Efficiency Arithmetic

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PREFACE

This book has been prepared in the belief that work in Arithmetic in the seventh and eighth grades should emphasize drill upon fundamentals and their application to living, vital problems that the average child is almost sure to encounter in his individual experiences. At the same time, it is recognized that for the great majority using the books of this series certain topics will never receive consideration in the school training unless presented in this volume. Great care has been taken to present these topics in a simple, clear manner which ought to make their meaning and significance intelligible even to the younger pupils.

The problems of the book, almost without exception, are actual problems taken from the various lines of business represented. Business men from all sections of the country have contributed problems, furnished definite and accurate information upon which to base problems, and have criticized the work from the standpoint of practical efficiency and reliability. Acknowledgment is hereby made to these gentlemen for their invaluable assistance.

The methods of presentation and explanation of topics new to the child have been carefully tested in the school room and their effectiveness is thereby assured. Simplicity, clearness, and the avoidance of unnecessary repetition we believe to be characteristic of this series, especially in the applications of percentage and practical measurements which so often unnecessarily confuse the pupil.

Many school systems are modifying their courses in mathemathics in order to permit elementary algebra to be commenced in the eighth grade. This volume permits, through its arrangement, a very simple omission of topics in Part I which will

enable any teacher to cover the essential topics in less than the customary two years. The arrangement also enables those who prefer to postpone some of the topics found in Part I to combine the seventh- and eighth-grade topics in such a way as to give a more extended discussion of closely related subjects. The fact that there are in reality only a few mathematical principles involved in ordinary arithmetic is kept clearly in mind. Too often the pupil has been led to believe that each new topic has little in common with preceding topics and therefore fails to learn the greatest educational lesson that can be taught the application of a known principle to a new condition. The effort in this book is to keep the relationship between mathematical facts constantly before the pupil.

Teachers of arithmetic must never forget that accuracy and reasonable rapidity in manipulation of numbers are one of the chief aims in this study. Pupils of the seventh and eighth grades need continued practice of this kind. Ample opportunity for this drill is furnished, and from the beginning to the end of the course there should be recurrence to these exercises.

While it is not possible, in the limited space, to make personal acknowledgment to the large number of educators who have rendered assistance of great value in the preparation of this volume, the authors desire to express their indebtedness especially to Miss Katherine L. McLaughlin of the Elementary School of the School of Education, University of Chicago, to Mr. Warren E. Hicks, Assistant for Industrial Education, Department of Public Instruction, Madison, Wisconsin, to Mr. Lewis A. Bennert, Principal of School No. 3, Patterson, New Jersey, and to Mr. James C. Thomas of the publishers' editorial department, for their invaluable criticisms and suggestions.

CONTENTS

PART I-SEVENTH YEAR

CHAPTER I. REVIEW OF THE FUNDAMENTALS-1-22

TRAINING FOR SPEED AND ACCURACY.

CHAPTER II. REVIEW OF FRACTIONS-23-44

THREE MEANINGS OF FRACTIONS, 23; REDUCTION OF FRACTIONS, 23;

ADDITION AND SUBSTRACTION OF FRACTIONS, 25; MULTIPLICATION AND

DIVISION OF FRACTIONS, 29; REVIEW OF DECIMALS, 34; APPLIED REVIEW

PROBLEMS IN FRACTIONS, 41.