A TREATISE OF PRACTICAL ARITHMETIC AND Book-Keeping, BY- SINGLE ENTRY. THE FIFTH EDITION, MUCH IMPROVED. BY WILLIAM TINWEL, TEACHER OF THE MATHEMATICS. Newcastle : PRINTED BY M. ANGUS AND SON, FØR THE AUTHOR. Best in 8-19-85 THE a manner. PREFACE.. HE intention of publishing this fyftem is to render the Study of Practical Arithmetic as easy as poffible, and to remove thofe redundancies which are too often found in books of this kind. For every difcerning teacher will allow, that the principles of any art cannot be laid down in too eafy and plain In pursuance of this defign, care has been taken, efpecially in the firft fimple rules, not to harass the fcholar with Many thing foreign to the rule he is learning. Addition, Subtraclion, Multiplication, and Divifion, are treated firft in integers; where the Scholar is troubled with nothing but merely to add, subtract &c. after which the manner of arranging the questions according to the rule is taught: and laftly, the numbers in the questions are given in words at length, which not only exercife the two first parts, but alfaexemplify Notation. As a further exercife, a large promifcuous collection of queftions is given to the firft five rules. In Reduction will be found a great many questions different from thofe commonly given, all tending to instruct, but none to puzzle the learner. Then follows a promiscuous collection of questions to illuftrate all the parts of Reduction. The compound rules come next in order, at the end of which will be found feveral bills of parcels, and book-debts, together with a number of questions for exercife. In the Rule-of-Three a rational and plain method is given to work all the questions belonging to it, whether direct or inverse, This rule is of fuch extenfive ufe, that the utmost care fhould be taken to render it familiar to the young accountant. The Rule-of-Five, as it is here entirely founded upon the Rule-ofThree, will be found, upon trial, very easy. Practice, Practice, being of fuch material use in real business, is very amply handled; as is alfo Tare and Trett and Bills of Parcels. It must be allowed, that, according to the proper order of teaching, Vulgar Fractions should have been put before Practice, as the reafons for the operations in that rule are entirely founded upon them. But as there are a great many who have not time to learn a complete fyftem of Arithmetic, fuch ought to be taught the order of the rules as they follow one another, and then Book-keeping by Single Entry, which is fufficient for common business. But in order to make a perfon expert in calculations, Vulgar Fractions are abfolutely neceffary, for which reafon they are very copiously treated, and the various methods laid dozun in manner. a clear In Decimal Fractions, befides what is generally given, fingle circulates, or repeaters, are introduced, as they occur fo often in meafuring by feet and inches. Exchange with foreign countries will be found more full and extenfive than ufual. Duodecimals is followed by a number of ufeful questions in Squaring dimensions, the utility of which is obvious. Book-keeping by fingle entry, although it is placed at the end of the Arithmetic, may be learned as foon as the fcholar has gone through the promiscuous collection of queftions after Practice. The feveral accounts in the Day-book are fo collected and arranged as to ferve for a general exercife to all the practical rules, therefore very much care fhould be taken to make the learner well acquainted with them. —A · Small Appendix is added, containing Receipts, Promissory Notes, and Bills of Exchange, with proper exercifes. This Edition is very much improved, as well with respectTM to a great number of new questions being introduced, as in the order and difpofition of the former ones. PRACTICAL ARITHMETIC. 1. PRACTI DEFINITIONS. RACTICAL ARITHMETIC is the art of computing by numbers. 2. A Unit is any thing confidered as one. 3. An Integer is any whole thing. 4. Integers, or whole numbers, are fuch as express any number of things, each of which is a unit. 5. An even number is that whose half is a whole number. 6. An odd number is that which cannot be divided into two equal whole numbers. 7. A fimple number confifts only of one denomination. 8. A compound number confifts of feveral denominations. 9. A fraction, or broken number, is one part or more of an integer, and is expressed by two numbers, the one above and the other below a line drawn between them; the number below is called the denominator, and the number above the numerator :— Thus 10: A mixt number confists of a whole number ́and à fraction, as 44 The following Signs are used in this Work. The fign of equality, and fignifies that the numbers it is fet between are equal, as 16=16. The fign of addition, and fignifies that the numbers it is fet between are to be added, as 8+2=10. The fign of fubtraction, and fignifies that the numbers it is fet between are to be fubtracted, as 8-2=6. The fign of multiplication, and fignifies that the numbers it is fet between are to be multiplied, as 8 × 2=16. The fign of divifion, and fignifies that the numbers it is fet between are to be divided, as 8- =2=4. A |