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TREATISE

PRACTICAL ARITHMETIC

AND:

Boek-Keeping,

BY

SINGLE ENTRY.

SH& FIFTH EDITION, MUCH IMPROVED.

BY

WILLIAM TINWEL,

TEACHER OF THE MATHEMATICS:

Pewcastle :
FRINTED BY M. ANGUS AND SON, FOR THE AUTHOR.

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The intention of publishing this system is to render the study of Practical Arithmetic as easy as p lible, and to remove those 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 easy and plain

In pursuance of this dehgn, care has been taken, <specially in the first simple rules, not to harass the scholar with many thing foreign to the rule he is learning. Addition, Subtraclion, Multiplication, and Divifion, are treated forft in integers ; - where the scholar is troubled with nothing but i merely to add, subtract &c. after which the manner of Carranging the questions according to the rule is taught ; and

lastly, the numbers in the questions are given in words at length, which not only exercise the two first parts, but alfa exemplify Notation.

As a further exercise, a large promiscuous collection of va questions is given to the first five rules

In Redučtion will be found a great many questions different from those commonly given, all tending to inftruét, but none to puzzle the learner.

Then follows a promiscuous collection of questions to illustrate all the parts of Reduction. The compound rules come next in order, at the end of which will be found

several bills of parcels, and book-debts, together with a number of questions for exercise. In the Rule-of-T hree a rational and plain method is given to work all the questions belonging to it, whether direct or inverse, This rule is of such extensive use, that the utmost care should be taken to render it familiar to the young accountant. The Rule-of-Five, as it is here entirely founded upon the Rule-ofIhree, will be found, upon trial, very easy..

Practice,

Practice, being of such material use in real businefs, is: very amply handled; as is also 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 reasons for the operations in that tule are entirely founded ipon them. But as there are a great many who have not time to learn a complete System of Arithmetic, such ought to be taught the order of the rules as they follow one another, and then Book- keeping by Single Entry, which is sufficient for common business. But in order to make a person expert in calculations, Vulgar Fractions are absolutely necessary, for which reojin they are very copiously · treated, and the various methods laid down in

inaniner.

In Daimal Fractions, besides what is generally given;', single circulates, or repeaters, are introduced, as they occur so often in ineasuring by feet and inches. Exchange with so foreign countries will be found more full and extensive than usual. Duodecimals is followed by a number of useful questions in Squaring dimensions, the utility of which is obvious.

Book-keeping by fengle entry, although it is placed at the end of the Arithmetic, may be learned as soon as the scholar has gone through the promiscuous collection of questions after. Practice

. The several accounts in the Day-book are collected and arranged as to serve for a general exercise to all the praclical rules, therefore very much care should be taken to make the learner well acquainted with them.-A Small Appendix is added, containing. Receipts, PromiforyNotes, and Bilts of Exchange; with proper exercises.

This Edition is very much improved, as well with respect". to a great number of new questions being introduced, as in the order and disposition of the former ones.

PRACTICAL ARITHMETIC.

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DEFINITIONS,
RACTICAL ARITHMETIC is the art of com.

puting by numbers.
2. A Unit is any thing considered as one.
3. An Integer is any whole thing.

4. Integers, or whole numbers, are such 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 nunbers.

7. A fimple number confifts only of one denomination.
8. A compound number consists of several 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

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Numerator.

7 Denominator. 10: A mixt number consists of a whole number and a frac. tion, as 47

The following Signs are used in this work. = The sign of equality, and signifies that the numbers it is fet between are equal, as 16=16.

+ The sign of addition, and Gignifies that the numbers it is set between are to be added, as 8+2=10.

The sign of subtraction, and signifies that the numbers it is set between are to be subtracted, as 8-2=6.

* The sign of multiplication, and signifies that the numbers it is set between are to be multiplied, as 8 x2=16.

• The sign of division, and signifies that the numbers it is fet between are to be divided, as 8:2=4.

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