This textbook is a sixth-grade course in arithmetic. The topics in book V are reviewed in this book. Some topics, as fractions, are completed as special subjects; and others, like percentage, enlarged. Compound numbers are completed, and ratio introduced. The latter subject will be found helpful in much of the higher work in percentage, and it has been introduced a little earlier than usual. Two or three topics are placed at the end of the book so that they may be more easily omitted unless the course of study demands that they shall be taught. A thorough mastery of any subject comes only from repetition; hence many review exercises are given so that the pupil may be able to rely upon himself and learn to work absolutely without assistance. Principles are taught, and not rules; and the work is made practical, so that the pupil can be prepared for the affairs of every-day life.