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FOR SCHOOLS.

BY

ROBERT MILLER, M.A.,

TEACHER OF ARITHMETIC AND MATHEMATICS,
GEORGE WATSON'S COLLEGE SCHOOLS FOR YOUNG LADIES, AND

THE PHILOSOPHICAL INSTITUTION, EDINBURGH,

PART I.

LONDON : SIMPKIN, MARSHALL, & CO.
EDINBURGH:J. MENZIES & CO., & W. A. MILLER.

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Also Published, Answers to the Exercises in the Practical Arithmetic.

Price 6d.

Exercise Tables in Elementary Arithmetic for Drilling

Classes Simultaneously. Price lzd.

EDINBURGH:
PRINTED BY JOHN GREIG AND SON.

PREFACE.

THE "PRACTICAL ARITHMETIC" is designed to supply a text-book in which vulgar fractions are introduced at a much earlier stage than usual. This is accomplished by a series of easy initiatory exercises suited to the attainments of the pupil. The difficulties which present themselves in the study of the compound rules, and even in some parts of the simple rules, as in division by factors, fractional multipliers, and divisors, &c., are thus not only overcome, but are found to afford scope for the continued revisal and application of the principles already studied, as well as to prepare the minds of the pupils for the better understanding of the more difficult exercises that follow. All discussion of theoretical principles, which can be best taught by the master in his own way, has been avoided, but lists of “Terms requiring to be Explained” have been introduced, which it is hoped may be found useful to the teacher, and afford assistance to the pupils in remembering the instructions they receive. A few explanatory notes

and fully wrought-out examples have also been added where necessary

In Mental Arithmetic, varied examples of exercises suited to the several stages of advancement are given; and only those rules are stated which are really useful and easily remembered.

To a few of the examples at the beginning of each new set of exercises the answers have been appended, which will often be found a source of instruction and encouragement to the pupil. The other answers and solutions of a few of the more difficult problems will be found in the key. Care has been taken to give the historical dates introduced into some of the questions, and which refer only to important events, in chronological order.

The exercise tables, which should be used daily in combination with the ordinary slate work, will be found of great value in drilling classes simultaneously, and as affording an interesting and useful method of securing accuracy and expertness.

Part II. will contain exercises in the Weights and Measures, Decimal Fractions, the Metric System, the various applications of Proportion, Roots, &c.

EDINBURGH, 13th September 1873.

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