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THE

ILLUSTRATIVE PRACTICAL

A R I T H M E T I C

BY A NATURAL METHOD,

WITH

DICTATION EXERCISES.

FOR COMMON SCHOOLS, HIGH SCHOOLS, NORMAL SCHOOLS,

AND ACADEMIES.

BY

GEO. A. WALTON, A.M., AND ELECTA N. L. WALTON,
AUTHORS OF “ WRITTEN ARITHMETIC,” “INTELLECTUAL ARITHMETIC,"

“ PICTORIAL PRIMARY ARITHMETIC,” ETC.

BOSTON:
BREWER AND TILESTON, 17 MILK STREET.

NEW YORK:
J. W. SCHERMERHORN & CO.

Proi, Vir 30 J. White,

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PUBLISHERS' NOTICE. EduaTl8.69.870

WALTONS' NORMAL SERIES.

This series of Arithmetics consists of three books, viz.: –

1. The Pictorial Primary Arithmetic (Normal Ed.).
2. The Intellectual Arithmetic (Normal Ed.).

3. The Illustrative Practical Arithmetic.
The Publishers present this series of Arithmetics in the hope that they may
meet the practical wants of the times, and the demand for text-books in which
the subjects are developed by a natural method.

The Primary and Intellectual Arithmetics have already an extensive circulation. As published in this series they retain all the features which have rendered them so generally popular. The definitions and explanations, and in some instances the phraseology of the examples have been modified to conform to the Illustrative Practical Arithmetic.

The Illustrative Practical Arithmetic is entirely new. It will, it is hoped, meet the wants of the large majority of the students of written Arithmetic, in all grades of schools, more fully than any other arithmetic before the public. For those who desire to pursue the subject further,

Waltons' Written Arithmetic

presents a more extended course and a fuller practice.

Walton's Dictation Exercises are supplementary to Waltons' Series, and afford a large amount of practice in the fundamental rules and in all the important practical applications of Arithmetic. They are designed for reviews and test exercises, and are adapted to every stage of the pupil's progress; they may be used in connection with any series of arithmetics.

Entered according to Act of Congress, in the year 1869, by

GEO. A. WALTON,
in the Clerk's Office of the District Court of the District of Massachusetts.

UNIVERSITY PRESS: WELCH, BIGELOW, & Co.,

CAMBRIDGE.

PREFACE.

THE plan of the Illustrative Practical Arithmetic is indicated by its title ; it embraces the following

GENERAL PRINCIPLES. 1. The subjects taught are presented in their natural order. Part I. contains an elementary course in the fundamental operations with applications to United States Money, Bills and Receipts. Part II. contains concise reviews of the fundamental operations, with rules ; Properties of Numbers ; Fractions, Common and Decimal; Compound Numbers and Metric System; Percentage, with its applications; Ratio and Proportion, with Partnership; Involution and Evolution; Mensuration. Contractions in Multiplication and Division, Annual Interest, etc., being incidental, are placed in an Appendix.

2. Ideas are excited by familiar illustrations, in which reference is always had to the objects themselves. See the treatment of the fundamental operations, Fractions, Percentage, etc.

3. The unknown is taught through the known. This principle is illustrated in every part of the book, which is so arranged that the occasion for knowledge which the pupil acquires is found in an illustration or in knowledge he previously possessed.

4. Each synthetic statement follows from a previous analysis. See the manner of deriving definitions and rules from the analysis of illustrative examples, with accompanying questions to be answered synthetically.

5. The language is an exact expression of the ideas excited by the illustrations. See definitions and explanations throughout the book.

It has been necessary in some instances to reject stereotyped forms of expression as meaningless, inappropriate, or contradictory, and to adopt language that describes the operations with greater accuracy, and whích in many cases is much more simple. See explanation of Subtraction, Multiplication, Fractions, Mensuration, etc.

6. Usually but one process is taught for a particular operation, and that the most practical. See Subtraction; Division of Integral Numbers and of Decimals; Interest ; Evolution, etc.

7. Matter and methods which have become obsolete or useless to the general student are rejected; such as English Notation ; much of Com

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