GORDON A. SOUTHWORTH SUPERINTENDENT OF SCHOOLS, SOMERVILLE, MASSACHUSETTS 66 66 AUTHOR OF ESSENTIALS OF ARITHMETIC," BOOKS I AND II, ENGLISH οὐ πόλλ' ἀλλὰ πολύ BENJ. H. SANBORN & CO. BOSTON, U.S.A. THE ESSENTIALS OF ARITHMETIC. Book II. For Both books are published with and without answers. Key to Book II. for use of Teachers only. COPYRIGHT, 1903, BY GORDON A. SOUTHWORTH. Norwood Press J. S. Cushing & Co. - Berwick & Smith MARVARD COLLEGE LIBRARY TRANSFERRED FROM THE LIBRARY OF THE GRADUATE SCHOOL OF EDUCAT PREFACE THIS book of Problems has been prepared by the author of "The Essentials of Arithmetic." It is sufficiently complete to be used independently as a text-book in arithmetic, or it may be used to furnish supplementary work in connection with any other book. It covers the work commonly assigned to the three upper grades in grammar schools. Oral and written problems are given, generally on opposite pages, in great variety and in nearly equal numbers. They are in the main comparatively simple, but they cover all essential principles. The more important subjects have received especial attention. Miscellaneous problems suitable for reviews and tests abound. Definitions, tables, and rules are given for reference if needed. Accuracy and speed in calculations are very desirable, and come from much careful practice in fundamental processes. The ability to see the relations of numbers, to understand principles and methods, to reason from premise to conclusion, and to know exactly what to do under given conditions, cannot be secured by mere repetition or the working of many similar examples. Fewer problems, if solved independently and logically analyzed, will do more toward attaining the higher purpose of arithmetical work. The thanks of author and publishers are extended to teachers and others who have made contributions to the book. iii |