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THE

MODEL

MENTAL ARITHMETIC;

CONTAINING

ORAL EXERCISES

FOR

Braded and Bran

rammar Schools.

BY

EDGAR A. SINGER,
PRINCIPAL OF HENRY W. HALLIWELL GRAMMAR SCHOOL, PHILADELPHIA.

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MARYARD CIEL.BRARY

FROM THE GIFT OF
CHARLES HERE! IT TIURBER

MAR 5 1926

EducT 118.76.793

THE

MODEL SERIES OF ARITHMETICS

COMPRISES

I. The Model Primary Arithmetic.
II. The Model Elementary Arithmetic.
III. The Model Common School Arithmetic,

IV. The Model Mental Arithmetic.
These text-books on Arithmetic are published in the belief that
they are based upon correct principles, and that a carefully matured
plan is consistently adhered to throughout the series.

Progress from the easy to the difficult is gradual, but sure and effective; inductive oral exercises render plain the principles underlying every operation in written Arithmetic; and these principles the pupil is required to apply, as soon as they are learned, in the solution of problems varied and practical, and adapted to his understanding and his stage of advancement.

Entered, according to Act of Congress, in the year 1876, by

ELDREDGE & BROT II ER,
in the Office of the Librarian of Congress, at Washington.

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PREFACE.

THE
HE present work is designed to review the principles of the

fundamental rules presented in the author's Primary Arithmetic, and to extend, by further illustrations and analyses, those included in the Elementary and the Common School Arithmetic. It is, however, complete in itself, and may be used independently or in connection with any series of Arithmetics.

The only essential difference between oral and written arithmetic is, that oral or mental arithmetic implies the performance of computations without the aid of written operations or solutions; hence, the arrangement of topics presented in the Written Arithmetics has been observed in this work. The same definitions, so far as they are necessary to a complete understanding of the subject, are given; as are, also, the same formal statements of principles. It is designed that pupils may perceive and understand that mental arithmetic is not a separate and distinct branch of the science of numbers; that it is not a substitute for written arithmetic; but that each is the complement of the other, and that both are but portions of one harmonious whole, which, in its entirety, requires a full and uniform development of all its subordinate parts.

The importance of mental arithmetic as a means of intellectual training can scarcely be overestimated. It ensures ability to catch principles from oral statement; to understand them; to carry them through a course of reasoning, and to apply them practically in the solution of problems. Its object, then, is twofold: First. To develop and strengthen the thinking and reasoning faculties. Second. To en

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