Basic Math & Pre-Algebra All-in-One For Dummies

Title Page
Copyright Page
Table of Contents
Introduction
	About This Book
	Foolish Assumptions
	Icons Used in This Book
	Beyond the Book
	Where to Go from Here
Unit 1 Getting Started with Basic Math & Pre-Algebra
	Chapter 1 Playing the Numbers Game
		Inventing Numbers
		Understanding Number Sequences
			Evening the odds
			Counting by threes, fours, fives, and so on
			Getting square with square numbers
			Composing yourself with composite numbers
			Stepping out of the box with prime numbers
			Multiplying quickly with exponents
		Four Important Sets of Numbers
			Counting on the counting numbers
			Introducing integers
			Staying rational
			Getting real
	Chapter 2 The Big Four Operations
		The Big Four Operations
			Adding things up: Addition
			Take it away: Subtraction
			A sign of the times: Multiplication
			Doing math lickety-split: Division
		Applying the Big Four Operations to Larger Numbers
			Calculating stacked addition
			Performing stacked subtraction
			Calculating with stacked multiplication
			Understanding long division
Unit 2 The Big Four Operations: Addition, Subtraction, Multiplication, and Division
	Chapter 3 Counting on Success: Numbers and Digits
		Knowing Your Place Value
			Counting to ten and beyond
			Telling placeholders from leading zeros
			Reading long numbers
		Close Enough for Rock ‘n’ Roll: Rounding and Estimating
			Rounding numbers
			Estimating value to make problems easier
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 3 Quiz
		Answers to Chapter 3 Quiz
	Chapter 4 Staying Positive with Negative Numbers
		Understanding Where Negative Numbers Come From
		Sign-Switching: Understanding Negation and Absolute Value
		Addition and Subtraction with Negative Numbers
			Starting with a negative number
			Adding a negative number
			Subtracting a negative number
		Knowing Signs of the Times (and Division) for Negative Numbers
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 4 Quiz
		Answers to Chapter 4 Quiz
	Chapter 5 Putting the Big Four Operations to Work
		Switching Things Up with Inverse Operations and the Commutative Property
		Getting with the In-Group: Parentheses and the Associative Property
			Distribution to lighten the load
		Understanding Inequalities
			Doesn’t equal (≠)
			Less than (<) and greater than (>)
			Less than or equal to (≤) and greater than or equal to (≥)
			Approximately equals (≈)
		Moving Beyond the Big Four: Exponents and Square Roots
			Understanding exponents
			Discovering your roots
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 5 Quiz
		Answers to Chapter 5 Quiz
Unit 3 Getting a Handle on Whole Numbers
	Chapter 6 Please Excuse My Dear Aunt Sally: Evaluating Arithmetic Expressions with PEMDAS
		The Three E’s of Math: Equations, Expressions, and Evaluation
			Seeking equality for all: Equations
			Hey, it’s just an expression
			Evaluating the situation
			Putting the Three E’s together
		Introducing Order of Operations (PEMDAS)
			Expressions with only addition and subtraction
			Expressions with only multiplication and division
			Mixed-operator expressions
		Handling Powers Responsibly
			Prioritizing parentheses
			Pulling apart parentheses and powers
			Figuring out nested parentheses
		Bringing It All Together: The Order of Operations
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 6 Quiz
		Answers to Chapter 6 Quiz
	Chapter 7 Turning Words into Numbers: Basic Math Word Problems
		Dispelling Two Myths about Word Problems
			Word problems aren’t always hard
			Word problems are useful
		Solving Basic Word Problems
			Turning word problems into word equations
			Plugging in numbers for words
			Send in the clowns
			Our house in the middle of our street
			I hear the train a-comin’
		Solving More-Complex Word Problems
			When numbers get serious
			Too much information
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 7 Quiz
		Answers to Chapter 7 Quiz
	Chapter 8 Divisibility and Prime Numbers
		Knowing the Divisibility Tricks
			Counting everyone in: Numbers you can divide everything by
			In the end: Looking at the final digits
			Count it up: Checking divisibility by adding and subtracting digits
			Less is more: Checking divisibility by subtracting
			Cross-checking: Using multiple tests
		Identifying Prime and Composite Numbers
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 8 Quiz
		Answers to Chapter 8 Quiz
	Chapter 9 Divided Attention: Factors and Multiples
		Knowing Six Ways to Say the Same Thing
		Understanding Factors and Multiples
		Finding Fabulous Factors
			Deciding when one number is a factor of another
			Understanding factor pairs
		Generating a Number’s Factors
		Decomposing a Number into Its Prime Factors
		Finding the Greatest Common Factor
		Generating the Multiples of a Number
		Finding the Least Common Multiple
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 9 Quiz
		Answers to Chapter 9 Quiz
Unit 4 Fractions
	Chapter 10 Understanding Fractions
		Slicing a Cake into Fractions
		Knowing the Fraction Facts of Life
			Telling the numerator from the denominator
			Flipping for reciprocals
			Using ones and zeros
			Mixing things up
			Knowing proper from improper
		Increasing and Reducing Terms of Fractions
			Increasing the terms of fractions
			Reducing fractions to lowest terms (simplifying fractions)
		Converting between Improper Fractions and Mixed Numbers
			Knowing the parts of a mixed number
			Converting a mixed number to an improper fraction
			Converting an improper fraction to a mixed number
		Comparing Fractions with Cross-Multiplication
		Working with Ratios and Proportions
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 10 Quiz
		Answers to Chapter 10 Quiz
	Chapter 11 Fractions and the Big Four Operations
		Multiplying and Dividing Fractions
			Multiplying numerators and denominators straight across
			Doing a flip to divide fractions
		Adding and Subtracting Fractions with the Same Denominator
		Adding and Subtracting Fractions with Different Denominators
			The easy case: Increasing the terms of one fraction
			The difficult case: Increasing the terms of both fractions
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 11 Quiz
		Answers to Chapter 11 Quiz
	Chapter 12 Mixing Things Up with Mixed Numbers
		Multiplying and Dividing Mixed Numbers
		Adding Mixed Numbers
			Adding mixed numbers that have the same denominator
			Adding mixed numbers that have different denominators
			Adding mixed numbers with carrying
		Subtracting Mixed Numbers
			Subtracting mixed numbers that have the same denominator
			Subtracting mixed numbers that have different denominators
			Subtracting mixed numbers with borrowing
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 12 Quiz
		Answers to Chapter 12 Quiz
Unit 5 Decimals and Percents
	Chapter 13 Getting to the Point with Decimals
		Understanding Basic Decimal Stuff
			Counting dollars and decimals
			Identifying the place value of decimals
			Knowing the decimal facts of life
		Performing the Big Four Operations with Decimals
			Adding decimals
			Subtracting decimals
			Multiplying decimals
			Dividing decimals
		Converting between Decimals and Fractions
		Simple Decimal-Fraction Conversions
			Changing decimals to fractions
			Changing fractions to decimals
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 13 Quiz
		Answers to Chapter 13 Quiz
	Chapter 14 Playing the Percentages
		Making Sense of Percentages
		Dealing with Percentages Greater than 100%
		Converting to and from Percentages, Decimals, and Fractions
		Converting Percentages to Decimals
		Changing Decimals to Percentages
		Switching from Percentages to Fractions
		Converting Fractions to Percentages
		Solving Percentage Problems
			Figuring out simple percent problems
			Turning the problem around
			Deciphering more-difficult percent problems
		Putting All the Percent Problems Together
			Identifying the three types of percent problems
		Solving Percent Problems with Equations
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 14 Quiz
		Answers to Chapter 14 Quiz
	Chapter 15 Word Problems with Fractions, Decimals, and Percentages
		Adding and Subtracting Parts of the Whole in Word Problems
			Sharing a pizza: Fractions
			Buying by the pound: Decimals
			Splitting the vote: Percentages
		Problems about Multiplying Fractions
			Renegade grocery shopping: Buying less than they tell you to
			Easy as pie: Working out what’s left on your plate
		Multiplying Decimals and Percentages in Word Problems
			To the end: Figuring out how much money is left
			Finding out how much you started with
		Handling Percent Increases and Decreases in Word Problems
			Raking in the dough: Finding salary increases
			Earning interest on top of interest
			Getting a deal: Calculating discounts
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 15 Quiz
		Answers to Chapter 15 Quiz
Unit 6 Reaching the Summit: Advanced Pre-Algebra Topics
	Chapter 16 Powers and Roots
		Memorizing Powers and Roots
			Remembering square numbers and square roots
			Keeping track of cubic numbers and cube roots
			Knowing a few powers of 2 and their related roots
		Changing the Base
			Negating a number raised to an exponent
			Finding powers of negative numbers
			Finding powers of fractions
			Mixing negative numbers and fractions with exponents
		Exponents of 0 and Negative Numbers
			Exponents of 0
			Negative exponents
		Fractional Exponents
			Exponents of 1/2
			Exponents of 1/3
			Exponents of 1/4,1/5,1/6
, and so forth
			Other fractional exponents
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 16 Quiz
		Answers to Chapter 16 Quiz
	Chapter 17 A Perfect Ten: Condensing Numbers with Scientific Notation
		First Things First: Using Powers of Ten as Exponents
			Counting zeros and writing exponents
		Exponential Arithmetic: Multiplying and Dividing Powers of Ten
		Working with Scientific Notation
			Writing in scientific notation
			Understanding order of magnitude
			Multiplying with scientific notation
		Dividing with Scientific Notation
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 17 Quiz
		Answers to Chapter 17 Quiz
	Chapter 18 How Much Have You Got? Weights and Measures
		Understanding Units
			Adding and subtracting units
			Multiplying and dividing units
		Examining Differences between the English and Metric Systems
			Looking at the English system
			Looking at the metric system
		Estimating and Converting between the English and Metric Systems
			Estimating in the metric system
			Converting units of measurement
		Converting between English and Metric Units
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 18 Quiz
		Answers to Chapter 18 Quiz
	Chapter 19 Getting the Picture with Geometry
		Getting on the Plane: Points, Lines, Angles, and Shapes
			Making some points
			Knowing your lines
			Figuring the angles
			Shaping things up
		Getting in Shape: Polygon (and Non-Polygon) Basics
		Closed Encounters: Shaping Up Your Understanding of 2-D Shapes
			Polygons
			Circles
		Squaring Off with Quadrilaterals
		Making a Triple Play with Triangles
		Getting Around with Circle Measurements
		Taking a Trip to Another Dimension: Solid Geometry
			The many faces of polyhedrons
			3-D shapes with curves
		Building Solid Measurement Skills
		Solving Geometry Word Problems
			Working from words and images
			Breaking out those sketching skills
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 19 Quiz
		Answers to Chapter 19 Quiz
	Chapter 20 Figuring Your Chances: Statistics and Probability
		Gathering Data Mathematically: Basic Statistics
			Understanding differences between qualitative and quantitative data
			Working with qualitative data
				Playing the percentages
				Getting into the mode
			Working with quantitative data
				Finding the mean
				Finding the median
		Looking at Likelihoods: Basic Probability
			Figuring the probability
			Oh, the possibilities! Counting outcomes with multiple coins
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 20 Quiz
		Answers to Chapter 20 Quiz
	Chapter 21 Setting Things Up with Basic Set Theory
		Understanding Sets
			Elementary, my dear: Considering what’s inside sets
			Sets of numbers
		Performing Operations on Sets
			Union: Combined elements
			Intersection: Elements in common
			Relative complement: Subtraction (sorta)
			Complement: Feeling left out
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 21 Quiz
		Answers to Chapter 21 Quiz
Unit 7 The X-Files: Introduction to Algebra
	Chapter 22 Working with Algebraic Expressions
		Seeing How X Marks the Spot
		Expressing Yourself with Algebraic Expressions
		Evaluating Algebraic Expressions
		Knowing the Terms
			Making the commute: Rearranging your terms
			Identifying the coefficient and variable
		Adding and Subtracting Like Terms
			Identifying like terms
			Adding and subtracting terms
		Multiplying and Dividing Terms
		Simplifying Expressions by Combining Like Terms
		Removing Parentheses from an Algebraic Expression
			Drop everything: Parentheses with a plus sign
			Sign turnabout: Parentheses with a negative sign
			Distribution: Parentheses with no sign
		FOILing: Dealing with Two Sets of Parentheses
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 22 Quiz
		Answers to Chapter 22 Quiz
	Chapter 23 Solving Algebraic Equations
		Understanding Algebraic Equations
			Using x in equations
			Choosing among four ways to solve algebraic equations
		The Balancing Act: Solving for x
			Striking a balance
			Using the balance scale to isolate x
		Rearranging Equations and Isolating x
			Rearranging terms on one side of an equation
			Moving terms to the other side of the equals sign
			Removing parentheses from equations
			Cross-multiplying
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 23 Quiz
		Answers to Chapter 23 Quiz
	Chapter 24 Tackling Algebra Word Problems
		Solving Algebra Word Problems in Five Steps
			Declaring a variable
			Setting up the equation
			Solving the equation
			Answering the question
			Checking your work
		Choosing Your Variable Wisely
		Solving More-Complex Algebraic Problems
			Charting four people
			Crossing the finish line with five people
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 24 Quiz
		Answers to Chapter 24 Quiz
	Chapter 25 Graphing Algebraic Equations
		Graphing on the xy-Plane
			Understanding the axes, the origin, and the quadrants
			Plotting coordinates on the xy-plane
			Graphing equations on the xy-plane
		Understanding Linear Equations
			Knowing the most basic linear equation
			Changing the slope (m)
			Changing the y-intercept (b)
			Understanding slope-intercept form
		Measuring the Slope of a Line
			Estimating slope
			Eyeballing slope on the xy-plane
			Using the two-point slope formula
		Graphing Linear Equations Using the Slope and y-intercept
		Practice Questions Answers and Explanations
		Whaddya Know? Chapter 25 Quiz
		Answers to Chapter 25 Quiz
Index
EULA