CONTRACTIONS. CASE I.—When there are ciphers at the right hand of the divisor, cut them off; likewise cut off the same number of digits from the right hand of the dividend ; then divide as usual, and to the remainder annex the digits cut off from the dividend. CASE II.- When the divisor is any number not. exceed ing 12. RULE.--First seek how often the divisor can be had in the first figure, or figures, of the dividend; put the result under the dividend ; multiply this quotient figure and the divisor together; mentally subtract their product from the part of the dividend taken; what remains call so many tens, which place, in idea, before the next figure of the dividend for a new dividual ; and so proceed through the whole dividend. When in subtracting, nothing remains, take the next figure ; if that be less than the divisor; take the next two, and place a cipher under the first. 1. 2. Quotient 12068873 Rem. Quotient 344324 Rem. 3. Divide 3764592 byt 527684 8 5. 1410217 9 6. 612948 11 7. 317926 12 i dison Case III.-If the divisor be a product of two or more numbers, divide continually by those numbers instead of the whole at once. NOTE.— It sometimes happens that there is a remainder to each of the quotients, and neither of them the true one but the true remainder may be found by the following rule. RULE.-Multiply the last remainder by the last divisor but one, and to the product add the preceding remainder ; multiply this sum by the next preceding divisor, and to this product add the next preceding remainder, and so on until all the remainders and divisors are used ; and the last sum will be the true remainder. 3. Divide 6421671 by 448 8x8x7=448 8)6421671 4. Divide 27162 by 62 8)8027087 7)1003384 APPLICATION. 1. Divide 3656 dollars equally among 8 men. Ans. 457 dols. to each. 2. There are 124 men who have 372 dollars among them; how much is one man's share, if it be divided equally? Ans. 3 dols. 3. If I wish to perform a journey of 3264 miles in 136 days, how far must I travel each day to complete it ? Ans. 24 miles. 4. A payment of 1272 dollars was made by a number of men, each of whom paid 3 dollars; how many men were there? Ans. 421. 5. I would plant 2072 trees, in 14 rows, 25 feet asunder; how long inust the grove be ? Ans. 3675 feet. 6. Divide 1000 dollars, between A, B, and C, and give A 129 more than B, and B 178 less than C. Ans. 360 dols. A's, 231 B's, and 409 C's. 7. Part 1500 acres of land between Saul, Seth, and Silas; and give Seth 72 more than Saul, and Silas 112 more than Seth. 41-43 Saul's share, 4869 Ans. Seth's and 5933 Silas's. 8. A brigade of borse corsisting of 384 men, is to be formed into a column, having 32 men in front; how many ranks will there be ? Ans. 12. 9. In order to raise a joint stock of 10,000 dols. L, M, and N, together, subscribe 8500, and 0 the rest. Now, M and N are known together to have set their hands to 6050, and N has been heard to say that he had undertaken for 420 more than M. What did each proprietor advance? Ans. L 2150, M 2815, N 3235, and O 1500. { PRACTICAL QUESTIONS, UNDER THE PRECEDING RULES. 1. Add fourteen thousand, five hundred and nine ; one thousand, nine hundred and twenty-one; six hundred and twenty thousand, three hundred and forty-seven; and five million, twenty-three thousand, and nineteen, together. Ans. 5659796 sum. 2. What is the sum of 76129+51216+39127+62357 +514026 ? Ans. 745855. 3. What is the difference between four inillion two hundred and ten thousand and twelve; and six hundred and fifty-nine thousand seven hundred and ninety-seven ? Ans. 3550215. 4. Take nine hundred and one thousand and fifteen, from one million one thousand one hundred and one ? Ans. 100086. 5. A farm of 460 acres is let for 2 dollars per acre ; how much does the rent amount to ? Ans. 920 dols. С 6. If a man's income be 6 dollars a day, how much does it amount to in a year, allowing 365 days in a year ? Ans. 2190 dollars. 7. What is the product of 376x54 ? Ans. 20304. 8. 64 men have 17280 dollars divided equally among them ; what is each man's part ! Ans. 270 dollars. 9. Multiply three hundred and seventy-eight thousand and five hundred, by thirty-four. Ans. 12869000 product. 10. What is the third part of 3669 ? Ans. 1223. 11. Divide 6764 by 19. Ans. 356 quotient. 12. What number must be added to 764 to make it 1256 ? Ans. 492. 13. By what number must I multiply 67, that the product may be 871 ? Ans. 13. 14. There are two numbers whose difference is 796, the greater number is 4320; I demand the less. Ans. 3524. 15. Supposing a man to have been born in the year 1762 ; how old was he in 1806 ? Ans. 44. 16. Suppose a man to have been 78 years old in the year 1806 ; in what year was he born ? Ans. 1728. 17. What will 12 tons of hay come to at 27 dollars Ans. 324 dollars. 18. What will 750 barrels of beef come to at 11 dollars per barrel; and what will the profits amount to in selling it, if I clear 3 dollars on each barrel ? 8250 dollars amount. per ton ? Ape. { 2250 dollars profit. 19. There is a town which contains 290 houses, and each house 6 inhabitants; how many inbabitants are there in that town ? Ans. 1740. 20. A prize of 48726 dollars is owned by 270 men; what is each man's share ? Ans. 18041 dollars. 21. If 12 bundles of wheat produce 1 bushel, how many bushels will 4764 bundles produce ? Ans. 397 bushels. 22. Borrowed of A, 12 sums of money, each 250 dollars; paid him at one time 97 dollars, and at another 35; the balance 1 am to pay him in six equal payments; what is one of those payments ? Ans. 478 dollars. TABLES OF MONEY, WEIGHTS, AND MEASURES. 1. Money,* 4 Farthings make one penny; gr. d. denote farthings and pence respectively. 12 Pence make one shilling Shilling. 20 Shillings 1 pound £ Pound. * Is one farthing, or one fourth; } is one halfpenny, or one half; } three farthings, or three fourths. OZ. 2. TROY WEIGHT. 24 Grains make one pennyweight, marked grs. dut. 20 Pennyweights 1 Ounce, 12 Ounces 1 Pound, By this weight are weigbed jewels, gold, silver, electuaries and liquors. Ib. or 16. D or oz. O ft. or 16. * 3. APOTHECARIES' WEIGHT. B0 Grains make 1 Scruple, marked gr. 7, or scr. 3 Scruples 1 Dram, 3, or dr. 8 Drams 1 Ounce, 12 Ounces 1 Pound, Apothecaries use this weight in compounding their medicines, but they buy and sell their drugs by Avoirdupois weight. Sterling money was, formerly, of the same value in all the Colonies of North-America. By reason, however, of the emission of paper money by the Legislatures of those Colonies, which afterwards depreciated, the Spanish dollar came to be reckoned, in different Colonies, at a higher or lower value, accordingly to the less or greater depreciation of their paper currencies. Still, though the pound was valued accordingly to this paper medium, it was, in every Colony, reckoned at twenty shillings, as in England. Thus, a Spanish dollar being worth 4s. 6d. in England, became, in Georgia and South-Carolina, where the depreciation of the paper was least, worth 48. 8d. ; in Canada and Nova-Scotia, where it was somewhat greater, 58. ; in NewEngland, Virginia, Kentucky, and Tennessee, 6s; in New-Jersey, Pennsylvania, Delaware and Maryland, 75, 6d. ; and in New-York, and North-Carolina, 8s. |