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APPLETONS”: MATHEMATICAL SERIES.

A A

MENTAL ARITHMETIC.

BY

G. P. QUACKENBOS, LL. D.,

AUTHOR OP

99

99

AN ENGLISHI GRAMMAR FIRST LESSONS IN COMPOSITION;' ADVANCED

A NATURAL PHILOSO
COURSE OF COMPOSITION AND RHETORIC
PHY; “ ILLUSTRATED SCHOOL HISTORY OF THE UNITED
STATES; “PRIMARY HISTORY OF THE UNITED

STATES,

ETC.

NEW YORK:
D. APPLETON AND COMPANY,
1, 3, AND Ď BOND STREET.

1882.

287559
WITHDRAWN YOV 11 1939

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A. Primary Arithmetic. Beautifully illustrated; carries

the beginner through the first four Rules and the simple Tables, combining mental exercises with examples for the

slate. 16mo. 108 pages. 22 cents. An Elementary Arithmetic. Reviews the subjects of the

Primary in a style adapted to somewhat maturer minds. Also embraces Fractions, Federal Money, Reduction, and the Com

pound Rules. 12mo. 144 pages. 40 cents. A Practical Arithmetic. Prepared with direct reference

to the wants of Common Schools, giving special prominence to the branches of Mercantile Arithmetic. 12mo. 336

pages. 80 cents A Mental Arithmetic. Designed to impart readiness in

mental calculations, and extending them to the various operations needed in business life. Introduces short methods, and

new and beautiful processes. 16mo. 168 pages. 35 cents. A Higher Arithmetic. 12mo. 420 pages. $1.10.

Entered, according to Act of Congress, in the year 1868, by

D. APPLETON & CO.,
In the Clerk's Office of the District Court of the United States for the

Southern District of New York.

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The study of Mental Arithmetic has two principal objects in view, to discipline the mind and impart quickness and accuracy in mental calculations. To secure these objects in the highest degree and in the pleasantest way to both teacher and learner is the aim of this little volume. It is intended for pupils who have gone through a Primary Arithmetic, and know how to read and write numbers up to thousands inclusive; and may be used either by itself to succeed the Primary or Elementary, or as an auxiliary to the Elementary or Practical, on alternate days.

Among the more important features of the present work are the following :-1. The gradual and inductive mode of unfolding the subject, with the aid of rigid but clear analyses expressed as briefly as possible. 2. The introduction of necessary definitions, too often excluded from Mental Arithmetics. 3. The great variety and practical bearing of the Examples ; the careful avoidance of obscurity in wording them, and the exclusion of all questions involving impossibilities or absurdities. 4. The presentation of the Metric System, hitherto confined mainly to text-books on written Arithmetic. 6. The teaching of short methods and processes actually used in the counting-room. 6. The extension of mental calculations to more of the operations of every-day business life than has hitherto been attempted; such as equation of payments, stock jobbing, U. S. securities, taxes, duties, &c. The value of this last feature, it is believed, can hardly fail to be appreciated in this practical age.

The interest and profit with which classes will use this work will depend entirely on the thoroughness with which the successive steps are taken. Review again and again if necessary, and let nothing pass till it is mastered. Short lessons should be given, to be prepared beforehand. The books should be closed at recitation, t}

question read but once, and the scholars should have no intimation
as to which of their number will be called on to solve it. The analy.
ses given in the Models should be followed (unless better ones can
be devised), with distinct articulation and in correct language. Let
the answer always be distinctly stated, when it is reached, in con-
nection with the denomination, as in the Model. Whenever any
particular form of analysis has become perfectly familiar, it will be
well to omit it in the case of some of the questions, and require im-
mediate answers, as well to encourage quickness of thought as to
economize time. A few questions from previous lessons, to be an.
swered thus promptly, will be found useful at each recitation.

The Author can only hope that this work may meet with as
cordial a reception as has been so kindly extended to the other
Numbers of the Series.

NEW YORK, May 22, 1868.

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der

ADDITION. [It is supposed that the pupil has learned the Addition, Subtraction, Multiplication, and Division Tables.

Let them be reviewed, as presented under Chapters 1, 2, 3, and 4, until he can say them promptly and perfectly, backward as well as forward.]

ADDITION TABLE.

2 and

3 and

4

5 and are 6

7

1 are 2 are 3 are 4 are 5 are 6 are 7 are

4 and

5
6
7
8

1 are 2 are 3 are 4 are 5 are 6 are

1 are 2 are 3 are 4 are 5 are

2 are 3 are 4 are

5 6 7 8

5

6
7
8

9
7 are 10

[blocks in formation]

1 and 1 are

2 2 are

3 3 are

4 4 are

5 5 are

6 6 are

7
7 are

8
8 are
9 are 10
10 are 11

6 and
1 are

7 2 are

8 3 are

9 4 are 10 5 are 11 6 are 12 7 are 13 8 are 14 9 are 15 10 are 16

[blocks in formation]

are 10 9 are 11 10 are 12 ng and

8

9 3 are 10

are 11 5 are 12 6 are 13 7 are 14 8 are 15 9 are 16 10 are 17

6 are 10
7 are 11
8 are 12
9 are 13
10 are 14

9 and
1 are 10
2 are 11
3 are 12
4 are 13
5 are 14
6 are 15
7 are 16
8 are 17
9 are 18
10 are 19

8 and

9 2 are 10 3 are 11 4 are 12 5 are 13 6 are 14 7 are 15 8 are 16 9 are 17 10 are 18

5 are 10 6 are 11 7 are 12 8 are 13 9 are 14 10 are 15

10 and 1 are 11 2 are 12 3 are 13 4 are 14 5 are 15 6 are 16 7 are 17 8 are 18 9 are 19 10 are 20

7 7

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