•The Co THE MACMILLAN COMPANY NEW YORK BOSTON CHICAGO DALLAS ATLANTA SAN FRANCISCO MACMILLAN & CO., LIMITED LONDON. BOMBAY CALCUTTA MELBOURNE THE MACMILLAN CO. OF CANADA, LTD. TORONTO JAMES C. BYRNES, B.S., PH.M. MEMBER BOARD OF EXAMINERS, DEPARTMENT OF JULIA RICHMAN LATE DISTRICT SUPERINTENDENT OF SCHOOLS, NEW YORK JOHN S. ROBERTS, A.M., PD.M. DISTRICT SUPERINTENDENT OF SCHOOLS NEW YORK' New York THE MACMILLAN COMPANY 1913 All rights reserved PREFACE BOOK SIX, THE COMPLETE ARITHMETIC, of The Pupils' Arithmetic is designed for grammar grades with special emphasis upon the grade work of the seventh and eighth years. It harmonizes with the previous numbers of the series, preserving the terminology, the definitions, and the model forms of computation and of explanation that were developed and elaborated in the other volumes. The chapters on fundamental rules, common fractions, and decimals, and their subdivisions, are adapted to classroom use in all grades, though relieved of the details of method appropriate to a first presentation. Beginning with percentage, however, there is continued as from previous volumes the exposition and exemplification of modern methods of presentation which, though originally designed for the pupils' understanding, seem to have satisfied a need felt by teachers. Thus, the chapters on percentage, interest, longitude and time, the algebraic equation, and ratio and proportion are elaborated sufficiently to exhibit the divisions and subdivisions of each topic, the various types of drills, and the types of V |