subtraction of Whole Numbers
		Subtracting Larger Whole Numbers
		Order of Operations
		Applications — Geometry
		Application — Alternative Fuels
		Exercises
		Answers
	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
		Answers
	1.4 Prime Factorization
		Divisibility
		Divisibility Tests
		Prime Numbers
		Factor Trees
		Exponents
		Application
		Exercises
		Answers
	1.5 Order of Operations
		Fraction Bars
		The Distributive Property
		Exercises
		Answers
	1.6 Solving Equations by Addition and Subtraction
		Equivalent Equations
		Operations that Produce Equivalent Equations
		Wrap and Unwrap
		Word Problems
		Exercises
		Answers
	1.7 Solving Equations by Multiplication and Division
		Word Problems
		Exercises
		Answers
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
		Answers
	2.2 Adding Integers
		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
		Answers
	2.3 Subtracting Integers
		Order of Operations
		Change as a Difference
		Exercises
		Answers
	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
		Answers
	2.5 Order of Operations with Integers
		Evaluating Fractions
		Absolute Value
		Exercises
		Answers
	2.6 Solving Equations Involving Integers
		Adding or Subtracting the Same Amount
		Multiplying or Dividing by the Same Amount
		Combining Operations
		Applications
		Exercises
		Answers
3 The Fundamentals of Algebra
	3.1 Mathematical Expressions
		Translating Words into Mathematical Expressions
		Combinations
		Exercises
		Answers
	3.2 Evaluating Algebraic Expressions
		Exercises
		Answers
	3.3 Simplifying Algebraic Expressions
		Speeding Things Up
		The Distributive Property
		Moving a Bit Quicker
		Extending the Distributive Property
		Distributing a Negative
		Exercises
		Answers
	3.4 Combining Like Terms
		Like Terms
		Combining Like Terms
		Speeding Things Up a Bit
		Simplify
		Applications
		Exercises
		Answers
	3.5 Solving Equations Involving Integers II
		Variables on Both Sides
		Exercises
		Answers
	3.6 Applications
		Consecutive Integers
		Consecutive Odd Integers
		Tables
		Exercises
		Answers
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
		Answers
	4.2 Multiplying Fractions
		Multiplication Rule
		Multiply and Reduce
		Multiply and Cancel or Cancel and Multiply
		Parallelograms
		Triangles
		Exercises
		Answers
	4.3 Dividing Fractions
		Reciprocals
		Division
		Exercises
		Answers
	4.4 Adding and Subtracting Fractions
		Adding Fractions with Different Denominators
		Least Common Multiple
		Least Common Multiple Using Prime Factorization
		Comparing Fractions
		Exercises
		Answers
	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
		Answers
	4.6 Adding and Subtracting Mixed Fractions
		Adding Mixed Fractions
		Working in Vertical Format
		Subtracting Mixed Fractions
		Working in Vertical Format
		Borrowing in Vertical Format
		Exercises
		Answers
	4.7 Order of Operations with Fractions
		Order of Operations
		Complex Fractions
		Application — Trapezoid
		Exercises
		Answers
	4.8 Solving Equations with Fractions
		Undoing Subtraction
		Undoing Addition
		Undoing Multiplication
		Clearing Fractions from the Equation
		Applications
		Exercises
		Answers
5 Decimals
	5.1 Introduction to Decimals
		Decimal Notation
		Pronouncing Decimal Numbers
		Decimals to Fractions
		Rounding
		Comparing Decimals
		Exercises
		Answers
	5.2 Adding and Subtracting Decimals
		Adding Decimals
		Subtracting Decimals
		Adding and Subtracting Signed Decimal Numbers
		Exercises
		Answers
	5.3 Multiplying Decimals
		Multiplying Signed Decimal Numbers
		Order of Operations
		Powers of Ten
		Multiplying Decimal Numbers by Powers of Ten
		The Circle
		Exercises
		Answers
	5.4 Dividing Decimals
		Decimal Divisors
		Dividing Signed Decimal Numbers
		Rounding
		Dividing by Powers of Ten
		Order of Operations
		Exercises
		Answers
	5.5 Fractions and Decimals
		Terminating Decimals
		Repeating Decimals
		Expressions Containing Both Decimals and Fractions
		Exercises
		Answers
	5.6 Equations With Decimals
		Combining Operations
		Combining Like Terms
		Using the Distributive Property
		Rounding Solutions
		Applications
		Exercises
		Answers
	5.7 Introduction to Square Roots
		Square Roots
		Radical Notation
		Order of Operations
		Fractions and Decimals
		Estimating Square Roots
		Exercises
		Answers
	5.8 The Pythagorean Theorem
		Exercises
		Answers
6 Ratio and Proportion
	6.1 Introduction to Ratios and Rates
		Rates
		Unit Rates
		Exercises
		Answers
	6.2 Introduction to Proportion
		Solving Proportions
		Applications
		Exercises
		Answers
	6.3 Unit Conversion: American System
		Units of Length
		Units of Weight
		Units of Volume
		Units of Time
		Converting Units of Speed
		Exercises
		Answers
	6.4 Unit Conversion: Metric System
		Units of Length
		Units of Mass
		Units of Volume
		Exercises
		Answers
	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
		Answers
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
		Answers
	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
		Answers
	7.3 General Applications of Percent
		Exercises
		Answers
	7.4 Percent Increase or Decrease
		Percent Increase
		Percent Decrease
		Discount
		Exercises
		Answers
	7.5 Interest
		Extending the Simple Interest Formula
		Exercises
		Answers
	7.6 Pie Charts
		Pie Charts
		Exercises
		Answers
8 Graphing
	8.1 The Cartesian Coordinate System
		Allowing for Negative Numbers
		Exercises
		Answers
	8.2 Graphing Linear Equations
		The Graph of an Equation
		Linear Equations
		Exercises
		Answers
Index
                        
Document Text Contents
Page 1

Prealgebra Textbook

Second Edition

Department of Mathematics
College of the Redwoods

2012-2013

Page 2

ii

Copyright

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]

This work is licensed under a Creative Commons Attribution-
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

http://creativecommons.org/licenses/by-nc-sa/3.0/

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

mailto:[email protected]
mailto:[email protected]
http://creativecommons.org/licenses/by-nc-sa/3.0/

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
.

Answer: −9


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.

Answer: −2/3


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
radical notation, 427

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
addition, 15
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

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