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DEFINITIONS, PRINCIPLES, AND RULES
AND SOLUTIONS OF THE MORE

DIFFICULT PROBLEMS

BY

JOHN H. WALSH

ASSOCIATE SUPERINTENDENT OF PUBLIC INSTRUCTION

BROOKLYN, N.Y.

GRAMMAR SCHOOL ARITHMETIC

BOSTON, U.S.A.
D. C. HEATH & CO., PUBLISHERS

COPYRIGHT, 1895,
BY JOHN H. WALSH.

LIBRARY OF THE
LELAND STANDO JR. UNIVERSITY.

a 52587

Norwood Press :
J. S. Cushing & Co. - Berwick & Smith.

Boston, Mass., U.S.A.

CONTENTS

(HIGHER ARITHMETIC Manual.)

PAGE

GENERAL HINTS. . .

Division of the work - Additions and omissions — Oral and

written work — Use of books — Conduct of the recitation — Drills
and sight work — Definitions, principles, and rules — Language
- Analysis — Objective illustrations - Approximate answers —
Indicating operations - Paper vs. slates.

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DEFINITIONS, PRINCIPLES, AND RULES . .

General definitions - Additions — Subtraction — Multiplication

– Division - Factoring - Cancellation - Greatest common divi-
sor — Least common multiple — Fractions — Decimals — Accounts
and bills — Denominate numbers — Percentage - Profit and loss
— Commercial discount — Commission — Insurance — Taxes —

Duties — Interest - Partial payments -- Bank discount — Ex-

change - Equation of payments — Ratio - Proportion - Partner-

ship — Involution — Evolution — Stocks and bonds — Notes,

drafts, and checks.

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INTRODUCTORY Plan and Scope of the Work. — In addition to the subjects generally included in the ordinary text-books in arithmetic, Mathematics for Common Schools contains such simple work in algebraic equations and constructive geometry as can be studied to advantage by pupils of the elementary schools. .

The arithmetical portion is divided into thirteen chapters, each of which, except the first, contains the work of a term of five months. The following extracts from the table of contents will show the arrangement of topics :

FIRST AND SECOND YEARS Chapter I. — Numbers of Three Figures. Addition and Subtraction.

THIRD YEAR Chapters II. and III. — Numbers of Five Figures. Multipliers and Divisors of One Figure. Addition and Subtraction of Halves, of Fourths, of Thirds. Multiplication by Mixed Numbers. Pint, Quart, and Gallon; Ounce and Pound. Roman Notation.

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