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PREFACE

THE object of this revision of Ray's "New Intellectual Arithmetic" is to adapt the book more thoroughly to modern methods of instruction, without destroying any of the features that have so long held the favor of thousands of teachers and pupils.

Many important improvements have been introduced, with a design to impart completeness, and give a concise and progressive course of arithmetical analysis.

The volume in its present form embraces :

1. Exercises on the primary principles and their applications, together with models of analysis in the shape of solutions.

2. A progressive and comprehensive presentation of Fractions, intended to render the subject intelligible and attractive.

3. General reviews, designed to test the pupil's knowledge of principles, preparatory to the applications of mental analysis which follow.

4. Reduction, Practical Measurements, and Percentage, with the application of the latter to Profit and Loss, Commission, Insurance, and Interest.

Much work in pure number has been added to supply the drill that leads to accuracy and rapidity in reckoning.

The value of Intellectual Arithmetic is so highly appreciated that little need be said in its favor. When properly taught, it is one of the most useful and interesting studies in which students can engage. It forces the pupil to reason, to analyze, to think for himself; while it imparts confidence in his reasoning powers and strengthens his mental faculties.

TO TEACHERS

THE solution of an example in Mental Arithmetic is herein regarded as a direct and natural response to the requirements of the problem; it aims to be a plain and simple statement of the successive steps leading to the final result or answer. The data afforded by the example are repeated in the solution no further than is necessary for its clear statement.

Every different class of examples is furnished with a solution; in a few instances more than one solution is given, the succeeding solutions offering a briefer method. No solution is repeated; and, when a solution, in whole or in part, occurs in a subsequent solution as a portion of the argument, its result is given as briefly as possible. Of course, there is nothing to prevent the teacher from elaborating any solution, or any portion of it, to the fullest extent he sees fit.

MODERN INTELLECTUAL ARITHMETIC

Written

Printed

The numbers from one to ten are written and printed as follows:

Written

Printed

One

1

1

ADDITION

Six

6

6

LESSON I

[blocks in formation]

1. Ella put 1 glove on her right hand and 1 on her left hand. How many gloves had she on?

Ans. 2.

Why? Ans. Because 1 and 1 are 2.

2. Herbert had 2 cents, and earned 1 cent more. How many cents had he in all? Ans. 3.

Why? Ans. Because 2 and 1 are 3.

3. Robert had 1 tennis ball, and bought 3 balls more. How many did he then have Ans. 4.

Why? Ans. Because 1 and 3 are

4. Ada had 4 books, and her mother gave her 1 book more. How many books had she all together?

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