To reduce a Mixed Number to an Improper Fraction ... To reduce a Fraction to its lowest name To reduce Fractions to a Common Denominator ... ... ... Examination Papers on all the foregoing Rules... ... PREFACE. THE aim of the present work is to supply the youthful student of Arithmetic with a complete course of instruction in the principles of the science of numbers, and at the same time to furnish him with the means of attaining the utmost proficiency in the practice of the art of computation. So far as the author is aware, there exists no book of moderate size and price in which the two departments of the subject are both adequately represented. The THEORETICAL portion of the work will be found to differ from other works having a similar aim, in the following particulars :— 1. In the illustrations or demonstrations of the various rules. The rules of arithmetic are of two kinds. They either describe a series of steps, which not only lead to the required answer but supply all that is essential to a complete demonstration-as for example the rule for Reduction; or while describing the several steps necessary to obtain the correct answer, they omit certain other steps necessary to complete the reasoning, as for example the rule for finding the Greatest Common Measure. In the present work rules of the first kind are followed by illustrative examples, while those of the second kind are preceded by demonstrative examples. In the latter the use of algebraical symbols has been avoided. 2. In the reiteration of fundamental truths whenever new applications of them occur. When a fundamental principle is first introduced it is distinctly enunciated and printed in bold type. It is further repeated on every fresh application of it in subsequent rules. [See paragraphs 54 and 137, and the chapter on Proportion in the second part of the work.] |