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Basic Maths For Dummies®

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Table of Contents

Introduction
About This Book
Conventions Used in This Book
What You’re Not to Read
Foolish Assumptions
How This Book Is Organised
Part I: Whole Numbers: The Building Blocks of Maths
Part II: Parts of the Whole
Part III: Sizing Up Weights, Shapes and Measures
Part IV: Statistically Speaking
Part V: The Part of Tens
Icons Used in This Book
Where to Go from Here
Part I: Whole Numbers: The Building Blocks of Maths
Chapter 1: Getting Started
You’re Already Good at Maths
Your First Homework Assignment
Talking Yourself Up
Whole Numbers: Party Time!
Parts of the Whole: Fractions, Decimals, Percentages and More
Mmmm, pizza! Everyday fractions
Percentages are easier than you think: Introducing the Table of Joy
Sizing Up Time, Weights, Measures and Shapes
Weights and measures you already know
Getting yourself into shape
Statistically Speaking
Why bother with charts and tables?
The man in the middle: Describing data
What are the chances?
The Tools You Need
Chapter 2: Setting Yourself Up for Success
Getting Properly Equipped
Tools of the trade
A space of your own
Discovering where you work best
Making your workspace better for studying
Staying Motivated
Remembering why you’re studying
Using the ‘calendar of crosses’
Rewarding yourself
Getting Your Head On Straight
Sitting up straight
Getting a breath of fresh air
Talking to yourself – not as crazy as it sounds
Learning from your mistakes
Keeping Good Notes
Deciding on a notebook or a computer
Recording the language of maths
Acing the Exam
Chapter 3: It All Adds Up: Addition and Subtraction
Nailing Down the Number Line
Adding and taking away with the number line
Adding and subtracting with two rulers
Understanding Odd and Even Numbers
Remembering Some Simple Sums
Meeting the adding table
Increasing your success with flash cards
What to do when you forget
Super-Size Me: Working with Bigger Numbers
Adding and taking away bigger numbers
Following recipes for adding and subtracting
Going Backwards with Negative Numbers
Chapter 4: Equal Piles: Multiplying and Dividing
Meeting the Basics of Multiplication and Division
Remembering Your Times Tables
Practising your times tables
Working around mind blanks
Working backwards
Multiplying Bigger Numbers
Multiplying a big number by a small number
Multiplying two big numbers
One for You, One for Me: Handling Division
Dividing and conquering
Taking one step at a time
Dealing with the left overs: Remainders
Working with bigger numbers
Figuring Out Formulas
Wait, those aren’t numbers! Looking out for letters
Missing out the multiply
Doing the sums in the right order
Working out a formula
Chapter 5: Are We Nearly There Yet? Rounding and Estimating
What’s Nearest?
A walk between two towns
Rounding on a ruler
Tie-breaks: What to do when you’re midway
A common misconception
Dealing with Decimal Places
Rounding to the nearest penny
The nearest 10p, and the nearest tenth
The nearest pound, the nearest ten pounds and so on
That’s About Right: Estimating Answers
Rough and ready: Rounding to the first digit
Checking your answers
Part II: Parts of the Whole
Chapter 6: Cake or Death: Fractions without Fear
Familiar Fractions
No half-measures
Time to split
Sizing Up Fractions
The bottom of the fraction: How big is your slice?
The top: How many slices?
The number in front
Cancel That!
Fractions in disguise
Making cancellation easy
Doing Sums with Fractions
Writing a number as a fraction of another
The same size of slice: Adding and taking away fractions
Calculating fractions of a number
Comparing fractions
Fathoming Fractions on Your Calculator
Using the fraction button
Doing fractions with decimals
A recurring theme
Chapter 7: What’s the Point? Dealing with Decimals
A Dot You Know: Decimals and Money
Looking before and after the dot
Missing off the last zero
A Whole Lot of Nothing: Place Values and Why They Matter
Hundreds, tens and units: Looking left of the decimal point
Tenths, hundredths and smaller: Roaming right of the decimal point
Zeroing in on zeros
Linking Decimals to Fractions
Converting decimals to fractions
Converting fractions to decimals
Remembering some common fractions and decimals
Doing Sums with Decimals
Dealing with the dot
Multiplying and dividing with decimals
Flipping into fractions, and vice versa
Doing decimals with a calculator
Chapter 8: It’s All Relative: Ratios and Proportions
Meeting the Table of Joy
Introducing the Table of Joy
Seeing how the Table of Joy works
Understanding what goes where
Getting Rational: Understanding Ratios
One for you, two for me: Sharing
Cancelling ratios
Applying the Table of Joy
Working with parts
Managing multiple ratios
Getting a Sense of Proportion
Defining proportion
Perfecting proportions with the Table of Joy
Applying proportion
Scaling recipes
Chapter 9: Perfect Percentages, 100% of the Time
Perusing Some Percentages You Already Know
Comparing Percentages, Decimals and Fractions
Percentages and decimals
Percentages and fractions
Working Out Percentages the Traditional Way
Percentages as hundredths
Percentages of the whole
Going up and going down
Working Out Percentages Using the Table of Joy
Finding a percentage of the whole
Going up and going down
Playing the Percentages
Tax needn’t be taxing
A keen interest
Changing prices
Part III: Sizing Up Weights, Shapes and Measures
Chapter 10: Clocking Time
Understanding the Vocabulary of Time
Fractions in time
Different date formats
Comparing the 12-hour and 24-hour clocks
Catching the Bus: Seeing How Timetables Work
Doing Sums with Time
When does something start?
When does something end?
How long does something take?
Speeding Along
Chapter 11: Working with Cold, Hard Cash
Seeing What You Already Know
Counting coins and notes
Exploring examples of money sums
Running the Numbers
Adding and subtracting money
Multiplying and dividing money
Rounding money numbers
Using Euros, Dollars and Other Currencies
Exploring exchange rates
Converting currency with the Table of Joy
Managing More Complicated Money Sums
Dealing with deposits and payment plans
Calculating commission
Sussing out sales prices
Choosing the right sum
Chapter 12: Taking the Weight Off Your Shoulders
Appreciating What You Already Know
Using digital scales
Using analogue scales
Using a balance
Measuring Weight
The metric system: Grams, kilograms and tonnes
The imperial system: Ounces, pounds and stones
Converting Weights
Using a table
Using a graph or a chart
Using a conversion factor
Weighing in Cookery
Buying by weight
Comparing value
Cooking by weight
Chapter 13: Feeling the Heat
Understanding Temperature
Fathoming Fahrenheit and Celsius
Using a formula
Using a table or a scale
Thinking about Thermometers
Looking at Everyday Temperatures
Get cooking!
Whatever the weather
Sploosh!
Fever!
Nailing Negative Temperatures
Ordering negative temperatures
Finding the difference between negative temperatures
Chapter 14: That’s About the Size of It
How Big Is That Suitcase?
Checking in: Dimensions of luggage
Sizing up the vocabulary you need
Meeting Some Common Measuring Tools
Reading a ruler
Minding the marks
Using Different Units of Length
Looking at Length, Distance and Perimeter
How long is a piece of string?
How many miles to Babylon?
Going all the way round
Summing up distance
Accessing All Areas
Recognising rectangles
Joining things up: Compound rectangles
Using formulas
Verifying Volume and Capacity
Reading Maps and Plans
Scales and distance
The best-laid plans
Chapter 15: Shaping Up
You’re Already in Good Shape
Sussing out shapes you know
Expanding your shapely vocabulary
What’s Your Angle?
Defining angles
Measuring angles
Playing with Symmetry
On reflection: Turning shapes over
Doing the twist: Rotating shapes
Pretty patterns: Tessellation
Understanding Nets, Plans and Elevations, Oh My!
Folding under pressure: Nets
Looking at every angle: Plans and elevations
Part IV: Statistically Speaking
Chapter 16: Data Mining (No Hard Hat Required)
A Spotter’s Guide to Graphs and Charts
Nailing number tables
Bringing in the bar charts
Poking about in pie charts
Looking at line graphs
Reading Graphs, Tables and Charts
Picking the right data from a table
Keeping up with keys and axes
Understanding graphs
Drilling Deeper into Graphs
Adding up totals and finding differences
Summarising graphs
Catching errors
Chapter 17: Top of the Charts
Turning the Tables
Making your own tables
Looking at a real-life table
Tallying up
Watching out for problems
Grappling with Graphs
Picking the right graph
Labelling and titling your graphs
Ordering at the bar chart
Cooking up a pie chart
Forming an orderly line graph
Drawing Graphs on the Computer
Building virtual bar charts
Creating virtual pie charts
Drawing virtual line graphs
Messing around with computer graphs
Chapter 18: Average Joe
Starting Out with Statistics
Meeting the Three Types of Average
A group of people: Who’s the most average?
The man in the middle: The median
Terribly common, darling: The mode
A mean, mean man
Home on the Range
Calculating range
Pulling range out of a graph
Chapter 19: What Are the Chances?
Probability as a Number
Considering certainty and impossibility
Tossing a coin
One in . . . whatever
Looking at the other side of the coin
Dealing cards
Practising probability with the number line
Experimenting and Estimating
Dice, cards and spinners
How many times . . . ?
Putting Many Things Together
Probability trees
Probability tables
Probability squares
Independence Day
You can’t have it both ways: Either/or events
Doing several things at once: Both or all events
Part V: The Part of Tens
Chapter 20: Ten Ways to Prepare Yourself Before You Start Studying
Talking Yourself Up
Sitting Up Straight
Breathing like a Rock Star
Putting Out the Welcome Mat
Making Mistakes
Working with Your Limits
Turning Studying into a Habit
Staying Fed and Watered
Getting Your Blood Flowing
Warming Up Gently
Chapter 21: Ten Tricks for Remembering Your Number Facts
Playing Games
Flashing Cards
Sticking Stickies
Counting on Your Fingers
Tricking out the Nines
Tricking Out the Other Big Numbers
Tricks of six
Straight to eight
What about seven?
Five alive!
Breaking Down and Building Up
Eight: halving over and over
Surprised by six
Nailing nine
Finally fives
Learning from Your Mistakes
Working from What You Know
Training Yourself with Treats
Chapter 22: Ten Pitfalls to Avoid
Taking Care with Your Calculator
You’re Out of Line!
Making Sure Your Answer Makes Sense
Distinguishing ‘More Than’ and ‘At Least’
Reading the Question
Fathoming the Phantom Forty Minutes
Getting the Wrong Percentage
Rounding Too Early
Mixing Up the Mean, Mode and Median
Forgetting to Convert
Chapter 23: Ten Ways to Make Any Exam Easier
Know What You’re Up Against
Practise the Hard Parts
Remember the Basics
Use the Final Few Minutes before Your Exam
Don’t Exhaust Yourself
Think Positive, or ‘I’ll Show Me!’
Have a Ritual
Manage Your Time
Guess If You Need To
Cheat Sheet

Basic Maths For Dummies®

by Colin Beveridge

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About the Author

Colin Beveridge is a maths confidence coach for Flying Colours Maths and co-author of the Little Algebra Book.

He holds a PhD in Mathematics from the University of St Andrews and worked for several years on NASA’s Living With A Star project at Montana State University, where he came up with an equation which is named after him. It’s used to help save the world from being destroyed by solar flares. So far so good.

He became tired of the glamour of academia and returned to the UK to concentrate on helping students come to terms with maths and show that not all mathematicians are boring nerds; some are exciting, relatively well-adjusted nerds.

Colin lives in Poole, Dorset with an espresso pot, several guitars and nothing to prove. Feel free to visit his website at www.flyingcoloursmaths.co.uk or follow him on Twitter at www.twitter.com/icecolbeveridge.

Author’s Acknowledgments

I’m very grateful to the team at Dummies Towers for their work and guidance in making this book awesome – particularly my editors Rachael Chilvers and Mike Baker.

The writing was largely fuelled by the Little Red Roaster coffee shop in Parkstone, and inspired by the students who helped me develop the ideas and make them simple enough to understand – extra-special thanks to Tain Duncan, Ethan Oak and Dale Bannister. LaVonne Ellis, Lisa Valuyskaya and Ryah Albatros from Customer Love all went above and beyond in getting me to just write the blasted thing.

It wouldn’t have been written at all without the work my brother Stuart and his colleagues at The Chase did on the Little Algebra Book, or the unfaltering support of my parents – Ken Beveridge and Linda Hendren – and the tireless encouragement of Melissa Day.

Dedication

For the teachers who taught me most of what I know: Brian Rodrigues, DJ Rowley, Dana Longcope and Naomi Dunford.

And for the students who taught me most of the rest.

Publisher’s Acknowledgements

We’re proud of this book; please send us your comments through our Dummies online registration form located at www.dummies.com/register/.

Some of the people who helped bring this book to market include the following:

Commissioning, Editorial, and Media Development

Project Editor: Rachael Chilvers

Commissioning Editor: Mike Baker

Assistant Editor: Ben Kemble

Development Editor: Colette Holden

Technical Editors: Samuel Harrison, Vincent Kwasnica

Proofreader: Jamie Brind

Production Manager: Daniel Mersey

Publisher: David Palmer

Cover Photo: © Shutterstock / Robert Spriggs

Cartoons: Ed McLachlan

Composition Services

Project Coordinator: Kristie Rees

Layout and Graphics: Corrie Socolovitch, Christin Swinford

Proofreader: Lauren Mandelbaum

Indexer: Becky Hornyak

Introduction

Hi! I’m Colin, and I want to change the world.

I live in a world where, when I say ‘I’m a maths tutor,’ people say to me ‘Oh, maths . . . I was never any good at that,’ or ‘I haven’t used maths since I left school.’

I live in a world where I have to bite my tongue rather than say ‘I don’t mind that you think maths is hard, but I am saddened that you’re proud of this,’ or ‘Are you sure about that? I bet you used maths six times before breakfast this morning.’

I want to live in a world where everyone is okay at maths. Not a world full of Einsteins, not a world full of geeks – just a world where having a solid level of maths is as natural to everyone as having a solid level of reading and talking.

This book is part of my vision – and I’m delighted that you’ve picked it up. You’ve taken the first step to being a bigger part of my ideal world, and I want to do everything I can to help you become as good at maths as you want to be.

I want to show you that maths makes sense, most of the time, and that you use maths countless times a day, often when you don’t even realise it. I want to show you that after you break problems down into smaller steps, those problems are so much more doable. I want to help you stop feeling stupid or afraid or troubled by maths. I know you aren’t stupid: you just haven’t got the hang of maths yet.

Most of all, I want to hear how you get on. The best way to catch me is on twitter (@icecolbeveridge) – I can’t promise I’ll get back to you straight away, but I promise I’ll read and reply if I possibly can.

About This Book

In this book, I try to help you understand not only how to do the maths you need, but why you do the maths in a certain way. I show you maths isn’t some mystical language of squiggles but instead is a concise and efficient way to communicate. One of the nice things about maths is that it changes very little from country to country. I studied maths in France for a year and was surprised that most of the words, even in the ridiculously advanced maths they thought I could do, were either basic French vocab or very similar to the English words. The sums were exactly the same. (I still couldn’t do them, but that’s a different story.)

Now, I’m pretty good at maths. I’ve been a full-time maths tutor since 2008. Before that I worked on a NASA project in the USA. I have an equation named after me. I know my stuff.

But – and this is a big ‘but’ – I know that being a good mathematician isn’t the same as being a good maths teacher. I’m lucky to have worked with enough people at the stage you are now – smart and interested, but needing help to understand – that I can break down maths into smaller, simpler parts that I hope you’ll understand.

Among other things, I cover the following in this book:

check.png Keeping calm instead of stressing about maths.

check.png Solving regular arithmetic problems – adding and taking away, multiplying and dividing.

check.png Rounding off and estimating your answers.

check.png Dealing with decimals, fractions, percentages and ratios.

check.png Messing about with measures of time, money, weight and temperature.

check.png Understanding shapes – how you measure them and how you move them around.

check.png Grappling with graphs – both reading and drawing.

check.png Summing up statistics, including averages and probabilities.

How could that not be fun?

This book is based on the UK Adult Numeracy Core Curriculum, from Entry Level 3 through to Level 2. Whether or not a Level 2 numeracy qualification is equivalent to an A–C pass at GCSE is a murky area I don’t want to muddy further, but I reckon they’re roughly the same level in difficulty, although the numeracy curriculum covers slightly fewer topics.

So, that means this book may help you do pretty well at GCSE level but won’t cover all of the topics involved – particularly algebra, which this book barely touches. If you read this book cover to cover and understand everything, you should ace any UK Adult Numeracy test thrown at you. Although I’ve based this book on the core curriculum, I sometimes dip into topics in a little more detail than needed. I also cover a few areas from a slightly earlier level in the curriculum if I reckon you may find the particular subject hard.

Whether you’re studying for a numeracy qualification or a GCSE, or just want to brush up on your basic maths skills, this book has what you need. Best of all, the book follows the For Dummies format. Divided into easy-to-follow parts, the book serves as both your reference and your troubleshooting guide.

Conventions Used in This Book

I keep the conventions to a minimum in this book. Here are the ones I use:

check.png I use italics for emphasis or to highlight new words or phrases.

check.png Boldfaced text indicates key words in bulleted lists or the key steps of action lists.

check.png Monotype font is used for internet and email addresses.

What You’re Not to Read

This book is designed to be an easy-access reference guide to basic maths. I cover each subject in its entirety in individual chapters, and the information doesn’t depend on what comes before or after. This means you can jump around the book to the subjects you want to focus on and skip those you feel comfortable with already or just aren’t interested in.

If you feel like you’re starting from scratch, I strongly recommend you peruse the whole book to get a solid idea of all that’s involved. If you already have a decent maths background, you probably want to focus on the areas you find are relatively weak for you – but you may also find some of the insights in other areas help to shore up your maths skills.

No matter what your background, you can skip paragraphs marked with the Technical Stuff icon without giving up an understanding of the primary subject. Also, sidebars supplement the primary text – you can skip them without missing the main point.

Foolish Assumptions

Making assumptions is always a risky business, but knowing where I’m coming from may put you at ease. So, in writing this book, I assume that:

check.png You know how to count and are familiar with the symbols for the numbers.

check.png You understand the idea of money and changing a banknote for an equivalent value of coins.

check.png You know what some basic shapes look like.

check.png You’re prepared to think fairly hard about maths and want either to pass a numeracy qualification or to simply brush up on your maths skills.

How This Book Is Organised

Like all For Dummies books, Basic Maths For Dummies is a reference and each topic is allotted its own part in the book. Within each part are individual chapters relating specifically to the topic in question.

Part I: Whole Numbers: The Building Blocks of Maths

If you want to be good at maths – and I presume you do, otherwise you’d have picked up a different book – being able to do three things really well is helpful:

check.png Stay calm: Maths can be hard enough when your mind isn’t complaining about how impossible it is and trying to sabotage your efforts. I give you tips on how to keep that under control and set yourself up for success.

check.png Do sums on paper: As a mathematician, I think this is the least important of the three for being good at maths. Unfortunately, the people who write exams disagree with me, so I walk you carefully through methods for adding, taking away, multiplying and dividing, and I try to show you why the sums work.

check.png Work out rough answers: Being able to give a ballpark answer quickly is far more important to me than being able to work out a huge long-division sum. I show you how to work out a rough answer without giving yourself a headache.

Part II: Parts of the Whole

Stand back, everybody – I’m going to use the F-word. A word some people would like to see banned from books in public libraries and never have to hear on the TV. That’s right, I’m talking about fractions. Gasp! I can’t believe he wrote that!

I’m here to tell you that there’s nothing dirty about fractions, even improper ones. There’s a lot of misinformation out there about fractions, and some teachers find talking about fractions very difficult without getting embarrassed. But don’t worry – in Part II I try to answer all of your questions about fractions in a frank and easy-to-understand manner. I also cover their close friends, decimals, percentages, ratios and proportion, which are all versions of the same thing.

I also introduce you to the Table of Joy – an easy way to work with percentages, ratios and literally dozens of other topics. I use this table throughout the book. In fact, the Table of Joy is probably the most useful thing I know.

Part III: Sizing Up Weights, Shapes and Measures

The third part of this book is about applying your maths knowledge to real-life things – generally things that you measure.

Some of these concepts are perfectly familiar – you’ve probably worked with time and money since you were old enough to throw a Monopoly board across the room. However, there are places you need to be careful – and this book gives you a few extra tips and tricks to pick up in those areas.

Some of the measuring concepts are a bit trickier. I look at the different ways to measure weight and temperature and show you some of their many applications.

I also look at size and shapes – again, there are different ways of measuring these and many facets of shape to play with.

Part IV: Statistically Speaking

Statistics has a reputation for being boring and difficult. For a long while, I bought into that story too – but then I started using statistics and applying it to something I cared about. Suddenly, I was drawing graphs that helped me understand my project, working out statistics that told me what was going on and making predictions based on probabilities . . . and I was hooked.

I can’t promise you’ll find statistics as exciting as I do, but I do my best to make the topic interesting. I cover the ins and outs and ups and downs of graphs and tables, how to interpret them and how to draw them; I look at averages; and I dip a toe into the murky and controversial world of probability.

Part V: The Part of Tens

All For Dummies books finish with The Part of Tens, a bunch of lists full of practical tips to help you manage the material in the rest of the book.

I run you through ways of calming down and some ideas for remembering your number facts. I show you some of the booby-trap questions examiners may set, and I offer some exam-technique tips so you can get in there and ace it. Good luck!

Icons Used in This Book

Here are the icons I use to draw your attention to particularly noteworthy paragraphs:

tip.eps Theories are fine, but anything marked with a Tip icon in this book tells you something practical to help you get to the right answer. These are the tricks of the mathematical trade.

remember.eps Paragraphs marked with the Remember icon contain the key takeaways from the book and the essence of each subject.

warning_bomb.eps The Warning icon highlights errors and mistakes that can cost you marks or your sanity, or both.

technicalstuff.eps You can skip anything marked with the Technical Stuff icon without missing out on the main message, but you may find the information useful for a deeper understanding of the subject.

Where to Go from Here

This book is set up so you can jump right into the topics that interest you. If you feel like an absolute beginner in maths, I recommend you read Parts I and II to build a foundation for the other topics. If you’re pretty comfortable with the mechanics of maths, use the table of contents and index to find the subject you have questions about right now. This book is a reference – keep it with your maths kit and turn to it whenever you have a question about maths.

Part I

Whole Numbers: The Building Blocks of Maths

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In this part . . .

If you can count, you can do maths.

It’s helpful to build up shortcuts to make maths easier, though – and that’s what this part is all about: making maths easier. I show you how to stay calm and focused (and shut up the little voices telling you you can’t do maths) and then help you figure out how to add, take away, multiply and divide whole numbers – the sums all of the others are based on.

You need to be able to see if your answer looks right: to do that, you need to be able to round off and to estimate so that you don’t say something daft like ‘The Eiffel Tower is four centimetres tall’.