PREFACE. THE design of the following work, is to furnish the several rules cf Arithmetic concisely expressed, together with a variety of applicative examples, arranged in such order, that the learner may advance by gradations, from what is simple to what is more abstruse, and be unobstructed in his progress by ignorance of particulars that he should previously have known. The compiler is aware, that a number of works of a similar nature is already in use, and that most of them are possessed of considerable merit; yet he believes he has in several respects improved upon them. Whether he has or not, after making a few remarks, he will submit to the judicious to determine. Under each of the rules in the TEACHERS' ASSISTANT, one or more wrought examples are given, which afford an opportunity of explaining and illustrating them. Of the examples for the application of the several rules, the easiest occur first, such as are similar mostly succeed each other, and all are delivered in as familiar terms as could readily be employed. Federal money, as far as the five primary rules are concerned, is treated of separately, and agreeably to the manner in which it is used in trade-mills being mostly rejected. Before entering upon Compound Addition, a portion of Reduction is introduced, which appears necessary, in order to explain that rule, as well as Compound Multiplication and Compound Division. Besides the foregoing particulars, a number more might be adduced that are conceived to be worthy of attention; such as the arrangement of the rules and examples in Practice, Simple Interest, Tare and Tret, &c.: but these, with the whole work, are referred to teachers and others interested ir the subject. A 2 into, with, or multiplied by; as, 6×2=12. Fourth Root; as, 4/16-2, &c. A Vinculum; denoting the several quantities ARITHMETIC. ARITHMETIC is the art of computing by numbers. It has five principal rules for its operations; viz. numeration, addition, subtraction, multiplication, and division. NUMERATION Numeration teaches to write or express numbers by figures, and to read numbers thus written or expressed. In treating of numbers, the following terms are employed: viz. unit, ten, hundred, thousand, and million; as also billion, trillion, and some others. But the latter are seldom used. A unit is a single one. A ten is ten units. A hundred is ten tens. A thousand is ten hundreds. A million is ten hundred thousands. Note. As it takes ten hundred thousands to make a million, when we express a number, greater than a thousand, and less than a million, we use tens of thousands, or hundreds of thousands, or both, as the case requires. Likewise, to express a number, greater than a million, we employ tens of millions, or hundreds of millions, &c. The following are the figures used in numeration, with their names above them. One two three four five six 1 2 3 4 5 6 7. 9 seven eight nine Each of these figures represents the number which its name denotes; but it is understood to be that number of units, or that number of tens, or that number of hundreds, &c. according to its relative place: which is exemplified in the following tables. TABLE FIRST. TABLE SECOND. -Hundred million -Million Hundred thousand Thousand These tables show that in using figures to express numbers they are placed in a horizontal row-the first figure at the right hand representing one or more units, the next tens, the next hundreds, &c. Thus a 1 is one unit, or one ten, or one hundred, &c. according to the place in which it stands; and in like manner, a 2 is two units, or two tens, or two hundreds, &c. The same rule determines the value of each of the other figures. In reading numbers, the units and tens are taken together. 1 ten and 1 unit are read eleven; 1 ten and 2 units, twelve; 1 ten and 3 units, thirteen, &c.: 2 tens and 1 unit are read, twenty-one; 3 tens and 1 unit, thirty-one, &c. Thus the number expressed by the row of figures in table first is read-one hundred and eleven millions, one hundred and eleven thousands, one hundred and eleven. That expressed by the figures in table second is read-two hundred and twenty-two millions, two hundred and twenty-two thousands, two hundred and twenty-two.. The succeeding tables will further illustrate the subject TABLE THIRD. |