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. UTICA, April, 1848. GEO. R. PERKINS. CONTENTS. To find all the divisors of any number, The number of divisors given, without exhibiting them, To reduce simple fractions to their lowest terms, To reduce improper fractions to mixed numbers, . To reduce mixed numbers to improper fractions, To reduce compound fractions to simple ones, PREFACE TO THE FOURTH EDITION. THE present edition, which is stereotyped, has been carefully revised, and, In this Appendix, we have discussed pretty fully what may properly be UTICA, April, 1848. GEO. R. PERKINS. Page. To reduce fractions from one denominate value to another, . 53 To find what fractional part one quantity is of another, Reduction of denominate fractions to whole denominate numbers 57 Continued fractions defined, . To convert a vulgar fraction into a continued fraction, |