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 remain der, if any, and the product will be the dividend. Note 1. When the divifor is the exact product of fome two factors in the multiplication table, first divide by one of them, and that quotient by the other. Multiply the first divifor into the laft remainder, if any, and to that product add the first remainder for the true one. 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. EXAMPLE S. Dividend 41 Quotient. Rem. 95 facit 578540 89 671 8009 569 2507 3883 1524 41659 18156 29485 87648 1 1 2625 13542 175296 11 2625 S476838 293048 2293048 476838 Note. answer 180/b. Note. If one or more ciphers be on the right of the divisor, omia them in the operation, separating from the right of the dividend as many figures, which annex to the remainder. 2 quota of each? E x A M P L E S. 1 Divi. 8317642500 by 814600 facit 10210 re, 576500 166341 32000 by 1629200 10210 3 87521885000 by 12749000 6865 4 350087540000 by 27460000 12749 Application. 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 expence of ere&ing a bridge be gozal. to be defrayed equally by 186 persons; how much must be the answer 271. 4 The quotient of an operation in division is 1763, the dividend 8435955 ; query the divisor? answer 4785 5 What number is that, which being multiplied by 7969, the product will be 1864746? 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, admit. ting the velocity of the fluid to be uniform? answer 3!4 gallons, at the rate of 784 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 11 Purchased 256 bundles of hemp, weighing 46080lbs. how much is in a bundle ? TABLE A Table of the Weight and Value of Coins as they pass in the respective States of the Union, with their Sterling and Federal value. Names of Coins. GOLD.) A Johannes, An Half Johannes, A Moidore, An English Guinea, Weight. Standard dwt. gr. Sterling New Hampshire Money Maffachufetis, New York Pennsylvania. [New Jersey, Federal value South and Delaware, Carolina. and and Rhode-Illan d. 4000000∞722 Carolina. Maryland. Georgia. 6 8 C 3 3 5 16 12 2 2 5 I 17 Of I 15 I o 18 O 3.7 All other gold coins. of equal fineness, at 89 cents per dut. and silver at 111 cents per oz. A TABLE of other foreign Coins, 50. with their value in -Federal Money as eftablished by a late act of Congress. Mill-ree of Portugalo 1, 2 4 0 Livre Turnois of France, Ruble of Russia ᄋ 0,66 B Real Plate of Spain, FEDERAL MONE Y. The denominations are: 1 dime, d. 1 Dollar, D. 10 dollars 1 Eagle, E. The Standard Weight. daut. gr. 1 A dime, 1 167, Silver, 17 An Eagle, 11 43 I part alloy of the United States, may be add. ed, 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 i dollar, how many cents? answer 100 In 6 dollars, how many cents ? answer 600 In jo dollars, how many cents ? Cents are brought into dollars by dividing by 100, or sepapating 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 500 cents, how many dollars and cents ? answer 5,06 In 1230 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 Ons wer I OOO ION |