ARITHMETIC BOOK TWO REVISED BY JOHN W. HOPKINS SUPERINTENDENT OF THE GALVESTON PUBLIC SCHOOLS AND P. H. UNDERWOOD TEACHER OF MATHEMATICS, BALL HIGH SCHOOL New York THE MACMILLAN COMPANY 1918 All rights reserved HARYARD COLLEGE LIBRARY GIFT OF GINN & CO. DEC 11 1930 COPYRIGHT, 1912, 1918, BY THE MACMILLAN COMPANY. Set up and electrotyped. Published April, 1912. Reprinted Norwood Press J. S. Cushing Co. Berwick & Smith Co. PREFACE THIS book assumes that the pupils using it have a working knowledge of the four fundamental principles of arithmetic as applied to integers and to United States money. It presents the essentials of practical arithmetic, arranged by topics in conformity with the courses of study in some of the best school systems, each chapter representing a year's work, commencing with the fifth grade. Its distinguishing features are the early introduction of decimals, the large number of problems based on the industries of our country, the clearness of illustration, and the omission of complicated problems of doubtful utility. It aims to teach principles rather than rules. As the unitary method is the simplest for the young learner, the first two chapters give prominence to it. The chief aim of teaching arithmetic is doubtless to develop accuracy and rapidity in the solution of problems arising in actual life and also to cultivate correct methods of reasoning. Both these aims are kept in view throughout the book. However, as students learn readily to follow processes, and, as the practice of arithmetic is of more importance to most people than its theory, especial attention is paid to the art of computation. Chapters III and IV give a thorough review of the principles and practice of arithmetic. In these chapters V |