Speed Mathematics: Secrets of Lightning Mental Calculation

296 Pages·2008·3.41 MB·English

by  Bill Handley

Contents
Preface
Introduction
Chapter 1: Multiplication: Part one
Multiplying numbers up to 10
To learn or not to learn tables?
Multiplying numbers greater than 10
Racing a calculator
Chapter 2: Using a reference number
Using 10 as a reference number
Why use a reference number?
When to use a reference number
Using 100 as a reference number
Multiplying numbers in the teens
Multiplying numbers above 100
Solving problems in your head
Combining methods
Chapter 3: Multiplying numbers above and below the reference
number
A shortcut for subtraction
Multiplying numbers in the circles
Chapter 4: Checking answers: Part one
Substitute numbers
Casting out nines
Why does the method work?
Chapter 5: Multiplication: Part two
Multiplication by factors
Checking our answers
Multiplying numbers below 20
Numbers above and below 20
Multiplying higher numbers
Doubling and halving numbers
Using 200 and 500 as reference numbers
Multiplying lower numbers
Multiplication by 5
Chapter 6: Multiplying decimals
Chapter 7: Multiplying using two reference numbers
Using factors expressed as a division
Why does this method work?
Chapter 8: Addition
Two-digit mental addition
Adding three-digit numbers
Adding money
Adding larger numbers
Checking addition by casting out nines
Chapter 9: Subtraction
Subtracting one number below a hundreds value from
another that is just above the same hundreds number
Written subtraction
Subtraction from a power of 10
Subtracting smaller numbers
Checking subtraction by casting out nines
Chapter 10: Squaring numbers
Squaring numbers ending in 5
Squaring numbers near 50
Squaring numbers near 500
Numbers ending in 1
Numbers ending in 2
Numbers ending in 9
Squaring numbers ending with other digits
Chapter 11: Short division
Using circles
Chapter 12: Long division by factors
Division by numbers ending in 5
Rounding off decimals
Finding a remainder
Chapter 13: Standard long division
Chapter 14: Direct division
Division by two-digit numbers
A reverse technique
Division by three-digit numbers
Chapter 15: Division by addition
Dividing by three-digit numbers
Possible complications
Chapter 16: Checking answers: Part two
Casting out elevens
Chapter 17: Estimating square roots
Square roots of larger numbers
A mental calculation
When the number is just below a square
A shortcut
Greater accuracy
Chapter 18: Calculating square roots
Cross multiplication
Using cross multiplication to extract square roots
Comparing methods
A question from a reader
Chapter 19: Fun shortcuts
Multiplication by 11
Calling out the answers
Multiplying multiples of 11
Multiplying larger numbers
A maths game
Multiplication by 9
Division by 9
Multiplication using factors
Division by factors
Multiplying two numbers that have the same tens digits and
whose units digits add to 10
Multiplying numbers when the units digits add to 10 and
the tens digits differ by 1
Multiplying numbers near 50
Subtraction from numbers ending in zeros
Chapter 20: Adding and subtracting fractions
Addition
Another shortcut
Subtraction
Chapter 21: Multiplying and dividing fractions
Multiplying fractions
Dividing fractions
Chapter 22: Direct multiplication
Multiplication by single-digit numbers
Multiplying larger numbers
Combining methods
Chapter 23: Estimating answers
Practical examples
Chapter 24: Estimating hypotenuse
Where the lengths of the sides are the same or similar
Where the lengths of the sides are different
Chapter 25: Memorising numbers
Phonetic values
Rules for phonetic values
Phonetic values test
Chapter 26: Phonetic pegs
An impressive demonstration
Six rules for making associations
Memorising square roots
Chapter 27: Memorising long numbers
Memorising pi
Mental calculation
Chapter 28: Logarithms
What are logarithms?
Components of logarithms
Why learn the table of logarithms?
Antilogs
Calculating compound interest
The rule of 72
Two-figure logarithms
Chapter 29: Using what you have learned
Travelling abroad
Temperature conversion
Time and distances
Money exchange
Speeds and distances
Pounds to kilograms
Sporting statistics
Sales tax or GST
Estimating distances
Miscellaneous hints
Apply the strategies
Afterword
Appendix A: Frequently asked questions
Appendix B: Estimating cube roots
Appendix C: Finding any root of a number
Appendix D: Checks for divisibility
Appendix E: Why our methods work
Appendix F: Casting out nines — why it works
Appendix G: Squaring feet and inches
Appendix H: How do you get students to enjoy mathematics?
Appendix I: Solving problems
Glossary
Index

Dedicated to
Benyomin Goldschmiedt
Also by Bill Handley: Teach Your Children Tables, Speed Maths for Kids and
Fast Easy Way to Learn a Language
(published by and available from Wrightbooks)
Third edition first published 2008 by Wrightbooks
an imprint of John Wiley & Sons Australia, Ltd
42 McDougall Street, Milton Qld 4064
Office also in Melbourne
First edition 2000
Second edition 2003
Typeset in 11.5/13.2 pt Goudy
© Bill Handley 2008
The moral rights of the author have been asserted
National Library of Australia
Cataloguing-in-Publication data:
Author: Handley, Bill.
Title: Speed mathematics / author, Bill Handley.
Edition: 3rd ed.
Publisher: Camberwell, Vic. : John Wiley and Sons Australia, 2008.
ISBN: 9780731407811 (pbk.)
Subjects: Mental arithmetic — Study and teaching.
Dewey Number:513.9
All rights reserved. Except as permitted under the Australian Copyright Act 1968
(for example, a fair dealing for the purposes of study, research, criticism or
review), no part of this book may be reproduced, stored in a retrieval system,
communicated or transmitted in any form or by any means without prior written
permission. All inquiries should be made to the publisher at the address above.
Cover design by Rob Cowpe
Author photograph by Karl Mandl