This textbook is for arithmetic students who can use numbers into the thousands in addition and subtraction, who know what ratio is and understand something about fractions, who know some facts of measures, and who have studied the multiplication tables. The book contains about a year's work, mostly in practice, partly in extension of knowledge. The new topics introduced here are direct outgrowths of earlier topics, and are presented in their simplest forms and relations. It also includes suggestions for teachers how to use the book for teaching. [Cover title varies: "Graded Arithmetics. Book Three--Grade IV."]