THE SOUTHWORTH-STONE ARITHMETIC A RATIONAL METHOD BOOK II. FOR INTERMEDIATE GRADES GORDON A. SOUTHWORTH AND JOHN C. STONE, A.M. ASSOCIATE PROFESSOR OF MATHEMATICS, STATE NORMAL COLLEGE, PREFACE "The Southworth-Stone Arithmetic" is a graded series of three Books each separated into two Parts. The series is designed to cover the work of all the elementary grades in which a text-book is commonly used, beginning with the third-year grade and ending with the last year below the high school. The books have been prepared not by theorists to exploit their peculiar notions, but by teachers of long and successful experience. They follow the order of subjects and the lines of development established by the highest educational authorities. No attempt has been made to follow the so-called "spiral plan," now decadent; each grade, however, thoroughly reviews and carries forward the work of the preceding grades, new topics being introduced in order to stimulate the interest of the student and to develop his power. In the presentation of subjects the inductive method has been employed throughout in a way that calls for study and effort and secures that mathematical training that never comes by mechanical figuring and imitation. This logical development of subjects differentiates the series from mere books of problems. To secure skill and proficiency in the more important subjects, abundant exercises for drill and practice have been provided. A profusion of oral and written problems is given in about equal proportion. The number to be used must depend upon the need of the student. It will be found that fewer problems carefully solved and logically analyzed will be more valuable than many mechanically performed. Many subjects heretofore treated in arithmetics have been omitted as non-essential or beyond the legitimate work of the ele547419 mentary schools. Enough has been given, however, to meet the demands of business and to furnish the requisite mental discipline. The methods employed in all the books of the series have been tested in manuscript in the model or training classes in the State Normal College at Ypsilanti, Michigan. The authors acknowledge their indebtedness to Miss Abigail Roe and Miss Mary Steagall and other teachers in that institution for valuable suggestions growing out of such tests. Especial thanks are due to President L. H. Jones of the College, for his counsel as the work has progressed and for his aid in making the books worthy of adoption and use. This Second Book of "The Southworth-Stone Arithmetic" Series is designed for the use of fifth and sixth year pupils in graded schools. It is arranged in two parts. Part I presents the fundamental processes, the relations of numbers, common fractions, decimals, denominate numbers, and measurements, with many simple oral and written exercises and problems. In Part II the same subjects are more fully treated by way of reviews and illustrated by more difficult exercises. Percentage and its simpler applications are added. Abundant review problems are furnished. The appendix contains definitions of all technical terms used, for reference and reviews. (See Index.) NOTE. CONTENTS In this table of contents italics are used to indicate work in which the Parentheses are used to indicate coördinated or correlated subjects, or to show the PART I.-FIFTH GRADE Notation and numeration, a decimal system . Multiplication-definitions, principles Division relation to multiplication - |