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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Learn to:
- Master maths with more than 2,000 practice questions
- Add, subtract, multiply and divide with confidence
- Work with decimals, fractions and percentages
- Size up weights and measures
Fun, friendly coaching and all the practice you need to tackle maths problems with confidence and ease
In his popular Basic Maths For Dummies, professional maths tutor Colin Beveridge proved that he could turn anyone even the most maths-phobic person into a natural-born number cruncher. In this book he supplies more of his unique brand of maths-made-easy coaching, plus 2,000 practice problems to help you master what you learn. Whether you're prepping for a numeracy test or an employability exam, thinking of returning to school, or you'd just like to be one of those know-it-alls who says, 'Oh, that's easy!' about any maths problem that comes your way, this book is for you.
- Master basic arithmetic, fast in no time, solving addition, subtraction, multiplication and division problems will seem as easy as tying your shoes
- Face down fractions you'll never again feel shy around fractions, decimals, percentages and ratios
- Juggle weights and measures like a pro whether it's a question of how much it weighs, how long (or far) it is, or how much it costs, you'll never be at a loss for an answer
- Make shapes your playthings circles, squares, triangles and rectangles you'll measure them, draw them and manipulate them with ease
Open the book and find:
- 2,000 pencil-and-paper practice problems
- The keys to mastering addition, subtraction, multiplication and division
- The lowdown on fractions, decimals and percentages
- Basic geometry made easy
- How to handle weights, measures and money problems
- How to read charts, tables and graphs at a glance
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Seitenzahl: 409
Veröffentlichungsjahr: 2012
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Basic Maths Practice Problems For Dummies®
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Table of Contents
Basic Maths Practice Problems For Dummies®
by Colin Beveridge
Basic Maths Practice Problems For Dummies®
Published by John Wiley & Sons, LtdThe Atrium Southern Gate Chichester West Sussex PO19 8SQ England www.wiley.com
Copyright © 2012 John Wiley & Sons, Ltd, Chichester, West Sussex, England
Published by John Wiley & Sons, Ltd, Chichester, West Sussex
All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, Saffron House, 6-10 Kirby Street, London EC1N 8TS, UK, without the permission in writing of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, England, or emailed to [email protected], or faxed to (44) 1243 770620.
Trademarks: Wiley, the Wiley logo, For Dummies, the Dummies Man logo, A Reference for the Rest of Us!, The Dummies Way, Dummies Daily, The Fun and Easy Way, Dummies.com, Making Everything Easier, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc., and/or its affiliates in the United States and other countries, and may not be used without written permission. All other trademarks are the property of their respective owners. John Wiley & Sons, Inc., is not associated with any product or vendor mentioned in this book.
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British Library Cataloguing in Publication Data: A catalogue record for this book is available from the British Library
ISBN 978-1-118-35162-8 (pbk); ISBN 978-1-118-35161-1 (ebk); ISBN 978-1-118-35159-8 (ebk); ISBN 978-1-118-35158-1 (ebk)
Printed and bound in Great Britain by TJ International, Padstow.
10 9 8 7 6 5 4 3 2 1
About the Author
Colin Beveridge is a maths confidence coach for Flying Colours Maths, author of Basic Maths For Dummies and Numeracy Tests For Dummies 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.
Dedication
In memory of my grandmother, Pat Knight, who taught me to be proud of being good with numbers.
Author’s Acknowledgments
I’m grateful, as always, to the team at Dummies Tower for knocking my book into shape - particularly my editors Simon Bell, Kate O’Leary and Mike Baker, and my technical editors Giles Webberley and Alix Godfrey.
Thanks again to the Little Red Roaster in Parkstone for keeping me supplied with coffee and encouragement, and the students who helped me crystallise the ideas, especially Rebecca Murray and Jasmine Cooper.
And, of course, I thank my parents, who brought me up to say ‘thank you’ – Ken Beveridge and Linda Hendren.
Publisher’s Acknowledgments
We’re proud of this book; please send us your comments at http://dummies.custhelp.com. For other comments, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002.
Some of the people who helped bring this book to market include the following:
Acquisitions, Editorial, and Vertical Websites
Project Editor: Simon Bell
Commissioning Editor: Mike Baker
Assistant Editor: Ben Kemble
Development Editor: Kate O’Leary
Copy Editor: Kate O’Leary
Technical Editors: Giles Webberley, Alix Godfrey
Proofreader: Mary White
Production Manager: Daniel Mersey
Publisher: David Palmer
Cover Photos: © Shutterstock/ Robert Spriggs
Cartoons: Ed McLachlan
Composition Services
Project Coordinator: Kristie Rees
Layout and Graphics: Carl Byers, Carrie A. Cesavice, Corrie Niehaus, Christin Swinford
Proofreader: Lindsay Amones
Indexer: Potomac Indexing, LLC
Publishing and Editorial for Consumer Dummies
Kathleen Nebenhaus, Vice President and Executive Publisher
Kristin Ferguson-Wagstaffe, Product Development Director
Ensley Eikenburg, Associate Publisher, Travel
Kelly Regan, Editorial Director, Travel
Publishing for Technology Dummies
Andy Cummings, Vice President and Publisher
Composition Services
Debbie Stailey, Director of Composition Services
Introduction
Hi! I’m Colin, and I want you to rock at maths.
I want you to have the skills you need to get the job you’re going for or to qualify for a course or to help your kids with their homework. I want you to be able to say things like ‘I use maths all the time . . . it’s not that hard’ or ‘I’m pretty good at fractions’. And I want you to have the confidence to look at a sum the same way you look at a Sudoku or crossword puzzle: anticipating the pleasure of solving a problem.
You don’t have to wear inch-thick glasses and a tweed jacket to do well enough at maths – and you don’t need to have done well at school, either. Like anything else you want to master, you just have to approach the task with a positive attitude, a fair amount of stubbornness and detailed instructions. The first two are down to you; the third you’ll find in this book!
I’m always keen to hear how you get on. The best way to reach me is via Twitter (@icecolbeveridge). I promise I’ll read your comments and get back to you if I possibly can.
About This Book
This book is designed to help you get on top of the maths you need for the national numeracy curriculum at Entry Level 3, Level 1 and Level 2. It may help you prepare for a GCSE at foundation level as well, although several GCSE topics (notably algebra) aren’t covered in this book at all.
This book is a companion to Basic Maths For Dummies (also written by me), which explains things in a bit more detail but doesn’t contain practice questions.
I show you how to do the kinds of questions you’re likely to come across in real life and in numeracy tests, particularly:
Solving regular arithmetic problems – multiplying, dividing, adding and taking away.
Rounding and estimating to get rough answers (or to check that your accurate answers make sense).
Dealing with decimals, fractions and ratios.
Messing about with measures of time, weight, temperature and money.
Understanding shapes – measuring them, drawing them and moving them around.
Grappling with graphs – how to read them and spot when someone’s pulling the wool over your eyes.
Summing up statistics, including averages and probabilities.
You have a lot to cover! But much of it is common sense, and if you can get past the – mistaken – idea that maths is really hard, you might even start to like it.
Conventions Used in This Book
I keep the conventions used in this book to a minimum! Here are the ones I use:
I use italics for emphasis or to highlight new words and phrases.
I use boldface for key words in bulleted lists or key steps in action lists.
I use monotype font 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 an overview of all the subjects I cover. If you already have a decent maths background, you probably want to focus on the areas you still find challenging – 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 foregoing an understanding of the primary subject. Sidebars likewise supplement the primary text – so 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:
You know how to count and are familiar with the symbols for the numbers.
You understand the idea of money and changing a banknote for an equivalent value of coins.
You know what some basic shapes look like.
You’re prepared to think fairly hard about maths and want either to pass a numeracy examination or to simply brush up on your maths skills.
How This Book Is Organised
Like all For Dummies books, Basic Maths Practice Problems For Dummies is a reference book and each topic is allotted its own part in it. Within each part are individual chapters relating specifically to the topic in question.
Part I: The Building Blocks of Maths
The first part of this book gives you the tools you need to get started with maths – if you can do basic arithmetic with whole numbers, it makes the rest of the book a lot easier! In this part, I show you how to:
Add and take away whole numbers
Multiply and divide whole numbers
Estimate and round off approximate answers
Part II: Working with 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!
I’m here to tell you that there’s nothing dirty about fractions, even improper ones. Lots of misinformation exists about fractions and even some teachers find talking about them difficult.
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 cover their close friends, too – decimals, percentages, ratios and proportions, 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: Real-life Maths
The third part of this book is about applying your maths knowledge to real-life subjects – 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 choose to be the top hat in a game of Monopoly. However, in some areas you need to be careful – and this book gives you a few extra tips and tricks for dealing with them.
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 shape – again, different ways exist to measure these and you encounter many facets of shape to play with.
Part IV: Speaking Statistically
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 the concept 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 these short, punchy chapters full of practical tips to help you manage the material in the rest of the book.
In this section, I show you how to check your work, remember your facts and make sure you get the right answer!
Icons Used in This Book
Here are the icons I use to draw your attention to particularly noteworthy paragraphs:
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.
Paragraphs marked with the Remember icon contain the key takeaways from the book and the essence of each subject.
The Warning icon highlights errors and mistakes that can cost you marks or your sanity – or both.
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 organised so that 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.
Good luck!
Part I
The Building Blocks of Maths
In this part . . .
In this part, I take you through the real foundations of Basic Maths: the skills you’ll need to have so you can master the other, more involved chapters.
You’re going to need to know how to add, take away, multiply and divide – as well as how to estimate and round numbers.
Once you’ve got all of that under your belt, the rest is easy!
Chapter 1
Getting Started
In This Chapter
Becoming better at maths
Handling whole numbers and fiddling with fractions
Managing measurements and speaking statistically
You can do this.
Before you start, sit up straight, breathe in and take a minute to reassure yourself that you’re smart and that you do maths all the time without realising it.
Every time you cycle to work, you perform feats of mathematics that would require supercomputers to work out in anything like the timescale your brain can do them in – from deciding which path to take to avoid the lorry, to figuring out exactly when to brake for the traffic lights, and even to remembering the combination for your bike lock.
Okay, maybe you don’t need a supercomputer for the last one, but the point stands: you’re much better at maths than you realise. Maybe you don’t yet have a handle on the kind of maths you need to do well in exams, but that’s just a matter of time.
In this chapter, I show you how to get better at that other kind of maths, the sort you need to get qualifications, and I take you quickly through the topics I cover in the rest of the book.
Covering the Basics
You may have a mental image of a mathematician – enormous forehead, crazy hair, thick glasses, tweed jacket over a tasteless shirt with pens neatly arranged in the breast pocket, gesticulating madly at a blackboard covered in crazy equations.
Actually, I do know mathematicians like that – but we’re not all so poorly adjusted. Being good at maths doesn’t automatically turn you into a socially awkward egghead.
That’s not the only good news, though: you’re also excused from having to understand all those crazy equations. Virtually no algebra is covered in the numeracy curriculum (just a few simple formulas). All you need to be able to do is:
Add, take away, divide and multiply confidently: If you can use all of these maths tools, you’ll probably find the chapters in Part I relatively easy to work through. If you can’t, Chapters 2 to 4 help you build a solid foundation to work from.
Figure out the right sum to do: Working out which tool to use to answer a question can be tricky, but if you keep a clear head and think through what the question is asking, it will make sense in the end. Promise.
Make sense of measures: ‘Measure’ doesn’t just mean being able to use a ruler, although that’s a good starting point. It’s also about weighing, taking temperatures, telling the time and working with shapes. For dealing with shapes, you just need to know a few simple formulas for area and volume.
Read and understand graphs and basic statistics: Once you ‘get’ graphs, the answers start to jump off the page. You only need to care about a mere handful of types of graph, and you just need to figure out where each of them is hiding the information. Until you know that, graphs can be a bit confusing – but don’t worry, I take you through them as gently as I can!
Talking Yourself Up
The stories you tell yourself are extraordinarily powerful. I used to tell myself I was useless and stupid, despite some evidence to the contrary. I was miserable, prone to panic attacks and generally conformed to what I’d told myself.
Eventually I made some changes to my life and told myself I was capable and intelligent instead. It was astonishing how quickly things got better – I still have the odd bad day, but at least I’m a functioning human being these days.
Unfortunately, the stories most people tell themselves about maths are just as poisonous as the stories I used to tell myself. So, before you get started, please do one thing for me: look at the stories you tell yourself. If you say things like ‘I don’t have a maths brain’ or ‘I’m rubbish at maths’, you’re digging a hole for yourself. Try telling yourself these stories instead:
‘I used to struggle with maths – but I’m putting that right now.’
‘I’m much better at maths than I thought!’
‘I’m working on my maths skills.’
You don’t need to tell yourself that you’re going to win the next series of Countdown (although practising with games is a great way of honing your mental arithmetic), just give yourself a good name to live up to!
Collecting the tools you need
A very popular joke among mathematicians states that maths is the second-cheapest subject to study because all you need is a pencil, some paper and a bin. Philosophy, of course, is cheaper because you don’t need the bin.
For this book, you can do an awful lot with just the pencil, paper and bin, but you may also find a few other bits and pieces useful, too:
A calculator: While you don’t need a calculator for working through this book, it’s quite a useful thing to have around. Most numeracy tests are non-calculator papers, but you’re allowed to study however you like. If you want to use a calculator, go ahead – just don’t rely on it!
A dedicated notebook or folder: This advice falls into the ‘do as I say, not as I do’ category – my notes are scattered all over my flat. The upshot is that I can never find anything I’m working on – and I don’t want that to happen to you! Keeping your notes in one place makes reviewing them a lot easier.
A geometry set: A ruler and a protractor may prove very useful – and if you’re going to have those, why not a compass, a set square and the stencil nobody ever uses?
A comfortable, quiet place in which to work: Working through maths problems is harder if you’re distracted. If at all possible, find a space in which you can sit comfortably without anyone bothering you for a while and work there.
Handling Whole Numbers
Whole numbers are the building blocks of maths. Pretty much anything you do in basic maths requires you to have a good handle on them. You need to be good at three sets of tools:
Adding and taking away: Adding up is probably the first thing you learn in maths after counting; taking away is a little more difficult, but not by much. If you can count, you can add and take away – and I show you how in Chapter 2.
Multiplying and dividing: These tools are slightly more difficult than adding and taking away; most people find multiplying (‘timesing’) a bit easier than dividing. I give you simple, reliable methods that make both of them straightforward in Chapter 3.
Rounding and estimating: In some ways, these tools are the most important. They stop you being overcharged in the supermarket and getting run over as you cross the road. I show you how to get rough answers and how to round off in Chapter 4.
Dealing with Parts of Numbers Basic maths involves some work on things smaller than whole numbers. That means . . . yes, fractions and decimals. Oh, and percentages, too. Look, don’t blame me, I’m just the messenger. And fortunately I have some good news: I introduce you to the Table of Joy, which makes ratios and percentages (and all manner of conversions) as easy as pie.
The chapters in Part II cover the following methods for dealing with part numbers:
Fractions: In basic maths you only need to find fractions of a whole number, cancel fractions down (and up) and add and subtract fractions. Chapter 5 covers all of these concepts. Once you get the trick, dealing with fractions is easy – honestly.
Decimals: You’re probably a bit more familiar with decimals – after all, most prices contain decimal points. The rules of arithmetic are no different for decimals than for whole numbers; you just need to keep your eye on the dot! I run you through the methods for working with decimals in Chapter 6.
Ratios and percentages: Dealing with ratios (Chapter 7) and percentages (Chapter 8) is a big favourite of maths examiners, presumably because they sometimes come up in real life. I show you how to use the Table of Joy to figure out which sum to do for both of these – soon you’ll be doing them in your sleep!
Managing Measurements
By measurements, I don’t just mean using a tape measure, although measuring distance is part of this subject. ‘Measurements’ could just as easily be called ‘real-life maths’ because it deals mainly with using your knowledge from Parts I and II to solve problems in the outside world. In more detail, I cover:
Time: You probably have a decent idea of how time works but, all the same, I take you through the different ways of telling time and working with timetables and other time sums in Chapter 9.
Money: Money is probably the bit of basic maths you use most in your everyday life. In Chapter 10, I show you how to deal with money sums – which work just like normal sums – and deal with more complicated things such as deposit schemes and exchanging currencies.
Weight: There’s not all that much to say about weight in Chapter 11, except that the sums you do work just like any other kind of sum. The only tricky bit might be converting between different units, but you have the Table of Joy for that!
Temperature: Temperature, which you read about in Chapter 12, is where things can get a bit tricky. You have to deal with negative numbers and possibly some formulas for converting between different temperature scales. Here’s some good news, though: temperature is almost always in whole numbers!
Size and shape: In Chapters 13 and 14 you find out about the difference between length, area, volume and angle, and how to figure each of them out!
Speaking statistically
In Part IV, I give you a very brief introduction to statistics, which is just using numbers to summarise data. Basic maths barely scratches the surface of statistics, which I used to hate; however, when I started using it for something actually relevant to me, it made much more sense! In this part, I tell you about:
Graphs and tables: In Chapters 15 and 16, you see how to read values from graphs and tables, and do more complicated sums with the results. I also give you a few ideas about drawing your own graphs.
Averages and spread: Chapter 17 is the place to go if you want to be able to tell your mean from your median and your mode! Working out the different kinds of average is a very typical exam question. Don’t worry, though; when you’ve completed the problems in this chapter, you’ll find working out averages and spread a walk in the park.
Probability: In Chapter 18, I show you the basics of probability. As the word suggests, this maths tool is all about working out how likely something is to happen.
Working through Questions and Answers
The whole point of this book is to help you get better at basic maths by following examples and answering sample questions.
Basic Maths Practice Problems For Dummies is organised so that each part builds on the parts before. If you feel that you need to start from scratch, starting at the beginning and working your way forward probably makes sense.
You can study however you like, though! Don’t feel that you have to run through the book from beginning to end; you’re perfectly free to jump around from chapter to chapter, or simply to do a handful of questions picked at random from anywhere in the book.
