Pre-Algebra Essentials For Dummies

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  • Edition: 1st
  • Format: Paperback
  • Copyright: 2010-05-17
  • Publisher: For Dummies
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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

Introductionp. 1
About This Bookp. 1
Conventions Used in This Bookp. 2
Foolish Assumptionsp. 2
Icons Used in This Bookp. 3
Where to Go from Herep. 3
Arming Yourself with Math Basicsp. 5
Understanding Sets of Numbersp. 5
The Big Four Operationsp. 6
Adding things upp. 6
Take it away: Subtractingp. 7
Multiplyingp. 7
Arriving on the dotp. 7
Speaking parentheticallyp. 8
Doing division lickety-splitp. 8
Fun and Useful Properties of the Big Four Operationsp. 9
Inverse operationsp. 9
Commutative operationsp. 9
Associative operationsp. 10
Distributing to lighten the loadp. 11
Other Operations: Exponents, Square Roots, and Absolute Valuesp. 11
Understanding exponentsp. 11
Discovering your rootsp. 12
Figuring out absolute valuep. 13
Finding Factorsp. 13
Generating factorsp. 13
Finding the greatest common factor (GCF)p. 14
Finding Multiplesp. 15
Generating multiplesp. 15
Finding the least common multiple (LCM)p. 16
Evaluating Arithmetic Expressionsp. 17
The Three E's: Equations, Expressions, and Evaluationsp. 18
Equality for all: Equationsp. 18
Hey, it's just an expressionp. 19
Evaluating the situationp. 19
Putting the Three E's togetherp. 20
Following the Order of Operationsp. 20
Order of operations and the Big Four expressionsp. 21
Expressions with only addition and subtractionp. 22
Expressions with only multiplication and divisionp. 23
Mixed-operator expressionsp. 24
Order of operations in expressions with exponentsp. 25
Order of operations in expressions with parenthesesp. 25
Big Four expressions with parenthesesp. 26
Expressions with exponents and parenthesesp. 26
Expressions with parentheses raised to an exponentp. 27
Expressions with nested parenthesesp. 28
Say What? Making Sense of Word Problemsp. 31
Handling Basic Word Problemsp. 32
Turning word problems into word equationsp. 32
Jotting down information as word equationsp. 32
Turning more-complex statements into word equationsp. 33
Figuring out what the problem's askingp. 34
Plugging in numbers for wordsp. 35
Example: Send in the clownsp. 35
Example: Our house in the middle of our streetp. 36
Solving More-Challenging Word Problemsp. 36
When numbers get seriousp. 37
Lots of informationp. 38
Putting it all togetherp. 40
Figuring Out Fractionsp. 43
Reducing Fractions to Lowest Termsp. 44
Multiplying and Dividing Fractionsp. 44
Multiplying numerators and denominators straight acrossp. 45
Doing a flip to divide fractionsp. 45
Adding Fractionsp. 46
Finding the sum of fractions with the same denominatorp. 46
Adding fractions with different denominatorsp. 47
Subtracting Fractionsp. 49
Subtracting fractions with the same denominatorp. 49
Subtracting fractions with different denominatorsp. 50
Working with Mixed Numbersp. 51
Converting between improper fractions and mixed numbersp. 51
Switching to an improper fractionp. 51
Switching to a mixed numberp. 52
Multiplying and dividing mixed numbersp. 52
Adding and subtracting mixed numbersp. 53
Adding two mixed numbersp. 53
Subtracting mixed numbersp. 55
Deciphering Decimalsp. 59
Performing the Big Four Operations with Decimalsp. 59
Adding decimalsp. 60
Subtracting decimalsp. 61
Multiplying decimalsp. 62
Dividing decimalsp. 63
Dealing with more zeros in the dividendp. 64
Completing decimal divisionp. 64
Converting between Decimals and Fractionsp. 65
Changing decimals to fractionsp. 66
Doing a basic decimal-to-fraction conversionp. 66
Mixing numbers and reducing fractionsp. 67
Changing fractions to decimalsp. 68
The last stop: Terminating decimalsp. 68
The endless ride: Repeating decimalsp. 69
Puzzling Out Percentsp. 71
Understanding Percents Greater than 100%p. 72
Converting to and from Percents, Decimals, and Fractionsp. 72
Going from percents to decimalsp. 73
Changing decimals into percentsp. 73
Switching from percents to fractionsp. 73
Turning fractions into percentsp. 74
Solving Percent Problemsp. 75
Figuring out simple percent problemsp. 76
Deciphering more-difficult percent problemsp. 77
Applying Percent Problemsp. 78
Identifying the three types of percent problemsp. 79
Introducing the percent circlep. 80
Finding the ending numberp. 81
Discovering the percentagep. 81
Tracking down the starting numberp. 82
Fraction, Decimal, and Percent Word Problemsp. 85
Adding and Subtracting Parts of the Wholep. 85
Sharing a pizza: Fractionsp. 86
Buying by the pound: Decimalsp. 86
Splitting the vote: Percentsp. 87
Multiplying Fractions in Everyday Situationsp. 88
Buying less than advertisedp. 88
Computing leftoversp. 89
Multiplying Decimals and Percents in Word Problemsp. 90
Figuring out how much money is leftp. 90
Finding out how much you started withp. 91
Handling Percent Increases and Decreases in Word Problemsp. 93
Raking in the dough: Finding salary increasesp. 94
Earning interest on top of interestp. 94
Getting a deal: Calculating discountsp. 96
Using Variables in Algebraic Expressionsp. 97
Variables: X Marks the Spotp. 97
Expressing Yourself with Algebraic Expressionsp. 98
Evaluating algebraic expressionsp. 99
Coming to algebraic termsp. 101
Making the commute: Rearranging your termsp. 102
Identifying the coefficient and variablep. 103
Identifying similar termsp. 104
Considering algebraic terms and the Big Four operationsp. 104
Adding termsp. 104
Subtracting termsp. 105
Multiplying termsp. 106
Dividing termsp. 107
Simplifying Algebraic Expressionsp. 108
Combining similar termsp. 109
Removing parentheses from an algebraic expressionp. 110
Drop everything: Parentheses with a plus signp. 110
Switch signs: Parentheses with a minus signp. 110
Distribute: Parentheses with no signp. 111
Foil: Two terms in each set of parenthesesp. 112
X's Secret Identity: Solving Algebraic Equationsp. 115
Understanding Algebraic Equationsp. 116
Using x in equationsp. 116
Four ways to solve algebraic equationsp. 117
Eyeballing easy equationsp. 117
Rearranging slightly harder equationsp. 117
Guessing and checking equationsp. 118
Applying algebra to more-difficult equationsp. 119
Checks and Balances: Solving for Xp. 119
Striking a balancep. 119
Using the balance scale to isolate xp. 120
Rearranging Equations to Isolate Xp. 122
Rearranging terms on one side of an equationp. 122
Moving terms to the other side of the equal signp. 123
Removing parentheses from equationsp. 124
Using cross-multiplication to remove fractionsp. 127
Decoding Algebra Word Problemsp. 129
Using a Five-Step Approachp. 130
Declaring a variablep. 130
Setting up the equationp. 131
Solving the equationp. 132
Answering the questionp. 133
Checking your workp. 133
Choosing Your Variable Wiselyp. 134
Solving More Complex Algebra Problemsp. 135
Geometry: Perimeter, Area, Surface Area, and Volumep. 139
Closed Encounters: Understanding 2-D Shapesp. 139
Circlesp. 140
Polygonsp. 140
Adding Another Dimension: Solid Geometryp. 141
The many faces of polyhedronsp. 141
3-D shapes with curvesp. 142
Measuring Shapes: Perimeter, Area, Surface Area, and Volumep. 143
2-D: Measuring on the flatp. 143
Going 'round in circlesp. 144
Measuring trianglesp. 146
Measuring squaresp. 147
Working with rectanglesp. 148
Calculating with rhombusesp. 148
Measuring parallelogramsp. 149
Measuring trapezoidsp. 150
Spacing out: Measuring in three dimensionsp. 151
Spheresp. 152
Cubesp. 153
Boxes (Rectangular solids)p. 153
Prismsp. 154
Cylindersp. 154
Pyramids and conesp. 155
Picture It! Graphing Informationp. 157
Examining Three Common Graph Stylesp. 158
Bar graphp. 158
Pie chartp. 159
Line graphp. 160
Using Cartesian Coordinatesp. 162
Plotting points on a Cartesian graphp. 162
Drawing lines on a Cartesian graphp. 164
Solving problems with a Cartesian graphp. 167
Ten Essential Math Conceptsp. 169
Playing with Prime Numbersp. 169
Zero: Much Ado about Nothingp. 170
Delicious Pip. 170
Equal Signs and Equationsp. 171
The Cartesian Graphp. 171
Relying on Functionsp. 172
Rational Numbersp. 172
Irrational Numbersp. 173
The Real Number Linep. 173
Exploring the Infinitep. 174
Indexp. 175
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