Fun with figures by KENNETH WILLIAMS

FUN WITH F GURES BRILLIANT MENTAL MATHS SHORT CUTS THAT WILL AMAZE EVERYONE! KENNETH WILLIAMS INSPIRATION BOOKS Download the full e-books 50+ sex guide ebooks 100+ ebooks about IQ, EQ, … teen21.tk ivankatrump.tk ebook999.wordpress.com Read Preview the book http://funwithfigures.com Copyright Notice This is NOT a free Ebook! This publication is protected by international copyright laws No part of this book may be reproduced or transmitted in any form by any means graphic, electronic or mechanical without express written permission from the publisher Inspiration Books Oak Tree Court Skelmersdale Lancs, WN8 6SP England ISBN 902517 01 © K.R.Williams 1998 All Rights Reserved Book design, cover and illustrations by David Williams, Tel 01695 50371 Printed by Chesil Design and Print, Skelmersdale, Tel 01695 50460 O n seeing this kind of work actually being performed by the little children, the doctors, professors and other “big guns” of mathematics are wonder-struck and exclaim: ‘Is this mathematics or magic?’ And we invariably answer and say: ‘It is both It is magic until you understand it; and it is mathematics thereafter’ Bharati Krsna Tirthaji Vedic Mathematics Scholar INTRODUCTION Ten-year old Truman Henry Safford (born 1836) was asked: “Multiply in your head 365,365,365,365,365,365 by 365,365,365,365,365,365.” He flew around the room like a top, pulled his pantaloons over the top of his boots, bit his hand, rolled his eyes in their sockets, sometimes smiling and talking, and then seeming to be in an agony, until, in not more than one minute, said he, “133,491,850,208,566,925,016,658,299,941,583,225!” ‘Lightning calculators’, are not that uncommon and while we may not be able to match the brilliance of a Truman Henry Safford, we can all develop, with the aid of this book, a talent at mental mathematics With these super-easy methods you need no longer be caught between the drudgery of the old dinosaur methods and the ‘cop-out’ of the calculator When Bharati Krsna Tirthaji reconstructed the ancient system of Vedic Maths (used in this book) earlier this century, he uncovered a beautifully integrated and complete system of maths which had been lost for centuries The Vedic system mirrors the way the mind naturally works and so is designed to be done mentally Fun with Figures is for those who think they are no good at maths – and for those who are good at maths It is for those who would like to steal a little lightning The book answers a need of our time, offering easy, enjoyable maths which improves mental agility and memory, promotes confidence and creativity – as well as being useful in everyday life Each double page shows a simple mathematical method and is independent of the others (with two exceptions, which are indicated) In addition to the various everyday situations indicated in this book, you will surely find many other occasions for the use of these easy methods There are many exercises for you to practise and answers at the end of the book CONTENTS AMAZE YOUR FRIENDS 10 IN THE SHOP 12 TABLES MAGIC 14 AT A PARTY 16 EXERCISE YOUR BRAIN CELLS 18 SHOW YOUR CLASS 20 ON A WALK 22 AT THE OFFICE 24 ON THE MOTORWAY 26 THE NINE-POINT CIRCLE 28 IN YOUR MATHS LESSON 30 CHECK YOUR BILL 32 CHECK YOUR CHANGE 34 IN THE DIY SHOP 36 HAVE A BREAK 38 AT THE POST OFFICE 40 IMPRESS YOUR PARENTS 42 DELIGHT YOUR CHILD 44 IMPROVE YOUR MIND 46 ON THE TRAIN 48 ANSWERS 52 RELATED BOOKS AMAZE YOUR FRIENDS Use the formula ALL FROM AND THE LAST FROM 10 to amaze your friends with instant subtractions „ For example 1000 - 357 = 643 We simply take each figure in 357 from and the last figure from 10: 0 - from from from 10 = So the answer is 1000 - 357 = 643 And that’s all there is to it! This always works for subtractions from numbers consisting of a followed by noughts: 100; 1000; 10,000 etc „ Similarly 10,000 - 1049 = 8951 , 0 - from from from from 10 = „ For 1000 - 83, in which we have more zeros than figures in the numbers being subtracted, we simply suppose that 83 is 083 So 1000 - 83 becomes 1000 - 083 = 917 Try some yourself: 1) 3) 5) 7) 9) 1000 - 777 = 1000 - 505 = 10000 - 9876 = 100 - 57 = 10,000 - 321 = 2) 1000 - 283 = 4) 10,000 - 2345 = 6) 10,000 - 1101 = 8) 1000 - 57 = 10)10,000 - 38 = Mathematics, rightly viewed, possesses not only truth but supreme beauty BERTRAND RUSSELL „ $10 - $2.30 = $7.70 Here “the last” is the as zero does not count So we take from and from 10 Try these: 1) $10 - $7.77 = 3) $10 - $6.36 = 5) $100 - $84.24 = 2) $10 - $4.44 = 4) $10 - $5.67 = 6) $100 - $31.33 = Zerah Colburn (1804-40), when he was eight, was asked to raise the number to the sixteenth power: he announced the answer (281,474,976,710,656) “promptly and with facility”, causing the academic audience to weep He was next asked to raise the numbers 2,3, to the 10th power: and he gave the answers so rapidly that the gentleman who was taking them down was obliged to ask him to repeat them more slowly 11 TA B L E S M A G I C Don’t know your tables? Never mind, in this system you don’t need them beyond x 5! „ Suppose you need x is below 10 and is below 10 Think of it like this: answer The answer is 56 The diagram below shows how you get it answer 12 You subtract crosswise: - or - to get 5, the first figure of the answer And you multiply vertically: x to get 6, the last figure of the answer That’s all you do: see how far the numbers are below 10, subtract one number’s deficiency from the other number, and multiply the deficiencies together „ x = 42 3 = 42 Here there is a carry: the in the 12 goes over to make the into Multiply these: 1) 8– – 2) 7– – 3) 9– – 4) 7– – 5) 9– – 6) 6– – The whole heaven is number and harmony ARISTOTLE 13 AT A PA R T Y At a party surprise your friends with this spectacular way of multiplying large numbers together in your head Here’s how to use VERTICALLY AND CROSSWISE for multiplying numbers close to 100 „ Suppose you want to multiply 88 by 98 Not easy, you might think But with VERTICALLY AND CROSSWISE you can give the answer immediately, using the same method as on the last page Both 88 and 98 are close to 100 88 is 12 below 100 and 98 is below 100 You can imagine the sum set out like this: 14 88 - 12 98 - 86 24 As before the 86 comes from subtractingcrosswise: 88 - = 86 (or 98 - 12 = 86: you can subtract either way, you will always get the same answer) And the 24 in the answer is just 12 x 2: you multiply vertically So 88 x 98 = 8624 This is so easy it is just mental arithmetic Try some: 1) 87 98 –– –– 2) 88 97 –– –– 3) 77 98 –– –– 4) 93 5) 94 96 92 –– –– –– –– 6) 64 99 –– –– 7) 98 97 –– –– Where there is life there is pattern and where there is pattern there is mathematics JOHN D BARROW 15 EXERCISE YOUR BRAIN CELLS While waiting in a queue, why not exercise your brain cells by multiplying numbers just over 100 „ 103 x 104 = 10712 The answer is in two parts: 107 and 12 107 is just 103 + (or 104 + 3), and 12 is just x „ Similarly 107 x 106 = 11342 107 + = 113 and x = 42 Again, just mental arithmetic 16 Try a few: 1) 102 x 107 3) 104 x 104 5) 101 x 123 2) 106 x 103 4) 109 x 108 6) 103 x 102 I proposed to him [Jedediah Buxton, 1702-72] the following random question: In a body whose sides are 23,145,789 yards, 5,642,732 yards, and 54,965 yards, how many cubical eighths of an inch? After once naming the several figures distinctly, one after another, in order to assure himself of the several dimensions and fix them in his mind, without more ado he fell to work amidst more than 100 of his fellow laborers, and after leaving him about hours, on some necessary concerns (in which time I calculated it with my pen) at my return, he told me he was ready: upon which, taking out my pocket book and pencil, to note down his answer, he asked which end I would begin at, for he would direct me either way I chose the regular method and in a line of 28 figures, he made no hesitation nor the least mistake 17 SHOW YOUR CLASS Teacher – show your class the easy way to add and subtract fractions Use VERTICALLY AND CROSSWISE to write the answer straight down! „ + = 10 + = 13 15 15 Multiply crosswise and add to get the top of the answer: x = 10 and x = Then 10 + = 13 The bottom of the fraction is just x = 15 You multiply the bottom numbers together 18 So: + = 20 + 21 = 41 „ 28 28 Subtracting is just as easy: multiply crosswise as before, but then subtract: „ - = 18 - 14 = 21 21 Try a few: 1) + = 2) + = 3) + = 4) - = 5) - = 6) - = nature is the realisation of the simplest conceivable mathematical ideas EINSTEIN 19 O N A WA L K Out walking with your friends, show them this quick way to square numbers that end in using the formula BY ONE MORE THAN THE ONE BEFORE „ 752 = 5625 752 means 75 x 75 The answer is in two parts: 56 and 25 The last part is always 25 20 The first part is the first number, 7, multiplied by the number “one more”, which is 8: so x = 56 75 = 56 25 x = 56 „ Similarly 852 = 7225 because x = 72 Try these: 1) 452 2) 652 3) 952 4) 352 5) 152 For the harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty D’ARCY THOMPSON 21 AT T H E O F F I C E Show your colleagues in the office this beautiful method for multiplying numbers where the first figures are the same and the last figures add up to 10 „ 32 x 38 = 1216 Both numbers here start with and the last figures (2 and 8) add up to 10 So we just multiply by (the next number up) to get 12 for the first part of the answer And we multiply the last figures: x = 16 to get the last part of the answer 22 Diagrammatically: x = 16 32 x 38 = 12 16 x = 12 „ And 81 x 89 = 7209 We put 09 since we need two figures as in all the other examples Practise some: 1) 43 x 47 = 3) 62 x 68 = 5) 59 x 51 = 2) 24 x 26 = 4) 17 x 13 = 6) 77 x 73 = The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful POINCARE 23 O N T H E M O T O R WAY On a car journey, get the children to find the digit sum of car number plates Any number of any size can always be reduced to a single figure by adding its digits „ For example 42 has two digits which add up to We say “the digit sum of 42 is 6” „ The digit sum of 413 is because + + = „ For 20511 the digit sum is Try a few: 1) 34 2) 61 3) 303 24 4) 3041 5) 21212 „ Now suppose we want the digit sum of 417 Adding 4, and gives 12 But as 12 is a 2-figure number we add its digits to get (1 + = 3) We could write 417 = 12 = „ And so 737 = 17 = We simply add the digits in the number and add again if necessary This is simple and one of its uses is in checking sums, as we will see Find the digit sum for each of the following: 1) 85 2) 38 3) 77 4) 99 5) 616 6) 7654 All things that can be known have number; for it is not possible that without numbers anything can be either conceived or known PHILOLAUS 25 ... http://funwithfigures.com Copyright Notice This is NOT a free Ebook! This publication is protected by international copyright laws No part of this book may be reproduced or transmitted in any form by. .. where the first figures are the same and the last figures add up to 10 „ 32 x 38 = 1216 Both numbers here start with and the last figures (2 and 8) add up to 10 So we just multiply by (the next... and illustrations by David Williams, Tel 01695 50371 Printed by Chesil Design and Print, Skelmersdale, Tel 01695 50460 O n seeing this kind of work actually being performed by the little children,