Signs. = Explanation of Arithmetical Signs. = (Equal.) The sign of Equality; thus, 4 qrs. 1 cwt. X (Multiplied by.) ÷ (Divided by.) The sign of Division; thus, 12÷4=3. PRACTICAL ARITHMETICK. ARITHMETICK, in theory, is the science of numbers; in practice, it is the art of computing or calculating by numbers. Arithmetick is comprehended in five principal rules, viz. Notation or Numeration, Addition, Subtraction, Multiplication, and Division. By the right application of these rules are solved all questions, in which arithmetick is concerned. NOTATION OR NUMERATION. NOTE. The difference between Notation and Numeration may be thus defined; Notation is the writing or representing of numbers; Numeration, the reading or expressing of numbers, by figures or letters. NOTATION OR NUMERATION teaches how to read or express any number or quantity, by the ten following characters: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.-o is called a cipher or nought; 1 one; 2 two; 3 three; 4 four; 5 five; 6 six; 7 seven ; 8 eight; 9 nine. By the various combination of the foregoing characters, which are called figures, or digits, all numbers are expressed; and, in any combination of figures, the value of each is determined by the place it occupies, as is shown in the following Explanation of the above Table. To enumerate any number of figures, begin at the right hand and proceed to the left. The first right hand figure of any number is called units; the second, tens; the third, hundreds; the fourth, thousands, &c. Each figure, from right to left, increases in a tenfold proportion; that is, the second figure from the right hand is ten times the value of the same figure in the place of units. B The third is ten times the value of the second; the fourth, that of the third; and so of the rest. EXAMPLE. In the third line of the Numeration Table (counting from the top) I find 3 in the place of hundreds, which is three hundred'; 2, in the place of tens, which is twenty; and 1, in the place of units, which is one; therefore, the whole value of that line is three hundred and twenty-one. APPLICATION. Write, in figures, the following numbers. 1st. Six hundred and twenty-five. 2d. Three thousand, one hundred and ten. 3d. Forty five thousand, two hundred and sixteen. 7th. Two million, three hundred and twenty thousand, five hundred and eleven. 8th. Sixty-nine million, eight hundred and two thousand, three hundred and five. 9th. Seventy-two million, thirteen thousand and nineteen. Write in words each line of the Numeration Table, respectively, beginning at the top. SIMPLE ADDITION teaches to collect into one sum, several numbers, which consist of one denomination only. RULE 1st. Place units under units; tens under tens; hundreds under hundreds, &c. RULE 2d. Begin with the right hand column, or line of units, when two or more numbers are to be added together. RULE 3d. Carry one for every ten ;* that is, in adding the first column of any sum, if it exceed ten, twenty, thirty, forty, c. set down what there are over ten, or tens, and carry as many to the second column, as there were tens in the first ;thus proceed with each column, till the last is added, under which set down the whole amount. The reason of this is, because the value of each figure from right to left increases in a ten fold proportion; that is, ten units, or ones, make ten; ten lens, an hundred; and ten undred, one thousand, &c. PROOF. Add each column as before, omitting the top line; set this amount under the first; then, if the amount of this and the top line be equal to the total sum, the work is right. In the first example, I say, five and two are seven and three are ten and six are sixteen: I then set down what there are over tem, which are six, then proceed with the second column thus,—one that I carry to one are two, and nine are eleven, and seven are eighteen; I set down eight, and carry one to three, which are four, and one are five, and four are nine, and three are twelve; I then set down the whole.In the next place, I add each column as before, omitting the top line, and set the amount under that of the whole sum; lastly, I add the sum of all except the top line, to the top line, and find the amount is equal to the whole sum; therefore, I conclude the work is right. Practical Questions. 1. A man has four farms. The first is worth two thousand, seven hundred, and twenty-five dollars :-the second is worth three thousand, eight hundred and nineteen dollars ;the third is worth one thousand, six hundred and ten dollars; the fourth is worth five hundred and twelve dollars; what are they all worth? Ans. 8,666 dols. 2. A man has four horses. The first is worth eighty-four dollars; the second is worth forty-five dollars ;-the third is worth as much as the second; and the fourth is worth as much as the first; what are they all worth? Ans. 258 dols. 3. A man possessed a tract of land, which contained fortynine thousand, eight hundred and thirty-five acres; now suppose he had six tracts of equal dimensions, how many acres did the whole contain? Ans. 299,010 acres. 4. Suppose one ox weigh one thousand and forty five pounds; another, eight hundred and twelve pounds; and a third, nine hundred and one pounds; what is their whole weight? Ans. 2,758 pounds. 5. The hind quarters of a cow weigh one hundred and three pounds each; the fore quarters weigh ninety-seven each; the hide, sixty-three, and the tallow, fifty-six; what is the weight of the cow? Ans. 519 pounds. Questions to be answered mentally. 1.5 are how many? 2. 108 are how many? 3. 1913 are how many? 4. 2111 are how many? 5. A person paid at one time, 16 cents, and at another 8; what was the amount paid? 6. A man bought a barrel of flour for 6 dollars, a bushel of nuts for I dollar, and a box of raisins for 5 dollars; what did the whole cost him ? 7. A, gave some money to B, to purchase some articles; B spent 50 dollars, and had 12 dollars left; how much did A give B? 8 A person said he was 18 years old when his father died, which was 27 years ago. Required his present age? 9. A person having 87 dollars, found that if he bad 13 more, he could purchase a horse. What was the price of the horse? 10. George Washington was born in the year 1732, which was 44 years before the declaration of Independence. In what year was it declared? 11. A labourer found that 25 days of his en- 12. A landlord received at one time 156 dol- SIMPLE SUBTRACTION Teaches to find the difference of two numbers, which are of one name or denomination, by taking the less from the greater. RULE 1st. Place the greater number uppermost, and the less directly under it, setting units under units, tens under tens, &c. RULE 2d. Having properly stated the question, draw a line underneath; then, beginning with units, subtract or take the less number from the greater, and set down the remainder, or difference. RULE 3d. Borrow ten; that is, whenever the lower figure happens to be greater than the upper, add ten to the upper figure, and subtract the lower figure therefrom, and set down the remainder, always remembering, when you borrow in one place to carry one to the next. PROOF. Add the difference of two numbers to the least number; if the amount be equal to the greatest number, the work is right. |