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THE

ELEMENTARY

ARITHMETIC,

ORAL AND WRITTEN.

BY

ALBERT N. RAUB, A.M.,

PRESIDENT OF DELAWARE COLLEGE, NEWARK, DELAWARE, AND

AUTHOR OF "THE COMPLETE ARITHMETIC."

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Edue T 118.94.723

MARWARD COLLEGE LOARY

GIFT OF THE
GRADUATE SCHOOL OF EDUCATION

21 F2

Copyright, 1877. by PORTER & COATES.
Copyright, 1894, by THE WERNER COMPANY.

PREFACE.

BELIEVING that Oral and written Arithmetic form properly but a single study, and that they are best taught together, the author has in this, as in his Complete Arithmetic, combined both oral and written exercises in the same book.

In the composition of the book two main objects have been steadily kept in view: first, that of teaching the elements of Arithmetic thoroughly; and, secondly, that of training the pupil to think for himself and apply his knowledge of the science to the actual business operations of life.

In order that the pupil may understand the practical application of Arithmetic, and at the same time acquire a knowledge of the business use of the science as he proceeds, the problems given are almost wholly drawn from the actual business operations of life.

Extended exercises are given in the application of the fundamental rules, because these are the basis of all the operations of Arithmetic.

The definitions are brief and accurate, and it is believed they are all clothed in such language as the pupils can readily comprehend.

Every effort has been put forth to make the book a desirable one, not only for the pupil in learning the elements of Arithmetic, but also for the teacher in presenting the principles to the mind of the learner. It is believed, and confidently hoped, that progressive teachers everywhere will find it well adapted to their wants.

A. N. R.

3

PAG.

... 130

SECTION CHAPTER I.

PAGE SECTION

CHAPTER V.

iFinn V. PAGE

INTEGERS...... .....

Decimal Fractions.............. 118

I. Notation and Numeration. 9 I. Notation and Numeration. 118

II. Addition....................... 19 II. Reduction of Decimals... 121

III. Subtraction..................... III. Addition of Decimals ...... 123

IV. Multiplication ............. | IV. Subtraction of Decimals. 124

V. Division ..................

V. Multiplication of Deci-

mals...... ................. 125

CHAPTER II.

VI. Division of Decimals ...... 126

UNITED States MONEY............ 66

I. Definitions and Principles. 66

CHAPTER VI.

II. Reduction of U.S. Money. 68 DENOMINATE NUMBERS. .......... 128

III. Addition of U. S. Money. 69 I. Definitions.... ..............

IV. Subtraction of U.S. Money 71 II. Tables and Measures......

V. Multiplication of U. S.

Money ........................ 72

Weight.....................

VI. Division of U. S. Money. 74 Extension ...............

Bills..........

............ 77

Volume ..................

..... 137

Capacity. ..............

......... 139

CHAPTER III.

Time.........

...... 141

PROPERTIES OF NUMBERS......... 79

Angles ......................

1. Factors and Multiples...... 79 Compound Numbers....... 146
Cancellation................

1. Addition of Com-

II. Greatest Common Divisor. 83

pound Numbers... 146

III. Least Common Multiple... 85 2. Subtraction of Com-

pound Numbers... 148

CHAPTER IV.

3. Multiplication of

FRACTIONS .............

Comp'd Numbers. 149

4. Division of Com-

II. Reduction of Fractions...

pound Numbers... 150

Common Denominator.. 96

Least Common Denom-

CHAPTER VII.

inator ..................... 97 PERCENTAGE........................ 152

III. Addition of Fractions..... 98 I. Definitions and Principles 152

IV. Subtraction of Fractions..101 II. Interest ....................... 159

V. Multiplication of Frac-

Simple Interest .......... 159

tions ..........................104

1. General Method... 159

VI. Division of Fractions......110

2. Decimal Method.. 161

Complex Fractions........115 | Review PROBLEMS......... ...... 162

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PRIMARY ARITHMETIC.

PART I.

LESSONS IN NUMBERS.

ORAL EXERCISE. 1. How many noses have you ? How many heads ?

2. Point to one boy; one book; one hand; one chair; one table; one window.

1. There was one bird on the bush and another has come; how many are on the bush now?

2. One bird and one bird are how many birds?

3. If there are two birds on the bush and one fly away, how many will remain ?

4. One bird from the two birds leaves how! many birds ?

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1. There were two books on the table, but I have put another there; how many books are on the table now?

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