WRITTEN EXERCISES. 185. 1. Reduce 1463 quarters to tons. OPERATION. 4)1463 qr. 20)365 3 qr. 18 T. 5 cut. Ans. 18 T. 5 cut. 3 qr. Since in 4 quarters there is 1 hundred, in 1463 quarters there are as many hundred as 4 quarters are contained times in 1463 quarters, which are 365, and 3 quarters remaining. Since in 20 hundred there is 1 ton, in 365 hundred there are as many tons as 20 hundred are contained times in 365 hundred, which are 18, and 5 hundred remaining. Therefore, there are in 1463 quarters, 18 T. 5 cwt. 3 qr. Rule. - Divide the given number by the number of its denomination required to make one of the next higher, and reserve the remainder, if any. Proceed in like manner with the quotient, and so continue till the whole is reduced to the required denomination. The number of the required denomination, with the several remainders, if any, will be the answer. In the second operation, to divide 1170 by 5, we first reduce both numbers to halves, by multiplying by 2, and have 2340 halves to be divided by 11 halves, which gives 212, and a remainder of 8 halves 4. 4. Reduce 305 pennyweights to pounds. 5. Reduce 183073 square yards to acres. 6. Reduce 361152 cubic inches to cubic yards. 7. Reduce 1008 quarts to hogsheads. 8. Reduce 1469 quarts to bushels. 9. Reduce 37038 seconds to hours. 10. Reduce 11056 seconds to degrees. 11. In 4900 pounds how many tons? 12. In 2708 gills how many hogsheads? 13. In 19600 ounces how many hundreds? 14. In 38040 minutes how many weeks? 15. In 10265 rods how many miles? 16. How many acres in 2315 square rods? 17. How many cords in 768 cord feet? 18. How many degrees in 165390 seconds? 186. The preceding rule, in its application to United States money, since the divisors will be 10, 100, or 1000, admits of an abridged operation. To reduce cents to dollars, point off Two figures from the right, and prefix the dollar mark; to reduce mills to dollars, point off THREE figures, and prefix the dollar mark. To reduce mills of two or more places of figures to cents, consider the figure on the right to express mills, and the other cents. 19. Reduce 9800 cents to dollars. 20. Reduce 1680 mills to cents. How can you reduce cents to dollars? Mills to dollars? to cents? Mills 21. Reduce 106000 mills to dollars. REVIEW. 1. How many pounds in 7 T. 18 cwt.? 9. How many quarts in 17 bu. 1 pk. 4 qt.? 12. In 215 feet how many rods? 13. Reduce 3 A. 3 R. 20 P. to square yards 14. Reduce 18755 square yards to acres. 15. Reduce 3 cu. yd. 9 cu. ft. 1480 cu. in. to cu. in. 16. Reduce 157000 cubic inches to cubic yards. 17. Reduce 506 d. 22 h. 40 min. to minutes. 18. Reduce 730000 minutes to days. 19. How many minutes in one common year? 20. How many years in 525600 minutes? How is Reduction Descending performed? Ans. By Multiplication. How is Reduction Ascending performed? Ans. By Division. How then do their operations differ? How is each kind of Reduction proved? Ans. Each by the process of the other. 21. Reduce 14° 5' to seconds. 22. Reduce 50700 seconds to degrees. 23. In 5 reams of paper how many sheets? 26. In 46050 mills how many dollars? 30. In 3199 cents how many dollars? 33. In 3 miles how many inches? 34. In 190080 inches how many miles? 35. In 57935 mills how many dollars? 36. In $57.935 how many mills? 37. In a pile of wood 96 feet long, 4 feet high, and 4 feet wide, how many cords? Ans. 12 cords. 38. How many square feet in a board 20 feet long and 2 feet wide? Ans. 40 square feet. 39. What cost 1 quarter-hundred of beef, at 9 cents a pound? SOLUTION. Since 1 quarter hundred is 25 pounds, 1 quarterhundred of beef, at 9 cents a pound, will cost 25 times 9 cents, which are 225 cents, or $2.25. Therefore, it will cost $2.25. 40. What cost a barrel of flour, at 6 cents a pound? 41. What is the value of a rectangular lot, 40 rods long, and 20 rods wide, at 50 cents a square rod? 42. In a block of stone, 6 feet long and 2 feet square, how many cubic feet? Ans. 24 cu. ft. REVIEW. - Recite the Table of United States Money. (69.) Of Avoirdupois Weight. (151.) Of Troy Weight. (152.) Of Linear Measure. (153.) 43. How many grains in 15 silver spoons, each weighing 6 pwt. 15 gr.? Ans 2385. 44. What is the cost of levelling a plat of ground, 20 rods long and 20 rods wide, or 20 rods square, at 25 cents a square rod? Ans. $100. 45. What is the value of a pile of wood 20 feet long, 6 feet high, and 4 feet wide, at 50 cents a cord foot? Ans. $15. 46. What will it cost to pave with marble the floor of a room, 4 yards square, at $1.25 per square foot? 47. How many hundred-weight of sugar, at 15 cents a pound, can be bought for $20.40? SOLUTION. There will be as many pounds as 15 cents are con◄ tained times in $20.40, or in 2040 cents, which are 136; and as many hundred-weight as are in 136 pounds, or 1 cwt. 1 qr. 11 lb. Therefore, there can be bought 1 cwt. 1 qr. 11 lb. 48. How many hogsheads of molasses, at 12 cents a quart, can be bought for $75.12? Ans. 2 hhd. 30 gal. 2 qt. 49. If the heart beat 70 times in a minute, how many days will be required for it to beat 705600 times? Ans. 7 days. 50. If a ship can sail at the rate of 8 miles an hour, how many weeks will be required for it to sail 4448 miles? Ans. 3 wk. 2 d. 4 h. 51. If a comet move through 10° in one day, how many signs will it move through in 14 days? Ans. 4 S. 20° 52. If 9 candles can be made from 1 pound of tallow, how many dozen can be made from 60 pounds? -- Ans. 45 dozen. REVIEW. Recite the Table of Square Measure. (159.) Of Solid Measure. (163.) Of Time Measure. (166.) Of Circular Measure. (175.) |