Maths is Easy , livre ebook

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ISBN: 9781910202081
First published in 2014 by Peter Watmough
Copyright © 2014 Peter Watmough. All rights reserved.
All rights reserved. Apart from any permitted use under UK copyright law, no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information, storage or retrieval system, without permission in writing from the publisher or under licence from the Copyright Licensing Agency Limited. Further details of such licenses (for reprographic reproduction) may be obtained from the Copyright Licensing Agency Ltd, Saffron House, 6-10 Kirby Street, London EC1N 8TS.
Typeset for How2become Ltd by Anton Pshinka.
Printed in Great Britain for How2become Ltd by Bell & Bain Ltd, 303 Burnfield Road, Thornliebank, Glasgow G46 7UQ.
INTRODUCTION
The purpose of this book is to start off by dealing with the necessary arithmetic. I will sometimes use UNUSUAL METHODS to explain things but this is because THEY WORK. The first step in a learning process must be to actually DO things and get the right answers. If you can't get the right answers you will just get discouraged and stop trying to learn.
This book will get you DOING things.
Not only that. You will be able to get the right answers as well.
It will show you that maths is easy and you can do it.
The chapters on arithmetic can be done in any order but I suggest you do it in the order they appear in the book.
Understanding numbers is ESSENTIAL and this understanding will slowly grow as the work progresses.
HOWEVER. I suggest you make an effort to learn your tables.
I do not mean pointless going through things in order such as four sixes equal 24, 5 sixes equal 30 and so on because just adding six each time is easy. Keep writing it in the WRONG ORDER. Four sixes equal 24, seven sixes equals 42 and so on until you have done them all. Memorise them in the wrong order.
This way you HAVE to think about it.
It becomes more of a challenge. AND it works!
This book is called Maths is Easy because it IS easy.
Use my methods to learn how to do things and build the confidence that will make you want to learn more.
You will find the book is full of interesting true facts.
There are real sunken treasure ships to locate on charts.
Car rallies to solve on different maps.
The secret of mazes.
The list goes on. The emphasis is always on being realistic.
By the end of the book you will be very conversant with arithmetic as used in many real situations, Bar charts, Pie charts, statistics, navigation, 24 hour clock and more.
Use my methods and be surprised at how quickly you learn.
About me.

I spent 5 years in the Royal Navy.
7 years as a motor mechanic.
5 years as a Fish and Chip shop owner.
Then I went to university and got an honours degree in mathematics.
Trained as a teacher and spent 25 years teaching.
During that time I got an honours degree in Computer Science.
Had a mathematics book published by Stanley Thornes.
Wound up as Head of IT at a large Public School.
Spent my last five working years as a computer programmer.
During my teaching career I developed techniques that I found made it easy for students to understand....and DO
It is these techniques and associated material that I present in my book.
CONTENTS
1. What is a Fraction?
2. Adding and Subtracting Fractions
3. The 24 hour Clock
4. Multiplying and Dividing Fractions
5. Brain Teasers
6. Multiplication of Whole Numbers
7. Bar charts and Pie charts
8. Adding and Subtracting Decimals
9. Statistics
10. Currency Exchange
11. Buying a Meal Abroad
12. Division of Whole Numbers
13. Multiplying and Dividing Decimals
14. Banking
15. Timetables
16. Car Rallies
17. Multiply and Divide by Multiples of 10
18. Percentages and VAT
19. Garage Repairs
20. Area
21. Holidays
22. Bearings and Treasure
23. Hire Purchase
24. Buying a Shop
Answers
1. WHAT IS A FRACTION?
The dictionary tells us that a fraction is a "small piece" or a "scrap". Unfortunately these "small pieces" can be all different sizes.

All you need to deal with these different size pieces is common sense. There is nothing mysterious about it.
Look at the examples above.

Piece A is 1 piece The shape has been cut into 4 EQUAL pieces
Piece A is Piece B is 1 piece The shape has been cut into 6 EQUAL pieces
Piece B is Pieces B and C are two pieces The coin has been cut into 8 EQUAL pieces
Pieces B and C together are
It's as simple as that. Fractions are just shorthand. Shorthand is the name given to anything that helps people to write faster.
So is just shorthand for "cut something up into 6 EQUAL pieces and take 2 of the pieces".
It's a good job you don't have to write long sentences like that every time. It is much easier to write than it is to write "cut something up into 4 EQUAL pieces and take 3 of the pieces".
But they both mean exactly the same thing.
is shorthand for "cut something up into five EQUAL pieces and take 1 of the pieces".
is shorthand for "cut something into 12 EQUAL pieces and take 5 of the pieces". Mathematicians are very lazy and often use shorthand....but so do other people.
Here is something written in 3 different ways.

These 3 ways might look different but they all mean the same thing.
Fractions occur all the time. We have all heard of half an hour (1/2 hr) or a quarter of a kilogram ( kg).
What actual thing could be talking about?
First remember what is shorthand for.
Cut something up into 7 EQUAL pieces and take 1 of the pieces.
It could be talking about a day, because if a week is cut into 7 equal pieces then each piece is 1 day.
could be talking about 2 days.
What else could be talking about? 2 of the 7 Deadly Sins or 2 of the 7 Seas.
Normally we use fractions without thinking about what they may be talking about.

Exercise 1
1. What could these fractions be talking about? There may be more than one answer to some of them.

When you have done these check your answers and make sure you understand how the fractions are working before going on to the next questions.
Now there are some sentences in maths shorthand. They look very strange. Turn them into ordinary English by writing them without any fractions. The first one is started for you.
2. You go along for a job. The boss says, "Each week you will work of a week, of each day with of each day for dinner.
of a week means 5 days (because of a week is one day). Therefore the beginning of the answer is:
"Each week you will work 5 days..."
3. You have just taken your shoes to be re-heeled. The shop owner says, "Can you wait a bit? It will take about of an hour."
4. The person in the ticket office said "You need change."
5. The card player said "I have only got of a pack and I should have 9/52 of a pack. Someone has got of a pack up their sleeve.
6. "I am out of training", said the athlete. "It will probably take me of a minute".
It is easy to see that could be talking about a whole week, or could be talking about a whole pack of cards.
Big numbers don't make any difference. minutes still means 1 whole minute.
minutes means cut a minute up into 3572 EQUAL pieces and take 3572 of the pieces. In other words take all of the pieces. Bit of a waste of time cutting it up in this case!
Certain problems can now be worked out.
When a lorry was full it carried 2 tonnes. How much could it carry when it was completely full?

In this case the fraction is 1/5 and you know that it will take 5 of these (5/5 ) to be a whole lorry full. Of course you can just work it out but see how a picture helps to make things clearer.
Interesting TRUE facts
A 1/4 of the fleas removed from a red squirrel came to 3000. How many fleas did the squirrel have altogether?

Exercise 2
1. A of the way up the Sears Roebuck skyscraper in Chicago is 22 floors. How many floors are there altogether?
2. In the deepest dive with one breath, of the way down was 86 feet. How deep was the dive?
3. of the passengers in a Jumbo jet is 50. How many passengers can the jet carry when it is full?
4. 2000 years ago of an average man's life was 3 years. How long did an average man live?
5. At the same time of an average woman's life was 3 years. How long did an average woman live?
6. In the Congo in 1950 of the average person's life was 13 years. How long did these people live?
7. Some South American Indians use poison from a particular frog to put on the tips of their arrows. It is one of the world's most dangerous poisons and of a gram would kill someone. How many people would 1 gram kill?
8. The world's most expensive perfume is De Beren's number 1. It costs £66.66 for of an ounce. How much does 1 ounce cost?
9. A of an ounce of gold would cost £147. How much would 1 ounce cost?
How full is the Jar?

This jar is 60 mm tall. It has some fluid in it. How full would you say it is?
It is clearly less than full. Is it full, or maybe full, or full. There must be a way of finding out.
Carefully measure the height of fluid. It comes to 18mm.
There are 60 mm to the top of the jar so the jar is full. This is because the jar is broken up into 60 EQUAL parts (each 1mm) and the fluid takes 18 of them. HOW EASY is that?
We wouldn't leave the answer as even though it is correct.
The answer can be made much simpler to understand and we will come back to this after the next section.
Turning Fractions into Easier Fractions

All the above fractions are the same. They all amount to a half. In the last case you cut the cylinder up into 18 EQUAL pieces and took 9 of them. But that means you still have half of the cylinder.
Fractions which are the same but look different (like and ) are called EQUIVALENT FRACTIONS. Equivalent is just a word that means the same as