Оглавление
Mark Zegarelli. Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online)
Basic Math & Pre-Algebra All-in-One For Dummies® To view this book's Cheat Sheet, simply go to www.dummies.com and search for “Basic Math & Pre-Algebra All-in-One For Dummies Cheat Sheet” in the Search box. Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Introduction
About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here
Getting Started with Basic Math & Pre-Algebra
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
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
The Big Four Operations: Addition, Subtraction, Multiplication, and Division
Counting on Success: Numbers and Digits
TELLING THE DIFFERENCE BETWEEN 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
Rounding numbers to the nearest ten
Rounding numbers to the nearest hundred and beyond
Estimating value to make problems easier
Practice Questions Answers and Explanations
Whaddya Know? Chapter 3 Quiz
Answers to Chapter 3 Quiz
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
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
Getting a Handle on Whole Numbers
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
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
Jotting down information as word equations
Writing relationships: Turning more-complex statements into word equations
Figuring out what the problem’s asking
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
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
Divisible by 2
Divisible by 5
Divisible by 10, 100, or 1,000
Count it up: Checking divisibility by adding and subtracting digits
Divisible by 3
Divisible by 9
Divisible by 11
Less is more: Checking divisibility by subtracting
Divisible by 4
Divisible by 8
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
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
Fractions
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)
Reducing fractions the formal way
Reducing fractions the informal way
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
Changing small improper fractions to mixed numbers the quick way
Working with larger improper fractions
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
Fractions and the Big Four Operations
Multiplying and Dividing Fractions
Multiplying numerators and denominators straight across
ONE IS THE EASIEST NUMBER
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
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
Decimals and Percents
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
Understanding trailing zeros
Moving the decimal point
Performing the Big Four Operations with Decimals
Adding decimals
Subtracting decimals
Multiplying decimals
Dividing decimals
Dealing with more zeros in the dividend
Completing decimal division
Converting between Decimals and Fractions
Simple Decimal-Fraction Conversions
Changing decimals to fractions
Doing a basic decimal-to-fraction conversion
Getting mixed results
Changing fractions to decimals
The last stop: Terminating decimals
The endless ride: Repeating decimals
Practice Questions Answers and Explanations
Whaddya Know? Chapter 13 Quiz
Answers to Chapter 13 Quiz
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
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
Reaching the Summit: Advanced Pre-Algebra Topics
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
Exponents of
Exponents of , , , and so forth
Other fractional exponents
Practice Questions Answers and Explanations
Whaddya Know? Chapter 16 Quiz
Answers to Chapter 16 Quiz
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
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
Approximating short distances: 1 meter is about 1 yard (3 feet)
Estimating longer distances and speed
Approximating volume: 1 liter is about 1 quart (1/4 gallon)
Estimating weight: 1 kilogram is about 2 pounds
Estimating temperature
Converting units of measurement
Understanding conversion factors
Canceling units of measurement
Converting units
Converting between English and Metric Units
Practice Questions Answers and Explanations
Whaddya Know? Chapter 18 Quiz
Answers to Chapter 18 Quiz
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
Triangles
Quadrilaterals
Polygons on steroids — larger 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
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
THE SILVER STANDARD
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
Setting Things Up with Basic Set Theory
Understanding Sets
Elementary, my dear: Considering what’s inside sets
Cardinality of sets
Equal sets
Subsets
Empty 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
The X-Files: Introduction to Algebra
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
Solving Algebraic Equations
Understanding Algebraic Equations
Using x in equations
Choosing among four ways to solve algebraic equations
Eyeballing easy equations
Rearranging slightly harder equations
Guessing and checking equations
Applying algebra to more difficult 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
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
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
Identifying slopes of 1, 0, and –1
Distinguishing positive and negative slope
Identifying vertical lines as undefined
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. A
B
C
D
E
F
G
H
I
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
About the Author
Dedication
Author’s Acknowledgments
WILEY END USER LICENSE AGREEMENT
