## Description

This is a basic, easy to read, book which shows that we do in fact calculate backwards. It explains the advantages of calculating from left to right and demonstrates how easy it is to work this way. It does not claim we should use only left to right methods.

## Details

108 + iii pages.

Size: 20cm by 13cm.

Paperback. 2010

Author: Kenneth R. Williams

ISBN 978-1-902517-23-0.

## Introduction

This book:

1) Shows that we do calculate backwards

2) Explains the advantages of calculating from left to right (i.e. forwards)

3) Demonstrates how to calculate from left to right

To expand:

1) We read, write and pronounce words and numbers from left to right; but we calculate from right to left (i.e we start with the units figures). From this point of view we calculate backwards.

2) The advantages are:

a) It's more natural because we read, write and pronounce words and numbers from left to right

b) It's more efficient because we get the most significant (left-hand) figures first instead of last: if you only want the first 2 or 3 figures of an answer you waste a lot of time and effort in working the usual way

c) It's more consistent as we do division from left to right and never right to left

d) Sometimes you cannot start at the right: to find a square root, solve a quadratic or trig equation there is no last figure to start from

e) Because all operations can be done left to right we can combine them. This leads to a very powerful technique which enables solutions to problems that would never normally be even attempted.

3) The book will not cover these more advanced applications but will show how we can do simple addition, subtraction and multiplication from left to right, just as easily as from right to left. For the more advanced applications see the books: "VM Teacher's Manual - Advanced Level", "Discover VM", "Vertically and Crosswise".

The book does not claim we should change to using only left to right methods, just that there are significant advantages in working left to right.

## Contents

**INTRODUCTION****PART 1 – IN YOUR HEAD**

1. ADDITION

2. SHORT MULTIPLICATION

3. VEDIC MATHEMATICS

4. SUBTRACTION

5. VEDIC MULTIPLICATION**PART 2 – ON PAPER**

6. ADDITION

7. MULTIPLICATION

8. BAR NUMBERS

9. MULTIPLICATION WITH BAR NUMBERS

10. SUBTRACTION**CONCLUSION****REFERENCES****APPENDICES****INDEX **

## Back Cover

Yes, we do calculate backwards! We read, write and pronounce numbers and words from left to right, but we calculate from right to left (starting with the units).

Not only is this inconsistent, it is unnecessary too. Because calculating left to right is extremely easy, as shown in this book.

But there are other, stronger reasons for working left to right.

The most significant (important) figures are always on the left, so in working from the left we get these figures first. And this means it’s far more efficient, especially for quick, mental calculations.

Also the left to right method allows us to combine operations which means we can do huge calculations and get the answer digit by digit to any required accuracy.

For these and other reasons left to right is the natural, sensible and easy way to calculate.

Whether it’s to improve your mental maths skills, or to understand the simplicity and extraordinary efficiency of this method, this book has the potential to change the way you calculate forever.

This book demonstrates that we calculate backwards, describes the advantages of working the alternative way from left to right, and shows how left to right calculations can be carried out.