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BOSTON, U.S.A.
D. C. HEATH & CO., PUBLISHERS

Oro

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PREFACE.

In preparing this book, the aim has been to make it complete, so that it might cover with sufficient fulness the topics usually required in common and grammar schools.

The aim also has been to make the work practical, i.e. to use only such rules, definitions, solutions, and problems as would accustom the learner to reason, compute, and estimate with the same facility and economy of thought with which business men reason, compute, and estimate in practical life.

Great care has been exercised to omit the merely theo retical and the unpractical, as well as problems that are too hard for the grades for which the book is intended.

The relations of the inductive work, the definition, the solution, the rule, are such that the learner, with a minimum of help, should easily master the difficulties through the logical progression of the steps from the known to the unknown.

While care has been exercised in selecting a great variety of practical business problems and in arranging them progressively, the development of mental power has been kept constantly in view.

The arrangement of this book is topical, but subjects previously studied are kept fresh in the minds of the pupils by frequent carefully prepared reviews.

iii

Questions of relation, as treated in connection with divi. sion of fractions, will be found helpful in overcoming a group of difficulties which, in the author's experience, are trying to all children. When these are mastered by the learner, he will later have little or no difficulty with Percentage and its applications.

The practice of referring percentage problems back to the original questions of relation has proved highly successful in the experience of many teachers.

A wide variety as well as a great number of topical review and miscellaneous problems are given in the last part of the book.

Thanks are due to the various superintendents of city schools who have kindly furnished copies of recent examination questions, which largely constitute the topical review of this book.

The author has also received invaluable aid from many leading educators, all of whom he desires to thank most cordially.

C. E. W. SYRACUSE, N.Y.,

January 24, 1901.

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