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BY

FREDERICK, H. SOMERVILLE, B.S.

THE WILLIAM PENN CHARTER SCHOOL, PHILADELPHIA

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NEW YORK.:. CINCINNATI .:. CHICAGO
AMERICAN BOOK COMPANY

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PREFACE

THE plan of the early pages of this text is to offer a gradual introduction to the subject without plunging the young student too deeply into new difficulties. The treatment of negative numbers as a natural extension of the familiar arithmetical numbers, and a generous amount of detail in the explanations of the early chapters, serve to clarify the beginnings of a subject so often troublesome. New processes are accomplished by the use of the simplest of symbols, and the undivided attention of the student is centered upon the new elements of the operation at hand. Definitions are introduced only as rapidly as new processes call for them, and the young mind is not confused and discouraged at the outset by the attempt to learn the meaning of a bewildering mass of strange terms.

In arrangement the book does not differ widely from the general scheme of the standard texts, but in some details there are changes that have been found to be of genuine value in the classroom. For example, in Factoring, the simple and the difficult types are separated; an elementary course gives a treatment free from complex forms, while a supplementary section provides for the preparation of college requirements. The Lowest Common Multiple and its immediate application to Addition of Fractions form a single chapter, and the plan suggested by this order has proved to be natural, practical, and sound. The classification of Simple Simultaneous Equations and of the Theory of Exponents is both new and teachable, and the logical arrangement of Affected Quadratic Equations provides a chapter that, while omitting no essential, gives a brief and clear general treatment of this important subject. Throughout the early chapters exercises for oral drill are frequent, and their introduction confines the simplest types

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