Isaac Asimov - Quick and Easy Math.pdf - Non-Fiction - iHomick

Quick and Easy Math

CONTENTS

hy Shortcus?

To copyreaders evewhere

Addition

who deeve so much redit

Naming e Pars of Adition

nd get so little

Cayig

Ading et o Right

ORH PRINTING

Roud Nues

Cckig Adition

Subraction

Adition in Re e

Cecking Subtaction

Multiplicaion

The Multiplication Table

Byond e Multiplation Tabe

Mking e Multiplier a Sum

Doubling

Ccking Multiplication

Diviion

The Peril s of Divi s on

Divisibiliy by 2, 5, and 10

Divisibiliy by 4 ad 8

Divisibiliy by 3, 6, and 9

OPT ® 194 BY SAC SMV

LL IGS R D NLDN G E IGHT O EPRODUCE

S O: OR PATS O F N NY FO M

l\Y OF CO NESS CATG C AD BR: -127 6

D N E U . S. A.

�

her Divisibilits

e Divison Tabe

Rewriting Divisions

ong Division

102

Cckig Division

109

Auhor's Note

112

Decmls

;'.,

112

118

122

132

139

142

147

153

eos in Rserve

Feeig e Decimal Point

Manipulating Decimals

Simpl

ing by Decimal

Dollars and Cens

Peene

Checking the Decimal Point

The Uses of Appoximation

TS BOOK describes methods for solving arihmeical prob

lems by "quick and easy" routes. These are not intendd

to replace he more systmatic methods familiar to every

one but to supplement hem.

It s customary in books such as this to include many

exercises to develop he reader's coidence and skill in

handing hese easy but possibly new techniques. However,

such exercises would clutter the book and reduce he room

available for explaining the principles behind the mehods;

and it is crucial, in my opinion, to eplain hese principles

horoughly.

I k it is fr to assume that anyone interested enough

n he subjct to read this book will have the wit and en

ry to make exercises of his own. Better yet, I hope he

ll take he trouble to exercise he methods describd n

is book on all aimetical problems that come his way

n day-to-day fe.

At irst s may actually slow him. Through sheer lack

159

Fracions

159

163

168

174

177

Manipulating Fractions

Factions and Decimas

Multiplication of Fctions

Fractions and Perenage

Changing Fractions ino Woe Numbes

181

Inex

.. f praie these short cuts may take more ime han would

.he "id-and-tue" methods. Let him bear up, though .

. .. h a ile patience, he will ind himself racing throuh

. to corect results n pracically no ime and wih pracically

'no p n.

SAC ASMOV

Why Shortcuts?

I SPOSE we have ll herd of "mental marvels" who

could add long columns of igures in a lash nd do com

piated calculations in their head. Perhaps we've even

wished we could do so in order to astonish our friends.

nd have thouht �at f we only took a litle time and

efort. we could lean how. Actually, it doesn't take a

'geis or a good mathematician to do such calculations.

To . e sure. some reat mathemaicians and some ex

remely inteigent men have indeed been able to per

-form mentl clculations in quick time. but o�ers have

not been able to do so. let Einstein always claimed

e was poor at calculations and that he had trouble

ing out s income tax.

Then. too. there have been many cases of people

�wihout ny educaion. and without much real intelli

nce. who were able to perform ll sorts of malie

:aticl ricks. Some were illiterate and cold make

ohing of themselves in their lives except for eang

money by putting on exhibitions of calculation.

But f it desn>t tke education or intelligence to e

, · a ightn ing calculator, what des it take? Is it a matter

f leng a few easy ricks wih ires?

2 Qick nd Esy Mah

Apparently not. Lightning calculators seem to have

unusually good memories for igures. f they multiply

two large numbers, they seem to be able to "write

down" the diferent steps in their minds as you would

on paper. They seem to remember what they "write

down" even, n some cases, f they have to stop the cal

culations for a considerable period of time. hey can

always go back to it afterward and continue, as you

would f you wrote it on paper.

Yet memories can be trained. If you are not bon

with a miraculous one, you can still exercise what you

do have and make it better. And then there are surely

tricks and shortcuts n calculation. f you can len

those, too, would you not be set? Perhaps so, f you did

two things. First, you must memorize ll the short-cut

rules for calculation. This is not hard f you're relly

serious about it and apply yourself, but n itself it is not

enough.

A magician can show you how to manipulate cards so

as to make whole decks seem to appear n your hand

out of nowhere, but you will have to practise constantly;

irst to mke your ingers nimble enough for the task

and then to keep them so. You can len how to read

music n a day and discover just exactly which piano

key to hit for every note shown; but to become a good

pianist you must practise every day for years.

And that is the second step, then, after you have

lened the rules: you must practise constantly. Even

those few who are bon "mental marvels" improve as

hy Shotus?

hey grow older and practise the art. Some of them

keep at it, practising every day. f they were to stop,

heir ability would begin to fade of.

Yet, even though you may memorize the rules and

practise daily, the chances are that you will not become

a lighning calculator. Mter all, many people study

piano and practise every day, but very few go on to

become reat concert pianists.

Well, then, f ll that is so, why m I bothering to

write a book on QUick and Ey Math - a book that is

to be full of methods for mking calculations simpler

and more rapid? The answer is that we are faced every

day with mll calculations that often take up unneces

sary time. You may have to be a mental marvel to look

at a long chain of large numbers and add them in a

lash, but you don't have to be one to look at 69 + 36

and see : a lash that the answer is 15. Or you can be

presented with the problem of multiplying 4 and 25

and say � at once, without putting pencil to paper.

Or you can ind that 0 of $15 is 9Q¢ without pain or

rouble. • T-

It's the little tings that count. You may not be able

o put on ehibitions with the ability to multiply 4 nd

5; you may not even be able to astonish your friends

more than once or twice. However, you can make life

easier for yoursef and save yourself time and errors.

You may feel, though, that you knw how to add

9 + 36 and get 105 as an answer. You were taught

how� long ago, in school.

Was the "school method"

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