PREFACE An arithmetic designed for pupils of the Fifth and Sixth Grades must combine drill upon fundamental operations, including decimals and common fractions, with as wide an application of these principles to the common experiences of life as possible. While the children in these grades are immature and have had very limited practical experiences, it is necessary to include simple examples drawn from real facts and from genuine business transactions. Wherever possible the applied problems are taken from the actual experiences of children themselves and in all cases the facts upon which the problems are based are accurate and of real informational value. The fact that many pupils leave school at the end of the Sixth Grade to go to work, and that there is an increasing tendency to substitute junior high school courses, make the intermediate arithmetic a fundamentally important text book. If for an appreciable number of pupils the intermediate arithmetic offers the last formal training in mathematics, it is necessary so far as possible to include the arithmetical processes and topics used under ordinary conditions of life. Attention is called to the psychological plan of this book, by which the previous knowledge of the child is utilized in introducing a new subject. The development of the subject of decimals is based upon the knowledge of common fractions already secured. In this way teachers find little difficulty in developing a subject which not infrequently has caused mental confusion. The fact that in the presentation of the subject of denominate numbers, the use of both decimals and common fractions in the solution of problems is emphasized, simplifies another subject often troublesome to children. In a similar way the treatment of percentage is based upon the knowledge of decimals and common fractions and, while giving a practical elementary knowledge, is in no way beyond the understanding of the child. In this book, as in the other books of the series, the idea of systematic, standardized drill is emphasized. The practice exercises in fractions presented in Chapter I, Part II, will prove of great value in developing a clear conception of simple fractions and ability to perform the fundamental operations in fractions with speed and accuracy. In the preparation of this Arithmetic, the authors have had the efficient aid of Miss Myra Banks, of the Winnetka (Ill.) Public Schools, and of Miss Katherine L. McLaughlin, of the School of Education, University of Chicago; and they are also indebted to Miss Annie J. Robinson, Principal of Case-Woodland School, Cleveland, for valuable criticisms and suggestions. CONTENTS PART I- - FIFTH YEAR CHAPTER I. REVIEW OF THE FUNDAMENTALS-1-40 EARNING MONEY, 1; READING AND WRITING NUMBERS, 3; ROMAN NUMER- Als, 5; ADDING BY ENDINGS, 6; Explanation of Addition, 9; EXPLANATION OF SUBTRACTION, 12; EXPLANATION OF MULTIPLICATION, 20; EXPLANATION OF CHAPTER II. FACTORS AND MULTIPLES-41-50 FACTORS, 41; DIVISIBILITY OF NUMBERS, 42; TESTS OF DIVISIBILITY, 46; CHANGING TO LOWEST TERMS, 59; ADDING FRACTIONS, 60; FRACTIONAL EQUIVALENTS, 61; CHANGING TO HIGHER TERMS, 63; SUBTRACTION OF FRAC- TIONS, 67; MULTIPLYING AN INTEGER BY A FRACTION, 70; MULTIPLYING A FRACTION BY A FRACTION, 72; MULTIPLYING A MIXED NUMBER BY A FRAC- TION, 75; DIVIDING A FRACTION BY AN INTEGER, 77; DIVIDING A FRACTION CHAPTER IV. DECIMAL FRACTIONS-95-115 U. S. MONEY, 95; DECIMAL PLACES, 97; ADDITION OF DECIMALS, 99; Sub- U.S. POSTAL SAVINGS BANKS, 116; CHRISTMAS SAVINGS CLUBS, 118; SCHOOL- CHAPTER VI. WEIGHTS AND MEASURES-124-140 MEASURES OF LENGTH, 124; TABLE OF LONG MEASURE, 125; TABLE OF SQUARE MEASURE, 129; AREAS OF RECTANGLES, 131; MEASURES OF WEIGHT, 133; Table of Avoirdupois WEIGHT, 133; CUBIC MEASURE, 135; Table of |