traction. The number to be divided is called the dividend; the dividing number is called the divisor; and the number of times the divisor is contained in the dividend, is named the quotient; while what is left after the division is termed the remainder. Rule.-When the divisor does not exceed twelve, place it on the left of the dividend, and separate them by a line. Find how often the divisor is contained in as many figures of the dividend as may be necessary for that purpose, and set down the quotient under; if there be a remainder, consider it as tens; place it before the next figure of the dividend, and divide by the divisor. Continue this operation to the end of the sum, and if there be any remainder, set it down on a line with the quotient, but separated from it by a mark. Examples. Divide 3429 by five. Divisor. Dividend. 5) 3429 Quotient 685 : 4 Remainder. Divide 7834 by twelve. Divisor. Dividend. Quotient. 652 : 10 Remainder. When the divisor is a composite number, and one of the component parts also measures the dividend, we may divide successively by the component parts. Example.-Divide 94152 by 21. 7) 31384 4483 3 When the divisor exceeds twelve, and consists of several figures, place the divisor before the dividend, as before, and find how often the divisor is contained in as many figures of the dividend as are necessary; place that number on the right of the dividend; multiply the divisor by that number, and set the product under the figures of the dividend, just divided; subtract this product from those figures of the dividend under which it stands; and bring down the next figure of the dividend, or more if necessary, to join on the right of the remainder. Divide the number so increased, as before; and continue the same operation until all the figures be brought down. If it be necessary to bring down more figures than one to make the remainder as large as, or larger than, the divisor, place a cypher in the quotient for every figure so brought down more than one figure. Example.-Divide 16524 by 54. 162 324 VOL. I. If there be cyphers on the right hand of the divisor, cut off those cyphers from the divisor, and an equal number of figures from the right hand of the dividend; then divide the remaining figures of the dividend, by the remaining figures of the divisor, and place the figures cut off from the dividend, on a line with the remainder, if there be any. Rule. Example.-Divide 630,27 by 500. Quotient 126,27 Remainder. COMPOUND DIVISION. When the dividend consists of different denominations, divide the higher denomination, and reduce the remainder into the next lower denomination, taking in the given number of that denomination, and then continue the division. Examples. L. s. d. £. s. d. 32) 550 18 10 (17 4 4 £. s. d. QUESTIONS. What is addition, and what is its rule? What is the rule for compound addition? What is the surest proof of addition? What is subtraction, and its rule of operation? What is the proof? What is the rule for compound subtraction? What is multiplication, its rule, its proof? What is the rule for compound multiplication? What is division, and its rule? What is the rule for compound division? CHAP. XII. ARITHMETIC- continued. DECIMAL FRACTIONS. THE formation and calculation of decimal fractions are founded upon the same principles, as is the numeration of integers. When a unit is divided into decimals, that unit is supposed to consist of ten parts, in the same manner as one ten in the arithmetic of integers, is worth ten units. The decimal parts of units, therefore, are tenths, and are placed at the right hand of the units, with a dot between them, to determine their place. Thus, thirty-five units and six tenths, are expressed as follows, 35.6. The first figure of a decimal fraction signifies tenth parts; the next hundredth parts, the next thousandth parts, and so on. The use of cyphers in decimals, as well as in integers, is to bring the significant figures to their proper places, on which their value depends. As cyphers, when placed on the left hand of an integer, have no sigification; but when placed on the right hand, increase the value, each, ten times; so cyphers when placed on the right hand of a decimal have no effect; but when placed on the left, diminish the value ten times each. Examples of notation and numeration of decimals. 4.7 signifies four integers, and seven tenth 0.47 0.047 0.407 4.07 4.007 parts. four hundredth parts, and seven four integers and seven hun- four integers and seven thousandth parts. Addition of decimals.-Rule. Place the numbers under each other according to their value, as in integers, so that all the decimal separating dots may stand exactly under each other. Then begin at the right hand; add up all the columns and place the dot in the amount, exactly below all the other dots. |