The use and applications of number vary with the changes and development of our industrial, commercial and social relations. The arithmetic of to-day is not the arithmetic of ten years ago. The fundamental principles and processes do not alter, but new applications constantly develop and older applications lessen in usefulness. In this sense, arithmetic is a living subject which deals with living phenomena.<br><br>In these days arithmetic is commonly used not only for the necessary routine computations incident to our private, business, or scientific affairs, but its processes are called upon to study facts through number and to interpret these facts - to put number into things rather than to take number from them. Moreover, the modern use of number often takes the form of a language, as in the construction or reading of numerical illustrations, and statements or statistics which are designed to impress upon others certain facts or conditions. Thus modern arithmetic may be said to have a use as a tool, i. e., for routine computation, an interpretive use, and a language use.<br><br>But accuracy and facility in the use of most working instruments presuppose a knowledge of the fundamental parts of the instrument, of the interrelation of these parts, of their working principles, and of the classes of material or work to which they may be applied. Thus, facility in the three "uses" of the arithmetic instrument is founded, primarily, on a logical working knowledge of the fundamental operations and principles. This is the more necessary because the arithmetic problems of actual life do not have a text-book form of statement. If formulated at all, they may offer no direct clue to a particular subdivision of the subject.