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Greenleaf's Mathematical Series.

THE

COMPLETE

ARITHMETIC,

ORAL AND WRITTEN,

ON THE BASIS OF WORKS

By BENJAMIN GREENLEAF, A.M.

THOS. R. SHEWELL & COMPANY

BOSTON NEW YORK CHICAGO

HARVARD
UNIVERSITY
LIBRARY

GREENLEAF'S

MATHEMATICAL SERIES.

INDUCTIVE COURSE.

FIRST LESSONS IN NUMBERS.
A BRIEF COURSE IN ARITHMETIC.
THE COMPLETE ARITHMETIC.

The “ Brief Course " and the “ Complete Arithmetic " are each published with and without Answers. · KEY to the “Complete Arithmetic,” for Teachers only.

COPYRIGHT, 1881, BY HENRY B. MAGLATHLIN.

COPYRIGHT, 1896, by HENRY B. MagLATHLIN.

Norwood Press :
Berwick & Smith, Boston, U.S.A.

PREFACE.

THIS Arithmetic, undertaken at the suggestion of many educators of distinction, has been prepared with special reference to training for practical business, and to development of mind power through fixed habits of attention and lucid processes of reasoning.

To secure skill, rapidity, and accuracy in the use of numbers, required in common transactions, a large number of comparatively simple business questions has been provided, and prominence has been given to subjects of the most practical value.

That useful mental discipline may be attained the theory and principles of numbers have been clearly presented, and problems have been given requiring thought and discrimination.

The inductive plan has been followed throughout, principles have been developed from methods, rules derived from analyses, and oral and written exercises combined in a rational manner.

The greatest care has been observed to have the definitions brief, clear, and accurate, and the solutions simple, concise, and logical.

The methods employed are those which business experience, or test in the school-room, has shown to be the best.

Decimals to three places, and United States money, are simply treated at the beginning with integers.

The problems are abundant and varied, based on recent and reliable data, and drawn from the actual experiences of life. In

commercial arithmetic the usages of the best business houses have been followed.

Several hundred examples which have been used in examinations by superintendents of public instruction, in various cities and towns leading in educational matters, have been collected, and arranged as exercises for testing proficiency, and for supplementary practice, to be drawn from at the teacher's discretion.

Much matter formerly considered necessary in an arithmetic, but which modern progress has rendered useless or antiquated, has been omitted.

The Appendix contains tables for reference; information of a somewhat technical nature for the business man, the mechanic, and the farmer; subjects of minor importance to the majority of pupils; and rules and applications not needed in the body of the work.

The course of this book may be abridged by the omission of the metric system, foreign exchange, compound proportion, cube root, and similar solids; likewise by omission of problems in interest, and review exercises in part. '

Indebtedness is gratefully acknowledged to all the able teachers who have aided in the preparation of the Inductive Course of which this book is a part; to school superintendents of various cities and towns for examination papers and suggestions; to prominent educators in Vermont for material for work in Interest and Taxes from actual business transactions; and to the reports of State and National officials for up-to-date information of great value.

SILVER LAKE, MASS., May, 1899.

CONTENTS.

Course

. 119

........

126

136

... 143

Notation and Numeration .....

Capacity Measures.........

Addition...

.......

Weights .......

... 120

Subtraction ...............

Time.......... ........ 121

Miscellaneous Exercises

Arc and Angle...... .. 123

Multiplication ............. 27 Miscellaneous.

: 124

Miscellaneous Exercises .... Compound Numbers..

Division ....................

Reduction .

. 126

Miscellaneous Exercises ....

Addition................

Review .........

Subtraction .......

Factors ...................

Multiplication ..... ... 138

Cancellation ............

Division.....

................. 138

Greatest Common Divisor..

Miscellaneous Exercises ....

Least Common Multiple.... The Metric System...

. 141

Miscellaneous Exercises ....

Length Measures......... 142

Common Fractions ..........

Surface Measures.....

Reduction of Fractions.....

Volume Measures......

Addition of Fractions...... Capacity Measures.......

Subtraction of Fractions ...

Weight Measures.........

... 146

Multiplication of Fractions. Reduction of Units. ...... 148

Division of Fractions...... Measurements .......

... 151

Miscellaneous Exercises ....

Surfaces.

Review .....................

Volumes ................

154

Decimal Fractions......

95 Wood Measure...........

Reduction of Decimals....

Board Measure...........

Multiplication of Decimals. Miscellaneous Exercises....
Division of Decimals....... 101 | Review ..

............ .....

..... 161

Miscellaneous Exercises .... Percentage .................

... 167

United States Money .......

... 106 Profit and Loss............

.. 173

Aliquot Parts......... ... 109 Commission ..... ... 175

Accounts and Bills.....

Insurance....

... 177

Weights and Measures....

Miscellaneous Exercises. ...

Length Measures. ...... 116 ! Interest ......... ...........

Surface Measures....... ... 117 Simple Interest........... 181

Volume Measures. ....... 118 | Exact Interest .............

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