DIVISION OPERATION. 17. BY DIVISION we find how many times one number is contained in another. The number to be divided, is called the DIVIDEND; the number by which to divide is called the Divisor; the number of times the dividend contains the divisor is called the Quotient. If anything is left after dividing, it is called the REMAINDER. 18. To perform Short Division. In dividing we first say, 7 in Divisor, 7)364 Dividend. 36, 5 times and 1 remainder; Quotient, 52 set the quotient, 5, under the 6 of the dividend, and then, imagining the remainder, 1, placed before the 4, say, 7 in 14, 2 times; set the 2 under the 4, and thus we find the quotient, 52. This process is called Short Division. 2. 3. 5. Divisor, 6)162 Dividend. 5)875 8)432 6)456 Quotient, 27 16. How much sugar, at 9 cents a pound, can be bought for 342 cents, or $3.42 ? Ans. 381b. 17. How many pigs, at $5 each, can be bought for $285 ? 18. If a horse travels 7 miles per hour, in how many hours will he travel 1001 miles ? 19. Divide 161 by 7. ? 20. Divide 204 by 6. 24. 9732 25. 1768 2=? 21. Divide 475 by 5. 26. 7648 - ? 22. Divide 345 by 3. 27. 4428 23. Divide 846 by 9. 28. 3762 OPERATION. 19. To perform Long Division. Ex. 29. Paid $4932 for 9 acres of land; what was the price per acre ? Having set the divisor and dividend as in 9)4932(548 Short Division, draw a curve at the right of the 45 dividend, and then say, 9 in 49, 5 times, and set 43 the 5 at the right of the dividend. Then 36 multiply the divisior by the quotient, 5, and set the product, 45, under the 49 of the dividend, 72 and substract the 45 from the 49. To the re72 mainder, 4, annex 3, the next figure of the 0 dividend, so forming a new partial dividend, and then say, 9 in 43, 4 times, and set the 4 as the next figure of the quotient. Multiply the divisor by this new quotient-figure, and substract the product from the partial dividend. Proceed in this manner until the whole dividend has been divided. This is called Long Division. 20. In the same manner solve the following examples ; also divide in the manner indicated by the signs. 30. 31. 32. 8)3568(446 12)6564(547 13)4753(365 92 60 39 {Bivide 144 34. { Bivide 309120 1728 : 72 90090 - 195 33. 12 4095 • 15 977523 27462 = 948 3724 : 39 37. How much tea, at 35 cents per pound, can be bought for $8,75 ? 36. {Bivide 59481 : 316 38. How much flour, at $9 per barrel, can be bought for $3762 ? 39. In how many days can a man walk 252 miles, if he walks 21 miles per day? 40. How many days are there in 1728 hours ? 41. How many dollars in 3168 shillings, if 6 shillings make a dollar ? If 8 shillings make a dollar ? 42. In how many days will a ship sail 5040 miles, if she sails 144 miles per day ? 43. A drover paid $1431 for 27 oxen ; what was the average price per ox? 44. In how many hours will a locomotive run 1225 miles, if it runs 25 miles per hour ? 45. A farmer raised 1458 bushels of corn on 27 acres; how many bushels per acre did he raise ? REDICTION. 21. From the Lessons in Section V, the learner will readily see the nature of the following examples. The changing or reducing numbers from one name or denomination to another, without altering their values, is called REDUCTION. 1. In 3bush. 2pk. 5qt. 1 pt. how many pints ? OPERATION. bush. pk. qt pt. 3 2 5 1 14 pk. 8 Multiply the 3 by 4 to change the bushels to pecks; to the product, 12, add the 2pk. given in the example, and the result is 14 pk. ; then multiply the 14 by 8 to change the pecks to quarts; to the product, 112, add the 59t. in the exaluple, and the result is 117qt.; so proceed till the example is solved. 2. In 5gal. 3qt. 1pt. 2gi. how many gills ? OPERATION. 9. Change 1843qr. to pounds, shillings, etc. First divide by 4 to reduce the far4)1843 qr. things to pence, giving 460d. and3qr. ; 12)460d. + 3qr. then divide the 460 by 12 to reduce pence to shillings, giving 38s. and 4d. ; then di20)38s. + 4d. vide the 38 by 20 to reduce shillings to 1£ + 18s. pounds, and thus obtain the Ans. Ans. 1£ 18s. 4d. 3qr. 10. Change 387na. to yards, quarters, etc. 11. Change 16879gr. Troy Weight to pounds, ounces, etc. 12. Change 16879gr. Apothecaries' Weight to pounds, etc. 13. Change 716893ur. to tons, etc. 14. Reduce 5327rd. to miles, furlonys, etc. 15. Reduce 47386sq. in. to square yards, etc. 16. Reduce 356482c. in. to cubic yards, etc. 17. Reduce 876gi. to gallons, quarts, etc. 18. Reduce 647pt. to bushels, pecks, etc. 19. Reduce 753986sec. to weeks, days, etc. 20. At 5c. a gill, what will 3gal. 2qt. 1 pt. 3gi.of wine cost ? 21. At 3c. apiece, what will 3 gross, 5 dozen, and 6 buttons cost? 22. At 2c. a sheet, what will 3 reams, 6 quires, and 8 sheets of paper cost ? 23. At $16 per ounce, what are 3 lb. 7oz. of gold worth? 24. At 2c. per ounce, what are 15 lb. 14oz. of iron worth? 25. At 2c. a pint, what are 5bush. 3pk. 6qt. 1pt. of corn worth? 26. If loz. of iron will make 3 nails, how many nails may be made of 7 lb. 15oz. of iron ? 27. At 2c. a pint, what are 5gal. 2qt. 1pt. of milk worth ? 28. At 3c. apiece, what are 6 dozen and 9 oranges worth ? 29. At 2c. apiece, what are 3 score and 15 lewons worth ? MISCELLANEOUS EXAMPLES. 1. Mr. Stone had 364 acres of land in one piece, and 274 acres in another piece; but he has sold 125 acres from the first, and 94 acres from the other; how many acres has he now? 2. Mr. Pray paid $115 for one piece of carpet, and $112 for another; he sold both pieces for $250 ; how much did he gain ? 3. What is the value of 65 acres of land at $137 per acre ? 4. How many men are there in a regiment of 15 companies, having 133 men in each company? 5. What will 36 barrels of four cost, if 9 barrels cost $99 ? 6. . What will 13 acres of land cost, if 52 acres cost $7488 ? 7. If 12 men can cut 60 cords of wood in a week, bow many cords can 17 men cut in the same time? 8. How many rods are there in 875 miles, 5 furlongs, and 33 rods? 9. How many farthings are there in 354£ 17s. 9d. Iqr. ? 10 A man has two farms which together contain 432 acres, and one farm is 7 times as large as the other; how many acres are there in each ? 11. Divide 1728 into two such parts that the first shall be 11 times as large as the second. 12. Reduce 940819 drams to tons, etc. 14. If a man can walk 23 miles per day, in how many days can he walk 391 miles ? 15. A road-builder employed 33 men, giving the same wages to each, and at the end of 2 months it took $1584 to pay them ; what were the wages of each per month? 16. In a certain house there are 8 rooms, having 3 windows in each room, and 12 panes of glass in each window; how many panes of glass are there in the house ? 17. A merchant having 3 pieces of cloth measuring 63yd., 45yd., and 56yd. severally, sold 22yd. from the first, 31yd. from the second, and 14yd. from the third ; how many yards had he remaining ? 18. Mr. Holt owed $3462, but paid $1362 in May, and $897 in June; how much did he still owe? 19. How many are 876 + 392 + 648 — 987 ? 20. How many are 689 + 9642 +87- 398 ? 21. From the sum of 384 and 426, take the difference between 567 and 432. 22. How many are 876 x 43 ? 968 X 382 ? |