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PREFACE

TO THE FOURTH EDITION.

The present edition, which is stereotyped, has been carefully revised, and, in some cases, new matter added in the body of the work, without, however, changing the order of the different articles. But what most distinguishes it from the preceding ones, is the addition of an APPENDIX.

In this Appendix, we have discussed pretty fully what may properly be considered the philosophy of some of the more difficult operations, as well as interesting properties of numbers. It is believed that much here added will be found instructive and interesting to the lover of arithmetical operations.

GEO. R. PERKINS. Urioa, April, 1848

CONTENTS.

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PREFACE

TO THE FOURTH EDITION.

The present edition, which is stereotyped, has been carefully revised, and,
in some cases, new matter added in the body of the work, without, however,
changing the order of the different articles. But what most distinguishes it
from the preceding ones, is the addition of an Appendix.

In this Appendix, we have discussed pretty fully what may properly be
considered the philosophy of some of the more difficult operations, as well as
interesting properties of numbers. It is believed that much here added will
be found instructive and interesting to the lover of arithmetical operations.

GEO. R. PERKINS.
UTICA, April, 1848

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DEFINITIONS, . . . . . . . . . . . . . . . . . 9

Symbols, . . . . . . . . . . . . . . . .

Examples illustrating definitions and symbols, . . . . . . 12

Multiplication of compound expressions, ....

Singular property of the figure 9, . . . . . . . . . . 17

Prime numbers, . ... ·

·

Table of prime numbers, . . . . . . . .

Numbers decomposed into prime factors, . . . . . . . . 21

First method of finding the greatest common measure,. .. 23

Second 66

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66

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. . . . 24

First method of finding the least common multiple, . ..

Second 6 "

" " . . . . . . 26

To find all the divisors of any number, . . . . . . . . 29

The number of divisors given, without exhibiting them, . . 30

CHAPTER II.

Vulgar fractions defined, . . . . . . . . . . . . . 32

Reduction of fractions, . . . . . . . . . . . . . 33

To reduce simple fractions to their lowest terms, . . . . . 34

To reduce improper fractions to mixed numbers, . . . . . 36

To reduce mixed numbers to improper fractions, . . . .

To reduce compound fractions to simple ones, . . . . . 38

To reduce fractions to a common denominator, ....

To reduce fractions to their least common denominator,.' . . 43

Addition of fractions, . . . . . . . . . . . . . . 44

Subtraction of fractions, . . . . . . . . . . . . . 46

Multiplication of fractions, . . . . . . . . . . . . 47

Division of fractions, . . . . . . . . . . . . . . 49

Reduction of complex fractions, . . . . . . . . . . 50

Reduction of fractions to a given denominator, . . . . . . 51

Reduction of denominate fractions defined, ...... 63

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