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<p><b>Introduction 1</b></p> <p>About This Book 1</p> <p>Foolish Assumptions 2</p> <p>Icons Used in This Book 2</p> <p>Beyond the Book 3</p> <p>Where to Go from Here 3</p> <p><b>Unit 1: Getting Started with Basic Math & Pre-algebra 5</b></p> <p><b>Chapter 1: Playing the Numbers Game 7</b></p> <p>Inventing Numbers 8</p> <p>Understanding Number Sequences 8</p> <p>Evening the odds 8</p> <p>Counting by threes, fours, fives, and so on 9</p> <p>Getting square with square numbers 9</p> <p>Composing yourself with composite numbers 10</p> <p>Stepping out of the box with prime numbers 11</p> <p>Multiplying quickly with exponents 12</p> <p>Four Important Sets of Numbers 13</p> <p>Counting on the counting numbers 13</p> <p>Introducing integers 13</p> <p>Staying rational 14</p> <p>Getting real 14</p> <p><b>Chapter 2: The Big Four Operations 15</b></p> <p>The Big Four Operations 15</p> <p>Adding things up: Addition 16</p> <p>Take it away: Subtraction 16</p> <p>A sign of the times: Multiplication 17</p> <p>Doing math lickety-split: Division 18</p> <p>Applying the Big Four Operations to Larger Numbers 18</p> <p>Calculating stacked addition 18</p> <p>Performing stacked subtraction 19</p> <p>Calculating with stacked multiplication 21</p> <p>Understanding long division 22</p> <p><b>Unit 2: the Big Four Operations: Addition, Subtraction, Multiplication, and Division 25</b></p> <p><b>Chapter 3: Counting on Success: Numbers and Digits 27</b></p> <p>Knowing Your Place Value 28</p> <p>Counting to ten and beyond 28</p> <p>Telling placeholders from leading zeros 29</p> <p>Reading long numbers 30</p> <p>Close Enough for Rock ‘n’ Roll: Rounding and Estimating 30</p> <p>Rounding numbers 30</p> <p>Estimating value to make problems easier 32</p> <p>Practice Questions Answers and Explanations 34</p> <p>Whaddya Know? Chapter 3 Quiz 35</p> <p>Answers to Chapter 3 Quiz 36</p> <p><b>Chapter 4: Staying Positive with Negative Numbers 37</b></p> <p>Understanding Where Negative Numbers Come From 38</p> <p>Sign-Switching: Understanding Negation and Absolute Value 39</p> <p>Addition and Subtraction with Negative Numbers 41</p> <p>Starting with a negative number 41</p> <p>Adding a negative number 41</p> <p>Subtracting a negative number 42</p> <p>Knowing Signs of the Times (and Division) for Negative Numbers 44</p> <p>Practice Questions Answers and Explanations 47</p> <p>Whaddya Know? Chapter 4 Quiz 51</p> <p>Answers to Chapter 4 Quiz 52</p> <p><b>Chapter 5: Putting the Big Four Operations to Work 55</b></p> <p>Switching Things Up with Inverse Operations and the Commutative Property 56</p> <p>Getting with the In-Group: Parentheses and the Associative Property 59</p> <p>Distribution to lighten the load 61</p> <p>Understanding Inequalities 63</p> <p>Doesn’t equal (≠) 63</p> <p>Less than (<) and greater than (>) 63</p> <p>Less than or equal to (≤) and greater than or equal to (≥) 64</p> <p>Approximately equals (≈) 64</p> <p>Moving Beyond the Big Four: Exponents and Square Roots 65</p> <p>Understanding exponents 66</p> <p>Discovering your roots 67</p> <p>Practice Questions Answers and Explanations 69</p> <p>Whaddya Know? Chapter 5 Quiz 72</p> <p>Answers to Chapter 5 Quiz 73</p> <p><b>Unit 3: Getting a Handle on Whole Numbers 75</b></p> <p><b>Chapter 6: Please Excuse My Dear Aunt Sally: Evaluating Arithmetic Expressions with PEMDAS 77</b></p> <p>The Three E’s of Math: Equations, Expressions, and Evaluation 78</p> <p>Seeking equality for all: Equations 78</p> <p>Hey, it’s just an expression 78</p> <p>Evaluating the situation 79</p> <p>Putting the Three E’s together 79</p> <p>Introducing Order of Operations (PEMDAS) 80</p> <p>Expressions with only addition and subtraction 81</p> <p>Expressions with only multiplication and division 81</p> <p>Mixed-operator expressions 82</p> <p>Handling Powers Responsibly 83</p> <p>Prioritizing parentheses 84</p> <p>Pulling apart parentheses and powers 85</p> <p>Figuring out nested parentheses 86</p> <p>Bringing It All Together: The Order of Operations 87</p> <p>Practice Questions Answers and Explanations 89</p> <p>Whaddya Know? Chapter 6 Quiz 98</p> <p>Answers to Chapter 6 Quiz 99</p> <p><b>Chapter 7: Turning Words into Numbers: Basic Math Word Problems 103</b></p> <p>Dispelling Two Myths about Word Problems 104</p> <p>Word problems aren’t always hard 104</p> <p>Word problems are useful 104</p> <p>Solving Basic Word Problems 105</p> <p>Turning word problems into word equations 105</p> <p>Plugging in numbers for words 109</p> <p>Send in the clowns 109</p> <p>Our house in the middle of our street 110</p> <p>I hear the train a-comin’ 110</p> <p>Solving More-Complex Word Problems 113</p> <p>When numbers get serious 113</p> <p>Too much information 115</p> <p>Practice Questions Answers and Explanations 120</p> <p>Whaddya Know? Chapter 7 Quiz 124</p> <p>Answers to Chapter 7 Quiz 125</p> <p><b>Chapter 8: Divisibility and Prime Numbers 127</b></p> <p>Knowing the Divisibility Tricks 128</p> <p>Counting everyone in: Numbers you can divide everything by 128</p> <p>In the end: Looking at the final digits 128</p> <p>Count it up: Checking divisibility by adding and subtracting digits 130</p> <p>Less is more: Checking divisibility by subtracting 134</p> <p>Cross-checking: Using multiple tests 135</p> <p>Identifying Prime and Composite Numbers 136</p> <p>Practice Questions Answers and Explanations 139</p> <p>Whaddya Know? Chapter 8 Quiz 142</p> <p>Answers to Chapter 8 Quiz 143</p> <p><b>Chapter 9: Divided Attention: Factors and Multiples 145</b></p> <p>Knowing Six Ways to Say the Same Thing 146</p> <p>Understanding Factors and Multiples 146</p> <p>Finding Fabulous Factors 148</p> <p>Deciding when one number is a factor of another 148</p> <p>Understanding factor pairs 148</p> <p>Generating a Number’s Factors 149</p> <p>Decomposing a Number into Its Prime Factors 150</p> <p>Finding the Greatest Common Factor 151</p> <p>Generating the Multiples of a Number 153</p> <p>Finding the Least Common Multiple 153</p> <p>Practice Questions Answers and Explanations 155</p> <p>Whaddya Know? Chapter 9 Quiz 158</p> <p>Answers to Chapter 9 Quiz 159</p> <p><b>Unit 4: Fractions 161</b></p> <p><b>Chapter 10: Understanding Fractions 163</b></p> <p>Slicing a Cake into Fractions 164</p> <p>Knowing the Fraction Facts of Life 165</p> <p>Telling the numerator from the denominator 165</p> <p>Flipping for reciprocals 166</p> <p>Using ones and zeros 166</p> <p>Mixing things up 167</p> <p>Knowing proper from improper 167</p> <p>Increasing and Reducing Terms of Fractions 169</p> <p>Increasing the terms of fractions 170</p> <p>Reducing fractions to lowest terms (simplifying fractions) 171</p> <p>Converting between Improper Fractions and Mixed Numbers 174</p> <p>Knowing the parts of a mixed number 174</p> <p>Converting a mixed number to an improper fraction 175</p> <p>Converting an improper fraction to a mixed number 176</p> <p>Comparing Fractions with Cross-Multiplication 178</p> <p>Working with Ratios and Proportions 180</p> <p>Practice Questions Answers and Explanations 182</p> <p>Whaddya Know? Chapter 10 Quiz 188</p> <p>Answers to Chapter 10 Quiz 189</p> <p><b>Chapter 11: Fractions and the Big Four Operations 191</b></p> <p>Multiplying and Dividing Fractions 192</p> <p>Multiplying numerators and denominators straight across 192</p> <p>Doing a flip to divide fractions 194</p> <p>Adding and Subtracting Fractions with the Same Denominator 196</p> <p>Adding and Subtracting Fractions with Different Denominators 198</p> <p>The easy case: Increasing the terms of one fraction 198</p> <p>The difficult case: Increasing the terms of both fractions 200</p> <p>Practice Questions Answers and Explanations 202</p> <p>Whaddya Know? Chapter 11 Quiz 208</p> <p>Answers to Chapter 11 Quiz 209</p> <p><b>Chapter 12: Mixing Things Up with Mixed Numbers 213</b></p> <p>Multiplying and Dividing Mixed Numbers 214</p> <p>Adding Mixed Numbers 216</p> <p>Adding mixed numbers that have the same denominator 216</p> <p>Adding mixed numbers that have different denominators 217</p> <p>Adding mixed numbers with carrying 217</p> <p>Subtracting Mixed Numbers 220</p> <p>Subtracting mixed numbers that have the same denominator 220</p> <p>Subtracting mixed numbers that have different denominators 221</p> <p>Subtracting mixed numbers with borrowing 222</p> <p>Practice Questions Answers and Explanations 225</p> <p>Whaddya Know? Chapter 12 Quiz 233</p> <p>Answers to Chapter 12 Quiz 234</p> <p><b>Unit 5: Decimals and Percents 241</b></p> <p><b>Chapter 13: Getting to the Point with Decimals 243</b></p> <p>Understanding Basic Decimal Stuff 244</p> <p>Counting dollars and decimals 244</p> <p>Identifying the place value of decimals 246</p> <p>Knowing the decimal facts of life 247</p> <p>Performing the Big Four Operations with Decimals 252</p> <p>Adding decimals 253</p> <p>Subtracting decimals 254</p> <p>Multiplying decimals 256</p> <p>Dividing decimals 257</p> <p>Converting between Decimals and Fractions 262</p> <p>Simple Decimal-Fraction Conversions 262</p> <p>Changing decimals to fractions 264</p> <p>Changing fractions to decimals 267</p> <p>Practice Questions Answers and Explanations 271</p> <p>Whaddya Know? Chapter 13 Quiz 279</p> <p>Answers to Chapter 13 Quiz 280</p> <p><b>Chapter 14: Playing the Percentages 285</b></p> <p>Making Sense of Percentages 285</p> <p>Dealing with Percentages Greater than 100% 286</p> <p>Converting to and from Percentages, Decimals, and Fractions 287</p> <p>Converting Percentages to Decimals 287</p> <p>Changing Decimals to Percentages 288</p> <p>Switching from Percentages to Fractions 288</p> <p>Converting Fractions to Percentages 289</p> <p>Solving Percentage Problems 290</p> <p>Figuring out simple percent problems 291</p> <p>Turning the problem around 292</p> <p>Deciphering more-difficult percent problems 293</p> <p>Putting All the Percent Problems Together 294</p> <p>Identifying the three types of percent problems 294</p> <p>Solving Percent Problems with Equations 295</p> <p>Practice Questions Answers and Explanations 299</p> <p>Whaddya Know? Chapter 14 Quiz 303</p> <p>Answers to Chapter 14 Quiz 304</p> <p><b>Chapter 15: Word Problems with Fractions, Decimals, and Percentages 307</b></p> <p>Adding and Subtracting Parts of the Whole in Word Problems 308</p> <p>Sharing a pizza: Fractions 308</p> <p>Buying by the pound: Decimals 309</p> <p>Splitting the vote: Percentages 309</p> <p>Problems about Multiplying Fractions 310</p> <p>Renegade grocery shopping: Buying less than they tell you to 310</p> <p>Easy as pie: Working out what’s left on your plate 311</p> <p>Multiplying Decimals and Percentages in Word Problems 313</p> <p>To the end: Figuring out how much money is left 313</p> <p>Finding out how much you started with 314</p> <p>Handling Percent Increases and Decreases in Word Problems 316</p> <p>Raking in the dough: Finding salary increases 316</p> <p>Earning interest on top of interest 316</p> <p>Getting a deal: Calculating discounts 317</p> <p>Practice Questions Answers and Explanations 319</p> <p>Whaddya Know? Chapter 15 Quiz 322</p> <p>Answers to Chapter 15 Quiz 324</p> <p><b>Unit 6: Reaching the Summit: Advanced Pre-algebra Topics 327</b></p> <p><b>Chapter 16: Powers and Roots 329</b></p> <p>Memorizing Powers and Roots 329</p> <p>Remembering square numbers and square roots 330</p> <p>Keeping track of cubic numbers and cube roots 330</p> <p>Knowing a few powers of 2 and their related roots 331</p> <p>Changing the Base 332</p> <p>Negating a number raised to an exponent 332</p> <p>Finding powers of negative numbers 332</p> <p>Finding powers of fractions 333</p> <p>Mixing negative numbers and fractions with exponents 333</p> <p>Exponents of 0 and Negative Numbers 334</p> <p>Exponents of 0 334</p> <p>Negative exponents 335</p> <p>Fractional Exponents 337</p> <p>Exponents of 1 2 337</p> <p>Exponents of 1 3 338</p> <p>Exponents of 1 4 , 1 5 , 1 , and so forth 6 339</p> <p>Other fractional exponents 339</p> <p>Practice Questions Answers and Explanations 341</p> <p>Whaddya Know? Chapter 16 Quiz 343</p> <p>Answers to Chapter 16 Quiz 344</p> <p><b>Chapter 17: A Perfect Ten: Condensing Numbers with Scientific Notation 347</b></p> <p>First Things First: Using Powers of Ten as Exponents 348</p> <p>Counting zeros and writing exponents 348</p> <p>Exponential Arithmetic: Multiplying and Dividing Powers of Ten 350</p> <p>Working with Scientific Notation 352</p> <p>Writing in scientific notation 352</p> <p>Understanding order of magnitude 354</p> <p>Multiplying with scientific notation 355</p> <p>Dividing with Scientific Notation 356</p> <p>Practice Questions Answers and Explanations 357</p> <p>Whaddya Know? Chapter 17 Quiz 360</p> <p>Answers to Chapter 17 Quiz 361</p> <p><b>Chapter 18: How Much Have You Got? Weights and Measures 363</b></p> <p>Understanding Units 364</p> <p>Adding and subtracting units 364</p> <p>Multiplying and dividing units 364</p> <p>Examining Differences between the English and Metric Systems 365</p> <p>Looking at the English system 365</p> <p>Looking at the metric system 369</p> <p>Estimating and Converting between the English and Metric Systems 372</p> <p>Estimating in the metric system 373</p> <p>Converting units of measurement 375</p> <p>Converting between English and Metric Units 377</p> <p>Practice Questions Answers and Explanations 381</p> <p>Whaddya Know? Chapter 18 Quiz 388</p> <p>Answers to Chapter 18 Quiz 389</p> <p><b>Chapter 19: Getting the Picture with Geometry 393</b></p> <p>Getting on the Plane: Points, Lines, Angles, and Shapes 394</p> <p>Making some points 394</p> <p>Knowing your lines 394</p> <p>Figuring the angles 395</p> <p>Shaping things up 396</p> <p>Getting in Shape: Polygon (and Non-Polygon) Basics 396</p> <p>Closed Encounters: Shaping Up Your Understanding of 2-D Shapes 397</p> <p>Polygons 397</p> <p>Circles 399</p> <p>Squaring Off with Quadrilaterals 400</p> <p>Making a Triple Play with Triangles 403</p> <p>Getting Around with Circle Measurements 405</p> <p>Taking a Trip to Another Dimension: Solid Geometry 406</p> <p>The many faces of polyhedrons 407</p> <p>3-D shapes with curves 408</p> <p>Building Solid Measurement Skills 409</p> <p>Solving Geometry Word Problems 413</p> <p>Working from words and images 413</p> <p>Breaking out those sketching skills 415</p> <p>Practice Questions Answers and Explanations 418</p> <p>Whaddya Know? Chapter 19 Quiz 425</p> <p>Answers to Chapter 19 Quiz 427</p> <p><b>Chapter 20: Figuring Your Chances: Statistics and Probability 431</b></p> <p>Gathering Data Mathematically: Basic Statistics 432</p> <p>Understanding differences between qualitative and quantitative data 432</p> <p>Working with qualitative data 433</p> <p>Working with quantitative data 436</p> <p>Looking at Likelihoods: Basic Probability 439</p> <p>Figuring the probability 440</p> <p>Oh, the possibilities! Counting outcomes with multiple coins 441</p> <p>Practice Questions Answers and Explanations 444</p> <p>Whaddya Know? Chapter 20 Quiz 447</p> <p>Answers to Chapter 20 Quiz 449</p> <p><b>Chapter 21: Setting Things Up with Basic Set Theory 451</b></p> <p>Understanding Sets 451</p> <p>Elementary, my dear: Considering what’s inside sets 452</p> <p>Sets of numbers 454</p> <p>Performing Operations on Sets 455</p> <p>Union: Combined elements 455</p> <p>Intersection: Elements in common 456</p> <p>Relative complement: Subtraction (sorta) 457</p> <p>Complement: Feeling left out 457</p> <p>Practice Questions Answers and Explanations 459</p> <p>Whaddya Know? Chapter 21 Quiz 461</p> <p>Answers to Chapter 21 Quiz 462</p> <p><b>Unit 7: the X-files: Introduction to Algebra 463</b></p> <p><b>Chapter 22: Working with Algebraic Expressions 465</b></p> <p>Seeing How X Marks the Spot 466</p> <p>Expressing Yourself with Algebraic Expressions 466</p> <p>Evaluating Algebraic Expressions 467</p> <p>Knowing the Terms 470</p> <p>Making the commute: Rearranging your terms 471</p> <p>Identifying the coefficient and variable 472</p> <p>Adding and Subtracting Like Terms 473</p> <p>Identifying like terms 473</p> <p>Adding and subtracting terms 474</p> <p>Multiplying and Dividing Terms 475</p> <p>Simplifying Expressions by Combining Like Terms 479</p> <p>Removing Parentheses from an Algebraic Expression 481</p> <p>Drop everything: Parentheses with a plus sign 481</p> <p>Sign turnabout: Parentheses with a negative sign 481</p> <p>Distribution: Parentheses with no sign 482</p> <p>FOILing: Dealing with Two Sets of Parentheses 484</p> <p>Practice Questions Answers and Explanations 487</p> <p>Whaddya Know? Chapter 22 Quiz 495</p> <p>Answers to Chapter 22 Quiz 496</p> <p><b>Chapter 23: Solving Algebraic Equations 499</b></p> <p>Understanding Algebraic Equations 500</p> <p>Using X in Equations 500</p> <p>Choosing among four ways to solve algebraic equations 501</p> <p>The Balancing Act: Solving for x 503</p> <p>Striking a balance 504</p> <p>Using the Balance Scale to Isolate X 504</p> <p>Rearranging Equations and Isolating x 506</p> <p>Rearranging terms on one side of an equation 506</p> <p>Moving terms to the other side of the equals sign 507</p> <p>Removing parentheses from equations 509</p> <p>Cross-multiplying 512</p> <p>Practice Questions Answers and Explanations 515</p> <p>Whaddya Know? Chapter 23 Quiz 525</p> <p>Answers to Chapter 23 Quiz 526</p> <p><b>Chapter 24: Tackling Algebra Word Problems 531</b></p> <p>Solving Algebra Word Problems in Five Steps 531</p> <p>Declaring a variable 532</p> <p>Setting up the equation 533</p> <p>Solving the equation 533</p> <p>Answering the question 534</p> <p>Checking your work 534</p> <p>Choosing Your Variable Wisely 536</p> <p>Solving More-Complex Algebraic Problems 539</p> <p>Charting four people 539</p> <p>Crossing the finish line with five people 540</p> <p>Practice Questions Answers and Explanations 545</p> <p>Whaddya Know? Chapter 24 Quiz 549</p> <p>Answers to Chapter 24 Quiz 550</p> <p><b>Chapter 25: Graphing Algebraic Equations 553</b></p> <p>Graphing on the xy-Plane 554</p> <p>Understanding the axes, the origin, and the quadrants 554</p> <p>Plotting coordinates on the xy-plane 554</p> <p>Graphing equations on the xy-plane 555</p> <p>Understanding Linear Equations 559</p> <p>Knowing the most basic linear equation 559</p> <p>Changing the slope (m) 560</p> <p>Changing the y-intercept (b) 561</p> <p>Understanding slope-intercept form 562</p> <p>Measuring the Slope of a Line 564</p> <p>Estimating slope 564</p> <p>Eyeballing slope on the xy-plane 566</p> <p>Using the two-point slope formula 569</p> <p>Graphing Linear Equations Using the Slope and y-intercept 572</p> <p>Practice Questions Answers and Explanations 574</p> <p>Whaddya Know? Chapter 25 Quiz 577</p> <p>Answers to Chapter 25 Quiz 581</p> <p>Index 583</p>

<p><b>Mark Zegarelli</b> earned degrees in mathematics and English from Rutgers University. He is the founder of SimpleStep Learning, an online educational platform that teaches courses in basic concepts in ten minutes or less, keeping students engaged and learning in every moment. Mark is also author of several other successful <i>For Dummies</i> books.</p>

<p><b>Wrap your mind around the whole numbers thing</b></p> <p><i>Basic Math & Pre-Algebra All-in-One For Dummies</i> is an absolute must-have study buddy for anyone who needs to conquer foundational math concepts such as operations, fractions, and basic statistics. This book helps to demystify the key ideas in terms you can understand. Plus, core chapters end with a little quiz, complete with the answer key, so you can track the amazing progress you’re making. (You’ll have access to more quizzes online, too!) Check out this one-stop reference and study guide and get ready — you’re about to slay basic math and pre-algebra. <p><b>FREE 1-year access to chapter quizzes online!</b> <p><b>Inside…</b> <ul><b><li>Integers and fractions</li> <li>Basic number theory, including whole and negative numbers</li> <li>Decimals and percentages</li> <li>Word problems and a first introduction to basic algebra</li> <li>Intermediate topics such as set theory and scientific notation</li></b></ul>

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