This textbook is a fifth-grade course in arithmetic. It contains a review of the work done in Book IV, the extension of the principles taught there to more difficult problems, and a few new topics. Notation and numeration receive more attention. The work in fractions is extended to include multiplication and division, using only small denominators. The subject of bills is introduced under the head of decimal fractions. The subject of compound numbers is enlarged and includes their addition. Examples in percentage previously performed by using the common fraction representing the percent, are now solved decimally. The work in measurements, believed to be a valuable feature of the previous grades, is here extended to area of circles, cylinders, and cones. Interest by an easy, short, and "business" method is taken up. The reason for introducing so many lessons of a miscellaneous character should not be overlooked. These lessons give a constant review, and are far more beneficial to a pupil than examples all classified and labeled for him.