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Table of Contents

## How to Calculate Quickly PDF

The author can awaken for you a faculty which is surprisingly dormant in accountants, engineers, scientists, businesspeople, and others who work with figures. This is “number sense” — or the ability to recognize relations between numbers considered as whole quantities. Lack of this number sense makes it entirely possible for a scientist to be proficient in higher mathematics, but to bog down in the arithmetic of everyday life.

This book teaches the necessary mathematical techniques that schools neglect to teach: Horizontal addition, left to right multiplication and division, etc. You will learn a method of multiplication so rapid that you’ll be able to do products in not much more time than it would take to write the problem down on paper. How to Calculate Quickly PDF

This is not a collection of tricks that work in only a very few special cases, but a serious, capably planned course of basic mathematics for self-instruction. It contains over 9,000 short problems and their solutions for you to work during spare moments. Five or ten minutes spent daily on this book will, within ten weeks, give you a number sense that will double or triple your calculation speed.

## Table of Content

CONTENTS

The Plan of This Book

ADDITION

Addition in General

Adding Single Columns by Pairs, starts on

Adding Single Columns by Trios, starts on

Mental Addition of Large Numbers, starts on

Two-Column Addition, starts on

SUBTRACTION

Subtraction in General

Left-to-Right Subtraction, starts on

MULTIPLICATION

Multiplication in General

Factoring, starts on

Direct Multiplication by Numbers Greater than 12, starts on

Multiplying Three Figures by One, starts on

Multiplying Two Figures by Two, starts on

Multiplying Three Figures by Two, starts on

Multiplying Three Figures by Three, starts on

DIVISION

Division in General

Direct Division by Numbers Greater than 12, starts on

Mental Division of Large Numbers, starts on

Division by Three Figures, starts on

Division by Two Figures, starts on

FRACTIONS

Fractions in General

Addition and Subtraction of Fractions, starts on

DECIMALS

Decimals in General

Decimal Equivalents of Fractions, starts on

SHORT CUTS

Horizontal Addition

Combined Addition and Subtraction

Multiplying by a Near Number

Aliquot Parts in Multiplication

Simplifying the Multiplier

Multiplication by Factoring

Factors between 11 and 19

Multiplying by 11

Multiplying by 21, 31, 41, etc

Squares of Numbers, starts on

Multiplying When Corresponding Orders Are Alike, starts on

Multiplying a Sum by a Difference

Multiplications Involving Fractions, starts on

Aliquot Parts in Division

Cubes of Numbers

Algebraic Multiplication

Table of Prime and Composite Numbers

ANSWERS

### THE PLAN OF THIS BOOK

The subject matter here presented might have been divided into sections on addition, subtraction, multiplication, etc., in the manner usual to text-books on arithmetic. Because, however, of the special purpose of this book, no such division is made. The general plan is to have several branches proceed simultaneously. Progress is not from subject to subject but from less to more difficult calculation. For each of the fundamental divisions of arithmetic there is a general introduction—for instance, Addition in General on page 3. In these introductions the special objects sought are described, as well as the methods by which these objects are attained. How to Calculate Quickly PDF

The student, therefore, always has a clear view of the ultimate aims of his studies and knows how the work immediately in hand fits into the general plan. Wherever anything new is introduced, it is clearly explained and illustrated. Usually the exercises that go with each explanation are spread through many succeeding pages. In a large number of cases the exercise calls for work with the numbers in a certain list or table (for instance, Table I on page 7). The same lists of numbers are used for various kinds of calculation. This method of presentation makes possible the remarkably great number (about 15,000) of practice examples that are included.

## Preface – How to Calculate Quickly PDF

Arithmetic is a science, but calculation is an art. Science is knowledge—art is skill. You have all the knowledge you could possibly need to determine that 57 times 25 equals 1425, but if you are asked to multiply 57 by 25 and cannot do this mentally in just about one second, you are not adept at the art of calculation. Genuine skill in the calculating art can be acquired by any person of ordinary intelligence, no matter what his schooling may have been. To develop such skill is the purpose of this book. Special forms of short, graded exercises, performed for the most part mentally, lead the student by easy steps to a point where he will possess really exceptional calculating ability. For instance, if you will look at Exercise No. 371 on page 191, you will find that you are expected to perform mentally such multiplications as 696 times 858, 858 times 878, etc. These are not “trick” examples—the student who systematically performs the practice examples presented in this book will be able to do many kinds of examples of this degree of difficulty by his sheer ability to hold and manipulate figures in his head. How is this skill developed? Essentially by developing number sense. Number sense consists in the ability to recognize the relations that exist between numbers considered as whole quantities, and to work with the thought of their broad relations always uppermost.How to Calculate Quickly PDF

Number sense is possessed by many people in all walks of life—particularly by accountants, bookkeepers, estimators, cashiers, storekeepers and the like. On the other hand, it is absent in many who have an excellent understanding of advanced mathematics. The engineering professions are full of those who require slide rules to perform calculations which the average billing clerk would do mentally. To give an example of what is meant by number sense, suppose you were asked to multiply mentally 11625 by 12. If you felt at all competent to try to do so, you would probably (unless you are the exceptional case) proceed like this: 12 times 5 is 60, remember 0 and carry 6; 12 times 2 is 24, put 0 before the other 0 and carry 3, etc. In this way you would eventually arrive at the correct answer —if you did not get all mixed up in the meantime; but at best you would take a long time, because number sense would have played no part whatever in your awkward method of approaching this very simple little problem. Suppose now that we introduce a little of this number sense—suppose that instead of dealing with plain figures, you were told to imagine that you had sold twelve machines on each of which you made a commission of $11.62 .

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