12. WHY DO WE CALCULATE BACKWARDS?

LEFT TO RIGHT IS BETTER

- details

112 pages. Size: 20cm by 13cm. Paperback. Author: Kenneth Williams;
ISBN 978-1-902517-23-0. First edition 2010.
Price $12 (including postage).

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.