SHORT DIVISION. Short division is that in which the divisor does not exceed twelve. RULE. Seek how often the divisor is contained in the first figure or figures of the dividend, under which set the result; if any remain, conceive it to be prefixed to the next figure, seek how often, the divisor is contained therein, and so proceed. PROOF. Multiply the quotient by the divisor, adding in the remainder, if any, and the product will be the dividend. Note 1, When the divifor is the exact product of some two factors in the multiplication table, first divide by one of them, and that quotient by the other. 2. Multiply the firft divisor into the laft remainder, if any, and to that product add the first remainder for the true one. EXAMPLES. 1 Divide 7463521 by 18 facit 414640 18 facit 4146401 Remainder. 2 73681090 by 48. LONG DIVISION. Long division is that wherein the divisor exceeds 12. RULE. Take, for the first dividual, as many only of the first figures of the dividend as will contain the divisor; try how often the divisor may be had therein; and set the resulting figure for the first of the quotient; subtract the product of this figure into the divisor from the dividual, and the remainder, with the next figure of the dividend annexed, will be the second dividual, with which proceed as before, &c. till the dividend figures are exhausted. PROOF. As in short division.-Or thus: the dividend, less the remainder, divided by the quotient, will quote the divisor. EXAMPLES. Dividend. Divisor 41) 9 4 9 7 9 ( 2 3 1 6 Quotient Note. If one or more ciphers be on the right of the divifor, omit them in the operation, feparating from the right of the dividend as many figures, which annex to the remainder. Application. 10210 6865 12749 I A person intending to go a journey of 3264 miles, would perform it in 136 days, how many miles must he travel each day? answer 24. 2 Several boys went to gather nuts, and collected 4275, which when shared among them, each had 855; how many boys were in company ? answer 5. 3 If the expense of erecting a bridge be 5022l. to be defrayed equally by 186 persons; how much must be the quota of each? 4 The quotient of an operation in division dividend 8435955; query the divisor? 5 What number is that, which being the product will be 1864746? answer 271. is 1763, the answer 4785 multiplied by 7969, answer 234 6 Being desirous to plant 2072 apple trees in 14 rows, how many will be in each row? answer 148 7 In 670320 yards, how many pieces and bales, allowing 35 yards in each piece, and 56 pieces in each bale? answer 19152 pieces, 342 bales. 8 If a cistern containing 15072 gallons be emptied in 4 hours, by 48 equal vents; what quantity is discharged by either adjutage in that time? also how much per hour, admitting the velocity of the fluid to be uniform ? answer 314 gallons, at the rate of 78 per hour. 9 Divide 42904 acres of land into 346 equal parts. facit 124 10 If 45000 dollars be divided among 25 persons; how many is that for each ? answer 1800 I Purchased 256 bundles of hemp, weighing 46080lb. how much is in a bundle? answer 180 lb. TABLE. Mill-ree of Portugal o I, 4 8 0 Mark Banco of Hamburg,o o, 3 3 5 FEDERAL Note. The Federal standard, for gold and silver, is 11 parts fine and 1 part alloy. be Federal money, or money of the United States, may added, subtracted, multiplied and divided, as integers or whole numbers, only separating the different denominations with a point, as fifty-nine eagles, five dollars, nine dimes, five cents, in figures 59,5,9,5: but as dollars and cents are the only denominations commonly used in accounts, the points after the eagles and dimes are omitted, as 595,95, five hundred and ninety-five dollars and ninety-five cents. Dollars are reduced to cents, by multiplying the number of dollars by 100, or, which is the same thing, by adding two ciphers to the right hand of the number of dollars, as, In 1 dollar how many cents? answer 100 answer 600 answer 1000 Cents are brought into dollars by dividing by 100, or separating the two last figures to the right hand by a point, which will be cents, and those to the left will be dollars, as, In 225 cents, how many dollars and cents ? answer 2,25 In 506 cents, how many dollars and cents? answer 5,06 In 1250 cents, how many dollars and cents? answer 12,50 Note. In writing down any number of cents less than 10, a cipher must be prefixed in the place of dimes. ADDITION, |