ARITHMETIC. Viewed as a science, arithmetic is a branch of mathematics; looken on as an art, its object is to carry out for practical purposes certain rules regarding numbers, without troubling it self to investigate the foundation on which those rules are based.
It is variously divided, as into integral and fractional arithmetic, the former treating of integers and the latter of fractions. Integral arithmetic is some times called vulgar or common arithme tic; and from fractional arithmetic is sometimes separated decimal arithmetic, treating, as the name implies, of decimal; There are also logarithmic arithmetic for computation by logarithms, and instru mental arithmetic for calculation by means of instruments or machines. An other division is into theoretical arith metic, treating of the science of numbers, and practical arithmetic, which points out the best method of practically work ing questions or sums. Political arith metic is arithmetic applied to political economy, as is done in the statistical re turns so continually presented to Parlia ment or Congress. Finally, universal
arithmetic is a name sometimes applied to algebra. The chief subjects generally treated under the science or art of arith metic are: (1) numeration and notation; (2) addition; (3) subtraction; (4) mul tiplication; (5) division; (6) reduction; (7) compound addition; (8) compound subtraction; (9) compound multiplica tion; (10) compound division; (11) simple proportion (rule of three) ; (12) compound proportion; (13) vulgar frac tions; (14) decimal fractions; (15) duodecimals; (16) involution; (17) evo lution; (18) ratios, proportions, and progressions; (19) fellowship or part nership; (20) simple interest; (21) com pound interest, and (22) position. Of these, the most important are the simple processes of addition, subtraction, multi plication and division, the judicious use of which, singly or in combination, will solve the most complex arithmetical questions.