Containing less than four hundred pages and more than five thousand problems, the COMPLETE EDITION will be found to embrace within convenient dimensions the largest and most varied collection of practical business problems ever before published. These problems have been systematically arranged under appropriate heads and sub-heads to facilitate their selection to illustrate any required principle of arithmetic or custom of business; and to test the pupil's discriminating knowledge of its subdivisions, each subject is concluded with a set of problems promiscuously arranged, numbering from twenty-five to one hundred and fifty according to its relative importance.

Most of the problems are reflexes of actual, every-day business transactions; though a few of a different character are occasionally introduced to develop and cultivate an ability for abstract reasoning, and thus prepare the pupil for the otherwise too sudden change from the study of arithmetic to that of the higher mathematics. The use of these purely disciplinary problems should however be limited to the class of pupils for whom they are intended.

To increase the usefulness of this arithmetic, every admissible subject is preceded by a set of carefully prepared inductive questions which, reasoning from the known to the unknown, exhibit the application of knowledge already acquired in developing the successive steps in the solution of a new class of problems. These inductive questions will be found more intelligible to the pupil and hence more permanent in remembrance than the explanations and rules of the older arithmetics, which, if used at all, are to the average pupil simply so many temptations to mechanical work.

The uniformly favorable criticisms of the educational press upon their INDUCTIVE ARITHMETIC, together with the many flattering commendations of teachers who have tested it in the school-room, encourage its authors to believe that the additional modern innovations upon obsolete methods contained in their HAND-BOOK OF ARITHMETIC will receive impartial investigation and merit equally favorable indorsement.

THE AUTHORS.

NUMERATION AND NOTATION.

By the Arabic method a number is written or read with direct reference to its
successive PERIODS, commencing with the highest; and by the Roman method, with
direct reference to its successive ORDERS.

Express, by means of figures, the following numbers:
69. Three hundred and eighteen dollars, fifty cents.
70. Five hundred and seven dollars, thirty-five cents.