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ENTERED ACCORDING TO ACT OF CONGRESS IN THE YEAR 1904.

BY CLEMENT C. GAINES, THE OFFICE OF THE LIBRARIAN OF CONGRESS AT WASHINGTON, D. C.

PREFACE.

For a number of years the authors of this work have felt the need of a Business Arithmetic that would meet the requirements of commercial schools and practical men, and, at the same time, be so complete as to embrace all divisions of the subject necessary to a text-book for grammar and high schools. The book was begun several years ago, and much time has been spent in original research, and in the compilation of material. The aims have been to make the work not only simple but eminently practical both as to subject matter and method of treatment. In its preparation, the needs of the business man, the farmer, the mechanic, and the clerk, have been no less considered than those of the teacher and his class-room. Nor has the private student been forgotten. Every process is presented in detail, and yet with such brevity, clearness, and simplicity that those deficient in the fundamental operations may become expert, and master the subject without the aid of a teacher.

The arrangement of the contents of the book is based, as nearly as may be, upon a logical order of sequence. The simpler and more practical subjects are presented first. Involution and Evolution are introduced earlier than in most arithmetics, because of the necessary applications of Square Root and Cube Root in such a comprehensive treatment of Practical Measurements as is found in this work.

The definitions are brief, clear, and exact; the explanations and solutions are simple and comprehensible; and the reasoning is logical, accurate, and conclusive. The authors have endeavored without a multiplicity of words to make every process so plain that any one who will study, not only may understand, but cannot fail to assimilate the method presented.

In the examples the development of the thinking faculty has not been overlooked. It is recognized that mental power is not less important than acquisition of knowledge. To attain both of these results much time and labor have been devoted to the explanations and solutions on which the rules given are founded and to the

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statement of the principles. While the authors have endeavored to lead the learner to see the reason for the different processes, thus enabling him to derive his own methods for similar operations, they nevertheless believe that a clear and concise statement of the method to be pursued, embraced in a rule, is always helpful to the student. For this reason rules are generally given in connection with the various operations.

Under every rule such exercises have been prepared as will enable the diligent student to become quick and accurate in all computations. The variety of subjects presented furnish a thorough knowledge of approved business calculations. Special attention is invited to the practical expedients for rapid work given under each of the four fundamental rules and to the great number and variety of newly prepared and carefully graded problems found throughout the book. The searching review exercises afford necessary tests of the student's knowledge. They also fix in the memory the principles already studied, train the mind to habits of independent thought, and thus develop the power of correct reasoning.

To students deficient in a knowledge of Fractions the clear treatment of Common Fractions and Decimal Fractions will prove very helpful. To others the Metric System or Practical Measurements may be more needed; to still others Bills and Accounts, Percentage, and its applications, as Marking Goods, Trade Discounts, Commission, Inter-st, Discount, Exchange, Stocks and Bonds, etc., may prove most important. The extensive Drill Exercises in Rapid Addition, the Short Processes, and the section devoted to Commercial Paper, will be found of inestimable value to all persons engaged in business.

The authors earnestly believe that the book will prove to be all they have labored to make it, and that it will meet with general favor because it answers a public need. POUGHKEEPSIE, N. Y.,

June 1, 1904.

CONTENTS.

PAGE

68

Definitions...

9 Properties of Numbers..... 65

Notation and Numeration ... 9

Drill Exercises...

66

Arabic System.....

9 Divisibility of Numbers..... 66

Numeration Table...

10 Factoring

67

To Read Numbers Expressed Cancellation...

by Figures...

11

Practical Problems...

70

To Write Numbers in Figures 11

Greatest Common Divisor... 70

United States Money..

13

Least Common Multiple..... 72

Exercises..

13

Roman Notation..

Fractions....

75

Exercises...

15 Reduction of Fractions ..... 77

Addition...

16

To Reduce Whole or Mixed

Addition Table..

17

numbers to Improper Frac-

tions.

77

Drill Exercises, etc...

17

To Add Large Numbers. 20

To Reduce Improper Frac-

tions to Whole or Mixed

Practical Problemr...

23

Numbers.....

78

Shori Methods in A 'dition... 24

To Reduce Fractions to High-

Adding by Tens.....

25

er Terms..

78

Adding by Hundreds:

26

To Reduce Fractions to Low-

Rapid Addition..

27

er Terms..

79

Tables. ....

27

To Reduce Dissimilar Frac-

Drill Exercises..

30

tions to Similar Fractions 79

Adding by Hundreds. 32

Addition of Fractions..

81

Other Methods...

33

Practical Problems..

82

Horizontal Addition..

36

Subtraction of Fractions.. 82

Subtraction....

38

Practical Problems..

83

Subtraction Table.

38

Multiplication of Fractions... 84

Drill Exercises, etc..

39

To Multiply a Fractiou by an

Practical Problems..

42

Integer..

84

Multiplication.....

44 To Multiply an Integer by a

Multiplication Table

45

Fraction....

85

Drill Exercises, etc... .45 & 48 To Multiply a Fraction by a

Practical Problems.. 47 & 51

Fraction....

85

Division.....

52

Practical Problems.

87

Division Table...

Division of Fractions.

88

53

To Divide a Fraction by an

Drill Exercises, etc..

53 & 57

Integer....

88

Practical Problems.. .56 & 60

To Divide an Integer by a

Signs of Aggregation..

61

Fraction ...

88

Relation of Terms in Division 62

To Divide a Fraction by a

Arithmetical Analysis... 63

Fraction.....

89

Review...

64

Practical Problems..

91

PAGE

PAGE

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