AMERICAN NIV OF COMPREHENSIVE ARITHMETIC BY M. A. BAILEY, A.M. PROFESSOR OF MATHEMATICS IN THE KANSAS STATE NEW YORK: CINCINNATI CHICAGO PREFACE In this work, the divisions of arithmetic are presented in their natural order. The fundamental operations upon integers, common fractions, decimals, denominate numbers, and numbers expressed by letters, are followed by their applications to business and to various employments. The introduction of the chapter on literal quantities is somewhat of an innovation, but is in accord with the views of leading teachers, and is based upon sound principles. The elementary parts of algebra should be studied before the advanced parts of arithmetic, because they are more easily comprehended, and because they afford valuable assistance in difficult problems. For the same reasons, the solution of many classes of problems should be taught by algebraic processes, before they are taught by the intricate methods required by analysis. The fact, too, that most pupils must leave school quite early, is a strong reason for introducing into arithmetic the elements of algebra and the conclusions of geometry. From the beginning, the pupil is taught to develop observation and thought power. Instead of being required to memorize a large number of rules and directions, he is encouraged to fix well in mind the result to be obtained, to consider carefully the |