Pre-Algebra Essentials For Dummies

by Zegarelli, Mark

• ISBN13: 9780470618387
• ISBN10: 0470618388
• Format: Paperback
• Copyright: 2010-05-17
• Publisher: For Dummies

Summary

Many students worry about starting algebra. Pre-Algebra Essentials For Dummies provides an overview of critical pre-algebra concepts to help new algebra students (and their parents) take the next step without fear. Free of ramp-up material, Pre-Algebra Essentials For Dummies contains content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical pre-algebra course, from fractions, decimals, and percents to scientific notation and simple variable equations. This guide is also a perfect reference for parents who need to review critical pre-algebra concepts as they help students with homework assignments, as well as for adult learners headed back into the classroom who just need to a refresher of the core concepts.The Essentials For Dummies Series Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

Author Biography

Mark Zegarelli is a math tutor and author of several books, including Basic Math & Pre-Algebra For Dummies.

Table of Contents

Introduction	p. 1
About This Book	p. 1
Conventions Used in This Book	p. 2
Foolish Assumptions	p. 2
Icons Used in This Book	p. 3
Where to Go from Here	p. 3
Arming Yourself with Math Basics	p. 5
Understanding Sets of Numbers	p. 5
The Big Four Operations	p. 6
Adding things up	p. 6
Take it away: Subtracting	p. 7
Multiplying	p. 7
Arriving on the dot	p. 7
Speaking parenthetically	p. 8
Doing division lickety-split	p. 8
Fun and Useful Properties of the Big Four Operations	p. 9
Inverse operations	p. 9
Commutative operations	p. 9
Associative operations	p. 10
Distributing to lighten the load	p. 11
Other Operations: Exponents, Square Roots, and Absolute Values	p. 11
Understanding exponents	p. 11
Discovering your roots	p. 12
Figuring out absolute value	p. 13
Finding Factors	p. 13
Generating factors	p. 13
Finding the greatest common factor (GCF)	p. 14
Finding Multiples	p. 15
Generating multiples	p. 15
Finding the least common multiple (LCM)	p. 16
Evaluating Arithmetic Expressions	p. 17
The Three E's: Equations, Expressions, and Evaluations	p. 18
Equality for all: Equations	p. 18
Hey, it's just an expression	p. 19
Evaluating the situation	p. 19
Putting the Three E's together	p. 20
Following the Order of Operations	p. 20
Order of operations and the Big Four expressions	p. 21
Expressions with only addition and subtraction	p. 22
Expressions with only multiplication and division	p. 23
Mixed-operator expressions	p. 24
Order of operations in expressions with exponents	p. 25
Order of operations in expressions with parentheses	p. 25
Big Four expressions with parentheses	p. 26
Expressions with exponents and parentheses	p. 26
Expressions with parentheses raised to an exponent	p. 27
Expressions with nested parentheses	p. 28
Say What? Making Sense of Word Problems	p. 31
Handling Basic Word Problems	p. 32
Turning word problems into word equations	p. 32
Jotting down information as word equations	p. 32
Turning more-complex statements into word equations	p. 33
Figuring out what the problem's asking	p. 34
Plugging in numbers for words	p. 35
Example: Send in the clowns	p. 35
Example: Our house in the middle of our street	p. 36
Solving More-Challenging Word Problems	p. 36
When numbers get serious	p. 37
Lots of information	p. 38
Putting it all together	p. 40
Figuring Out Fractions	p. 43
Reducing Fractions to Lowest Terms	p. 44
Multiplying and Dividing Fractions	p. 44
Multiplying numerators and denominators straight across	p. 45
Doing a flip to divide fractions	p. 45
Adding Fractions	p. 46
Finding the sum of fractions with the same denominator	p. 46
Adding fractions with different denominators	p. 47
Subtracting Fractions	p. 49
Subtracting fractions with the same denominator	p. 49
Subtracting fractions with different denominators	p. 50
Working with Mixed Numbers	p. 51
Converting between improper fractions and mixed numbers	p. 51
Switching to an improper fraction	p. 51
Switching to a mixed number	p. 52
Multiplying and dividing mixed numbers	p. 52
Adding and subtracting mixed numbers	p. 53
Adding two mixed numbers	p. 53
Subtracting mixed numbers	p. 55
Deciphering Decimals	p. 59
Performing the Big Four Operations with Decimals	p. 59
Adding decimals	p. 60
Subtracting decimals	p. 61
Multiplying decimals	p. 62
Dividing decimals	p. 63
Dealing with more zeros in the dividend	p. 64
Completing decimal division	p. 64
Converting between Decimals and Fractions	p. 65
Changing decimals to fractions	p. 66
Doing a basic decimal-to-fraction conversion	p. 66
Mixing numbers and reducing fractions	p. 67
Changing fractions to decimals	p. 68
The last stop: Terminating decimals	p. 68
The endless ride: Repeating decimals	p. 69
Puzzling Out Percents	p. 71
Understanding Percents Greater than 100%	p. 72
Converting to and from Percents, Decimals, and Fractions	p. 72
Going from percents to decimals	p. 73
Changing decimals into percents	p. 73
Switching from percents to fractions	p. 73
Turning fractions into percents	p. 74
Solving Percent Problems	p. 75
Figuring out simple percent problems	p. 76
Deciphering more-difficult percent problems	p. 77
Applying Percent Problems	p. 78
Identifying the three types of percent problems	p. 79
Introducing the percent circle	p. 80
Finding the ending number	p. 81
Discovering the percentage	p. 81
Tracking down the starting number	p. 82
Fraction, Decimal, and Percent Word Problems	p. 85
Adding and Subtracting Parts of the Whole	p. 85
Sharing a pizza: Fractions	p. 86
Buying by the pound: Decimals	p. 86
Splitting the vote: Percents	p. 87
Multiplying Fractions in Everyday Situations	p. 88
Buying less than advertised	p. 88
Computing leftovers	p. 89
Multiplying Decimals and Percents in Word Problems	p. 90
Figuring out how much money is left	p. 90
Finding out how much you started with	p. 91
Handling Percent Increases and Decreases in Word Problems	p. 93
Raking in the dough: Finding salary increases	p. 94
Earning interest on top of interest	p. 94
Getting a deal: Calculating discounts	p. 96
Using Variables in Algebraic Expressions	p. 97
Variables: X Marks the Spot	p. 97
Expressing Yourself with Algebraic Expressions	p. 98
Evaluating algebraic expressions	p. 99
Coming to algebraic terms	p. 101
Making the commute: Rearranging your terms	p. 102
Identifying the coefficient and variable	p. 103
Identifying similar terms	p. 104
Considering algebraic terms and the Big Four operations	p. 104
Adding terms	p. 104
Subtracting terms	p. 105
Multiplying terms	p. 106
Dividing terms	p. 107
Simplifying Algebraic Expressions	p. 108
Combining similar terms	p. 109
Removing parentheses from an algebraic expression	p. 110
Drop everything: Parentheses with a plus sign	p. 110
Switch signs: Parentheses with a minus sign	p. 110
Distribute: Parentheses with no sign	p. 111
Foil: Two terms in each set of parentheses	p. 112
X's Secret Identity: Solving Algebraic Equations	p. 115
Understanding Algebraic Equations	p. 116
Using x in equations	p. 116
Four ways to solve algebraic equations	p. 117
Eyeballing easy equations	p. 117
Rearranging slightly harder equations	p. 117
Guessing and checking equations	p. 118
Applying algebra to more-difficult equations	p. 119
Checks and Balances: Solving for X	p. 119
Striking a balance	p. 119
Using the balance scale to isolate x	p. 120
Rearranging Equations to Isolate X	p. 122
Rearranging terms on one side of an equation	p. 122
Moving terms to the other side of the equal sign	p. 123
Removing parentheses from equations	p. 124
Using cross-multiplication to remove fractions	p. 127
Decoding Algebra Word Problems	p. 129
Using a Five-Step Approach	p. 130
Declaring a variable	p. 130
Setting up the equation	p. 131
Solving the equation	p. 132
Answering the question	p. 133
Checking your work	p. 133
Choosing Your Variable Wisely	p. 134
Solving More Complex Algebra Problems	p. 135
Geometry: Perimeter, Area, Surface Area, and Volume	p. 139
Closed Encounters: Understanding 2-D Shapes	p. 139
Circles	p. 140
Polygons	p. 140
Adding Another Dimension: Solid Geometry	p. 141
The many faces of polyhedrons	p. 141
3-D shapes with curves	p. 142
Measuring Shapes: Perimeter, Area, Surface Area, and Volume	p. 143
2-D: Measuring on the flat	p. 143
Going 'round in circles	p. 144
Measuring triangles	p. 146
Measuring squares	p. 147
Working with rectangles	p. 148
Calculating with rhombuses	p. 148
Measuring parallelograms	p. 149
Measuring trapezoids	p. 150
Spacing out: Measuring in three dimensions	p. 151
Spheres	p. 152
Cubes	p. 153
Boxes (Rectangular solids)	p. 153
Prisms	p. 154
Cylinders	p. 154
Pyramids and cones	p. 155
Picture It! Graphing Information	p. 157
Examining Three Common Graph Styles	p. 158
Bar graph	p. 158
Pie chart	p. 159
Line graph	p. 160
Using Cartesian Coordinates	p. 162
Plotting points on a Cartesian graph	p. 162
Drawing lines on a Cartesian graph	p. 164
Solving problems with a Cartesian graph	p. 167
Ten Essential Math Concepts	p. 169
Playing with Prime Numbers	p. 169
Zero: Much Ado about Nothing	p. 170
Delicious Pi	p. 170
Equal Signs and Equations	p. 171
The Cartesian Graph	p. 171
Relying on Functions	p. 172
Rational Numbers	p. 172
Irrational Numbers	p. 173
The Real Number Line	p. 173
Exploring the Infinite	p. 174
Index	p. 175
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