**About The Book**

The Curious Hats of Magical is an introductory workbook on Vedic Mathematics. It is leads you into unique, enjoyable and very quick methods of working with numbers. There are full descriptions of these methods together with worked examples for you to follow and plenty of practice exercises. This is a workbook and you can write your answer into the spaces provided.

The system of Vedic Mathematics was constructed from ancient Vedic sources by Bharati krsna Tirthaji about a hundred years ago. It is based on sixteen simple rules called sutras, each of which is represented by a “Curious Hat”. The sutras briefly encapsulate rules of mental working, principles or guiding maxims. Through simple practice you can enjoy mathematics, become adept and quick at mental written calculations, losing any fear of numbers along the way.

The author’s understanding of Vedic Mathematics and his qualities as a teacher shine out in these excellent volumes. The simplicity and efficiency of the Vedic system are brought out through the clearly explained examples and there are many exercises and puzzles to stretch the young mind. Easy proof of all the techniques are given, the topics are well structures and the text is very readable. I must thoroughly recommend these books to students and teachers.

**About The Author**

James Glover has been developing the use of Vedic Mathematics in education for over thirty years and written five books on the subject. He is one of the foremost teachers of Vedic Maths and has run many public courses and lectures on the subject. He lives and teachers in Londor.

**Book 1**

**Author’s Preface**

This book is designed for young and old who might enjoy learning and practising the Vedic methods of Mathematics. Vedic mathematics is unconventional and not very well known and so readers are invited to be open-minded in their approach. The system uses the nature of number and natural mental processes to provide quick and easy methods for all sorts of calculations. Many difficult-looking problems can be solved at lightning speed with the answer coming digit-by-digit and without stress or anxiety. When practised the methods give great delight and a sense of the magical quality of numbers. The amazing simplicity and wonderment of obtaining the answers so easily has led some to ask, is this maths or magic? The answer is that it is magic until you have understood how it works and thereafter it is both maths and magic.

It has been nearly twenty years since I wrote Vedic Mathematics for Schools Books 1, 2 and 3 and have long felt that a completely new format is needed. In those previous books I attempted to cover, from a Vedic standpoint, the topics common to many schools teaching maths to 11 - 13 year-aids. In these second editions my aim is just to introduce the main topics of Vedic maths relevant to children of a similar age and which can be used as either support or extension material for teachers or just for interest by anybody. Books 1 and 2 are designed to be workbooks in which there are spaces to write the answers. Book 1 covers the main basic methods of calculation which use the Vedic rules. They are not blanket rules as there are plenty of methods used for specific cases as well as covering the general case. Vedic mathematics is highly flexible in two senses. Firstly, there are often several ways to get to an answer, all of which are entirely valid and correct and the reader can then have the flexibility of choosing whichever one seems most appropriate. Secondly, each of the rules has many varied and different applications and uses. They are flexible in themselves.

Some of the Vedic rules are short yet fairly cryptic. I had the idea of representing each sutra by a hat with a particular design. Hence the title of the book. The design of each hat in some way reflects the meaning of the rule.

It is my sincere hope that, in working through this book you will come to enjoy and love working with number and with the sutras.

I am greatly indebted to my daughters Sophie and Amy - Sophie for designing and producing the wonderful illustrations for the hats as well as the cover design and Amy for her help in checking the answers. I would like to thank them for their support and assistance.

**Introduction**

The Curious Hats of Magical Maths is an introductory workbook on Vedic Mathematics. It leads you into some unique, enjoyable and very quick methods of working with numbers. There are full descriptions of these methods together with worked examples for you to follow and plenty of practice exercises. This is a workbook and you can write your answers into the spaces provided. You will find the answers at the back of the book to check your work. The problems and methods are suitable for any age but probably most apt for 11 - 13 year-olds, Indian Class VI - VII, UK Years 7 - 8. The aim is to introduce some of the Vedic mathematical techniques and not to cover the whole of the mathematics syllabus for 11 - 13 year-olds. So the book can be used for support material, extension material or simply by those wishing to find fast techniques for solving problems.

**Veda**

Vedic Maths is a system from India and, in modern times, was first written about by a spiritual teacher named Bharati Krishna Tirtha. Mathematics was his hobby and he discovered the system from his own studies of ancient teachings. The word Veda means knowledge and so Vedic Maths means Know/edge Maths. It is based on sixteen simple rules called sutras (pronounced "sootras") and a sutra is a thread of knowledge. Veda is also as the name for the ancient teachings of India, thousands of years old, which deal with all manner of aspects of life, both spiritual and worldly. In fact, this is the most common use of the name. Traditionally, these teachings were handed down by word of mouth and learnt by heart. This is called an oral tradition. It is therefore not possible to know their exact age. It is also possible that not all of these teachings are published anywhere. Be that as it may, Tirtha was a brilliant scholar and an inspiring mathematician. He left behind one volume giving illustrative descriptions of some applications of the sutras first published in 1965. Since then there has been an increasing interest in his system of Vedic mathematics and there are now several websites available to learn more about it.

**Sutras **

The sixteen sutras of Vedic mathematics are short, easily memorised, statements giving principles, patterns of working or rules of thumb for solving all sorts of mathematical problems by the fastest and easiest routes. The aim of the sutras is to provide easy methods involving mental working. For the most part each sutra covers a wide range of topics and this book deals with introductory applications which are then further developed in Book 2.

This book introduces you to methods of multiplication, division and subtraction using the Vedic sutras as well as other aspects of arithmetic and algebra. Many of the methods will be new to you and others you may know. There are many short cuts in maths which will be natural to you. For example, if you mentally add 465 and 299, most will find the easiest way is to add 300 and take 1 off, leaving 764. This is quite natural and not unknown. You will have used a deficiency, the fact that 299 is 1 less than 300. The Vedic sutras follow these natural processes and point them out. So there are special methods as well as general methods

The last chapter provides puzzles and problems which can be solved using the sutras. There may be nothing out of the ordinary in the way you solve these problems because the sutras are quite natural. You can answer the questions and the sutras indicate the way you think about the problems.

**Numbers**

Mathematics is based on number and numbers begin with unity at 1. The numbers are 1 to 9 and these, together with zero, make up all the numbers we use in everyday life. If you treat these as ten friends then there is no need to fear them. Just like good friends they are completely reliable and trustworthy. They do not change with time. No matter how big a number is, it is always made up of these nine and the zero. This is described by means of a story in Chapter 6.The symbols we all use for numbers have become universal. All children throughout the world learn them. But they originate, including the zero, from thousands of years ago in India. It is therefore fitting that this wonderful system of Vedic mathematics also comes from India. No one knows why there are nine numbers and a zero and that we use a base ten for our number system. Some say that it is because we have ten fingers on our hands. Others say that it follows an ancient description of the creation involving nine elements. In Chapter 12 is another story briefly describing these elements.

**Magic Hats**

Each sutra is represented as a 'magic hat'. Just as a nurse wears a hat or a jockey wears a hat which helps them think and act in a way suitable for their work so you can pretend to wear each magic hat to help remind you of the way to think.

The hats give a visual representation of the sutras.

**Contents**

Introduction | vi | |

Chapter 1 | Nikhilam Multiplication | 1 |

Chapter 2 | Complements | 8 |

Chapter 3 | The Deficiency | 14 |

Chapter 4 | Number Patterns | 18 |

Chapter 5 | Multiplying above the base | 25 |

Chapter 6 | How many numbers are there? | 30 |

Chapter 7 | Multiplication by Vertically and Crosswise | 35 |

Chapter 8 | Subtraction by On the Flag | 42 |

Chapter 9 | Nikhilam Subtraction | 46 |

Chapter 10 | Nikhilam Division | 53 |

Chapter 11 | Proportionately | 63 |

Chapter 12 | The meaning of number | 68 |

Chapter 13 | Algebra and equations | 72 |

Chapter 14 | A few short cuts for multiplying | 82 |

Chapter 15 | Digital Roots | 86 |

Chapter 16 | Further steps with Nikhilam multiplication | 94 |

Chapter 17 | Working with decimal fractions | 98 |

Chapter 18 | Puzzles and problems | 104 |

Appendix The Sutras of Vedic Mathematics | 112 | |

Answers | 115 |

**Book 2**

**About The Book**

The Curious Hats of Magical Maths Book 2 is the second workbook in the series on Vedic Mathematics. It leads you into unique, enjoyable and very quick methods of working with numbers. Vedic methods for calculations are carefully described with step-by-step worked examples for you to follow. There are plenty of practice exercises so that you can gain some mastery over the techniques.

**Introduction**

This book is the second edition of Vedic Mathematics for Schools but there are so many changes from the previous edition that it carries a new name. It follows on from The Curious Hats of Magical Maths Book 1. It is aimed at providing enrichment as well as foundation and support material for children in years 8 and 9 (UK) and classes VII and VIII (India), grades 7 and 8 (USA). It concentrates entirely on the Vedic arithmetic and algebraic methods useful for children at these stages in their mathematical education. By the very nature of the subject, however, it can be read and worked through by anyone. This is because most people are unfamiliar with the efficient and delightful methods within Vedic mathematics. So this book does not cover the whole maths syllabus and, being free from the constraints of school curricula, can have a wider appeal.

Since it is a workbook you can write the answers in the spaces provided. There are plenty of examples with step-by-step instructions. You will need to follow the steps carefully before working through each exercise. The answers are in the back and so you can check your work as you go.

One aim of this book is to provide further grounding in the Vedic methods which can then be applied elsewhere in mathematics. Of particular importance is the ability to solve a given problem in different ways because this lays the foundation for learning about strategies.

Vedic Mathematics offers a wonderful approach to solving problems with extremely fast methods for calculating. It's fun and does not take long to learn but you must be prepared to practise. Many of the methods develop further those shown in Book 1 whilst others are introduced for the first time.

By following the system you will also learn about strategies for problem-solving. There is usually more than one way to solve a problem and Vedic Maths is a flexible system that encourages you to find the most efficient method for getting to the answer. For example, if you have to add mentally 239 and 399 you can add 9 and 9, 3 and 9 an 2 and 3, take account of the carry digits and then come up with the answer. That is the conventional method and is quite long. Vedic Maths teaches you to look at the problem in the round, as it were, and say 399 is one less than 400. So I will add 400 to 239 and then subtract 1, making 638. This method will be obvious to most. But the use of a deficiency for multiplication and division is not well known. It does lead to stunningly quick methods for special cases and these are described in this book. Vedic Mathematics deals with both special cases and general cases; and this is worthwhile, particularly where a conventional method is long, slow and cumbersome.

Where does this system come from and why is it called Vedic Maths? During the last century there was a revered spiritual teacher, a Sankaracarya, named Sri Bharati Krishna Tirtha. In his younger days he was a brilliant scholar and was mostly interested in the ancient spiritual teachings of India called Veda. The Veda are texts, thousands of years old, and contain knowledge both spiritual and practical. They contain a philosophy which forms the basis of many Indian religions. Bharati Krishna Tirtha studied these texts, together with associated commentaries and appendices, and hit upon various clues concerning mathematics. Fired by his own love of mathematics he followed the clues and came up with a system based on sixteen rules or sutras. There are also a similar number of sub-rules or sub-sutras. His sutras might not be found in the ancient texts but according to the other meaning of Veda, which has to do with knowledge in the present moment, his methods and sutras can be described as Vedic.

In his introduction he describes the process which ancient seers used for discovering the laws relating to number as true visualisation. It is quite possible that his own experience was similar. His understanding of the word Veda appears to be quite different from the usual version of a collection of ancient texts and relates more to living knowledge. Whatever the case as to the origin of the sutras ''the proof of the pudding is in the eating", as it were. In other words, if it works and is consistent with right reasoning then it should be accepted and if not, then rejected. He encourages us to keep our minds ever open. This is good advice because the methods for such things as multiplication and division are quite different from the conventional long versions. Vedic mathematics leans towards mental methods so that, for example, with practice, you can multiply or divide any numbers in one line. And even when faced with a problem which you solve intuitively, just by looking, this is also included in the system.

It would be a mistake to think that Vedic mathematics provides a complete set of methods different from conventional maths. Yes, it does have many methods which are far slicker, but it also includes conventional methods. For example, when transposing terms from one side of an equation to the other, with a change of sign, this is taught conventionally.

In this case the Vedic system simply points out the sutra which is used for that same process, namely, Transpose and Adjust. So in that sense Vedic maths gives you a different perspective, a different orientation to the mental workings as you solve problems. The sutras describe the patterns of working within your mind.

Sutras

This book uses fifteen of the sutras and sub-sutras and, as with Book 1, many of them are represented by the image of a hat - like a thinking cap! These can be found on the next page.

**Contents**

Introduction | viii | |

Prologue | xi | |

Chapter 1 | The Mighty Vinculum | 1 |

Chapter 2 | Nikhilam Multiplication | 8 |

Chapter 3 | Multiplication By Vertically And Crosswise | 18 |

Chapter 4 | Division Using A Base | 33 |

Chapter 5 | Squaring | 46 |

Chapter 6 | Products, Factors, Multiples And Primes | 53 |

Chapter 7 | Fractions | 62 |

Chapter 8 | Algebra | 72 |

Chapter 9 | Casting Out | 82 |

Chapter 10 | The Working Base | 88 |

Chapter 11 | Further Fractions | 102 |

Chapter 12 | Ratio And Proportion | 111 |

Chapter 13 | Percentages | 119 |

Chapter 14 | Equatios | 130 |

Chapter 15 | Averages | 142 |

Chapter 16 | Working With Decimals | 148 |

Chapter 17 | Straight Division | 154 |

Chapter 18 | Decimal Fractions | 164 |

Answers | 176 | |

Appendix | 202 | |

Index | 204 |

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Publisher:
Motilal Banarsidass publishers Pvt. Ltd.
Pages:
361 (Throughouts Color Illustations)
Weight:
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Paperback (Edition: 2015)
James GloverMotilal Banarsidass publishers Pvt. Ltd.
Language: EnglishSize: 11.0 inch X 8.5 inchPages: 361 (Throughouts Color Illustations)Weight of the Book: 1.0 kg
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