This textbook is second in a series of arithmetic books that apply the principles discovered by the psychology of learning, by experimental education, and by the observation of successful school practice, to the teaching of arithmetic. Parts One and Two are intended for grades five and six respectively. Part One provides for mastery of the four operations with such common fractions as the pupils will meet in life, and for ability in the four operations with decimal numbers, in simple cases. Part Two completes the training with decimals, gives mastery of computations with percents and with such denominate numbers as the pupil will meet, and provides experience in simple accounting. The training of Part One in observing and using the relations of numbers is extended and systematized. The applications of arithmetic include simple problems in computing areas, volumes, wages, commissions, discounts, and advances. [For Book One, see ED623794.]