19. To perform Long Division. Ex. 29. Paid $4932 for 9 acres of land; what was the OPERATION. 45 43 36 72 Having set the divisor and dividend as in. 72 0 20. In the same manner solve the following examples; 37. How much tea, at 35 cents per pound, can be bought 12463 816 42 3746 24 27462 948 372439 for $8.75? 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 ? 21. REDUCTION. 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. 1pt. how many pints? OPERATION. bush. pk. qt. pt. 4 14 pk. 117 qt. 2 235 pt., Ans. 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 14pk.; then multiply the 14 by 8 to change the pecks to quarts; to the product, 112, add the 5qt. in the example, and the result is 117qt.; so proceed till the example is solved. 2. In 5gal. 3qt. 1pt. 2gi. how many gills? 4. In 3wk. 4d. 6h. 12m. 20sec. how many seconds? 6. Reduce 7yd. 3qr. 2na. to nails. 7. Reduce 3sq. m. 320a. 2r. 20sq. rd. to rods. 8 Reduce 3c. 5c. ft. 12cu. ft. 1654c. in. to inches. 9. Change 1843qr. to pounds, shillings, etc. OPERATION. 4)1843 qr. First divide by 4 to reduce the farthings to pence, giving 460d. and 3qr.; 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. 118s. 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, 14. Reduce 5327rd. to miles, furlongs, etc. 20. At 5c. a gill, what will 3gal. 2qt. 1pt. 3gi. of wine cost? tons 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 1oz. 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 lemons 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 com panies, having 133 men in each company? 5. What will 36 barrels of flour 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, how 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. 1qr.? 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. 13. Reduce 907336 seconds to weeks, days, 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 + 392648987 ? 20. How many are 689 + 964287-398? 21. From the sum of 384 and 426, take the difference between 567 and 432. 22. How many are 876 × 43 ? 968 X 382 ? How many are 87 × 33 +36 × 27 ? 16. What cost 54 tons of hay, at $18 per ton ? 27. A farmer sold 75 bushels of wheat, at $2 per bushel, for which he received 15 yards of cloth, at $4 per yard, and the balance in money; how much money did he receive? 28. A man's income is $1687 a year, and his expenses are $4 a day; what does he save in a year of 365 days? 29. The earth, in going round the sun, moves 19 miles per second; how far does it move in an hour? 30. Light moves 192000 miles in a second; how far does it move in an hour? One of these 31. I owe 3 notes, whose sum is $368. notes is for $125, another for $84; for what is the third one? 32. A and B start from the same place, and travel in the same direction, A at the rate of 48 miles, and B 64 mile per day; how far apart are they in 1 day? In 24 days? 33. A and B start from the same place, and travel in opposite directions, A at the rate of 36 miles, and B 44 miles, per day; how far apart are they in 35 days? 34. The President of the United States receives a salary. of $25000 a year; what will he save in a year of 365 days, if his expenses are $40 per day? 35. In 1 hogshead of wine there are 63 gallons; how many gallons in 36 hogsheads? 36. How many yards of cloth in 25 bales, each bale containing 54 pieces, and each piece 36 yards? 37. The last transit of Venus across the sun's face was in 1769, and the next will be in 1874; how many years between these two transits ? 38. Bonaparte was born in the year 1769, and lived 52 years; in what year did he die? 39. The first settlement in New England was made at Plymout in 1620; how many years is it since that time? 40. Fow long since the Declaration of American Independence in 1776 ? 41. A rectangular piece of ground is 72 rods long and 36 rods wide; how many square rods are there in the piece? How many rods is it round the piece? 42. A piece of ground is 42 rods square; cost to build a wall around it, at $2 per rod? piece of ground worth, at $3 per square rod? what will it 1 |