"AN ENGLISH GRAMMAR;" "FIRST LESSONS IN COMPOSITION;" "ADVANCED
COURSE OF COMPOSITION AND RHETORIC; "A NATURAL PHILOSO

PHY;

"ILLUSTRATED SCHOOL HISTORY OF THE UNITED
STATES; "PRIMARY HISTORY OF THE UNITED
29
STATES, ETC.

NEW YORK:
D. APPLETON AND COMPANY,

1, 8, AND 5 BOND STREET.

1882.

28755911

WITHDRAWN NOV 11 1939

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 Compound 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.

Lina. Malone

PREFACE.

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. 5. 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, the

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.

CHAPTER FOURTEENTH, STOCKS,-U. S. SECURITIES,

143

CHAPTER FIFTEENTH,

MISCELLANEOUS EXAMPLES,

150

MENTAL ARITHMETIC.

CHAPTER

FIRST.

ADDITION.

[Ir 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.]