THE NEW AMERICAN ARITHMETIC, Part Second, is designed for the use of those who have completed Part First of the series, or some similar work.

The Fundamental Rules are first given, with exercises upon them, but pupils have not been wearied by a great number of pages on subjects with which, it is fair to presume, they are already somewhat familiar.

Problems in United States Money are next introduced, as being of greater practical importance than any others within the range of the pupil's ability.

Fractions are then explained in advance of denominate numbers, for the reason that some knowledge of the former is necessary to a thorough understanding of the latter.

Relation of Numbers, Bills and Accounts, Denominate Numbers, and Decimals, complete the book, in the order named.

The important elements of Arithmetic needed in intermediate schools, or in the lower grades of a grammar school, are thus presented in a compact form.

The excessive number of rules usually given in works on Arithmetic has been a serious obstacle to their successful use; burdening the memory of the pupil with unnecessary matter, and frequently involving him in doubt as to the correct rule for the working of an example. In this book a single rule is often made to do the work of three or four of the rules found elsewhere; and it has seldom been thought necessary to give more than one rule for the same operation.

Review Problems are given wherever needed; Oral Exercises preface each subject, and everything has been done. which, in the judgment of the authors, would tend to simplify a topic, or make it clear to the mind of the pupil.

S. M.

PHILADELPHIA, 1877.

Copyright, 1877, by J. H. BUTLER & CO.

SHERMAN & Co. PRS. PHILA.

G. M. S.

THE

NEW AMERICAN ARITHMETIC.

PART II.

DEFINITIONS.

A Unit is a single thing of any kind; as one, one man, 1 dollar, 1 cent.

A Number is a unit, or a collection of units.

An Abstract Number is a number which is not applied to any object; as, 1, 2, 3.

A Concrete Number is a number applied to some object; as 5 dollars, 3 men, 2 pints.

A Simple Number is either an abstract number, or a concrete number of one denomination; as 50, 30 bushels, 4 acres.

A Compound Number is a concrete number which expresses two or more denominations; as 1 gallon 3 quarts 2 pints.

An Integer, or Whole Number, is a number which expresses units that are not divided.

A Fraction, or Fractional Number, is a number which expresses equal parts of anything; as half a pound, one-third of an acre, one-fourth.

Arithmetic is the science of numbers and the art of computation.

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