161. From the preceding illustrations we derive the following GENERAL RULE FOR REDUCTION. I. To reduce compound Nos. to lower denominations. Multiply the highest denomination given, by that number which it takes of the next lower denomination to make ONE of this higher; to the product, add the number expressed in this lower denomination in the given example. Proceed in this manner with each successive denomination, till you come to the one required. II. To reduce compound Nos. to higher denominations. Divide the given denomination by that number which it takes of this denomination to make ONE of the next higher. Proceed in this manner with each successive denomination, till you come to the one required. The last quotient, with the several remainders, will be the answer sought. 162. PROOF.-Reverse the operation; that is, reduce back the answer to the original denominations, and if the result correspond with the numbers given, the work is right. OBS. Each remainder is of the same denomination as the dividend from which it arose. (Art. 66. Obs. 2.) STERLING MONEY. (ART. 147.) 5. In £35, 4s. 6d. how many pence? QUEST. 161. How are compound numbers reduced to lower denominations? How reduced to higher denominations? Obs. Of what denomination is each remainder? 162. How is Reduction proved? 7. In £43, 12s. how many shillings? 8. In 17 shillings, how many farthings? 9. In 1176 pence, how many pounds? 10. In 12356 farthings, how many shillings? 11. In 175 pounds, how many farthings? 12. In £84, 16s. 7 d., how many farthings? 13. In 25256 pence, how many pounds? 14. In 56237 farthings, how many pounds? 15. In £25, 9s. 74d., how many farthings? TROY WEIGHT. (ART. 148.) 16. In 11 lbs., how many pennyweights? Ans. 2640 pwts. 17. In 15 ounces, how many grains? 18. In 10 lbs. 5 oz. 6 pwts., how many grains? AVOIRDUPOIS WEIGHT. (ART. 149.) 22. Reduce 25 pounds to drams. Ans. 6400 drams. 23. Reduce 36 cwt. 2 qrs., to pounds. 24. Reduce 5 tons, 7 cwt. 15 lbs. to ounces. 25. Reduce 3 quarters, 15 lbs. 10 oz. to drams. 26. Reduce 875 ounces to pounds. 27. Reduce 1565 pounds to hundred weight. 28. Reduce 1728 drams to quarters. 29. Reduce 5672 ounces to tons. 30. Reduce 15285 pounds to tons. 31. Reduce 26720 drams to hundred weight. APOTHECARIES' WEIGHT. (ART. 150.) 32. How many drams are there in 70 pounds? Ans. 6720 drams. 33. How many scruples in 156 pounds? 34. How many ounces in 726 scruples? 35. How many pounds in 1260 drams? 37. In 45 furlongs, how many inches? 528 2 11)1056 Ans. 96 We first reduce the feet to yards, by dividing by 3; next, reduce the yards to rods, by dividing by 54. But to divide by 5, we reduce it to halves, and also reduce the dividend (528 yds.) to halves, then divide 1056 by 11. (Art. 139. I.) 39. In 1728 inches, how many rods? 40. In 26400 feet, how many miles? 41. In 25 leagues, how many inches? 42. In 40 leagues, 2 inches, 6 furlongs, how many feet? 43. In 750324 inches, how many miles? 44. How many barleycorns in the circumference of the earth? CLOTH MEASURE. (ART. 152.) 45. How many quarters in 45 yards? 49. Reduce 1824 nails to French ells. SQUARE MEASURE. (ART. 153.) 51. In 175 square rods and 7 yards, how many feet? 52. In 56 acres and 3 roods, how many square feet? 53. In 1275 square miles, how many acres? 54. How many square rods in 25640 feet? 55. How many acres in 1865 roods? 56. How many acres in 2135680 yards? 163. The area of a floor, a piece of land, or any surface which has four sides and four right angles, is proved by multiplying its length and breadth together. OBS. 1. The area of a figure is the superficial contents or space contained within the line or lines, by which the figure is bounded. It is reckoned in square inches, feet, yards, rods, &c. 57. How many square feet are there in a table which is 4 feet long and 3 feet wide? Suggestion. Let the table be represented by the subjoined figure, the length of which is divided into 4 equal parts, and the breadth into 3 equal parts, which we will call linear feet. Now it is plain that the table will contain as many square feet as there are squares in the given figure. But QUEST.-163. How do you find the area or superficial contents of a surface having four sides and four right angles? Obs. What is meant by the term area? How is it reckoned? What is a figure which has four sides and four right angles, called? the number of squares in the figure is equal to the number of equal parts (linear feet) which its length contains, repeated as many times as there are equal parts (linear feet) in its breadth; that is, equal to 4×3, or 12. The table therefore contains 12 square feet. OBS. 2. A figure which has four sides and four right angles, like the preceding, is called a Rectangle, or Parallelogram. 58. What is the area of a garden which is 8 rods long and 5 rods wide ? Ans. 40 square rods. 59. How many square feet in a floor, 18 feet long and 17 feet wide? 60. How many square yards in a ceiling, 20 feet long and 18 feet wide? 61. What is the area of a field which is 36 rods long and 25 rods wide? 62. How many acres are there in a piece of land 80 rods long and 48 rods wide? CUBIC MEASURE. (ART. 154.) 63. In 75 cubic feet, how many inches? 64. In 37 tons of round timber, how many inches? 65. In 28124 cubic feet, how many tons of square timber? 66. In 16568 cubic feet of wood, how many cords? 67. In 65 cords of wood, how many cubic feet? 164. The solidity, or cubical contents of boxes of goods, piles of wood, &c., are found by multiplying the length, breadth, and thickness together. 68. How many cubic inches are there in a box, whose length is 30 inches, its breadth 18, and its depth 15 inches? Ans. 8100 in. 69. How many cubic inches in a block of marble, 43 inches long, 18 inches broad, and 12 inches thick? QUEST.-164. How are the cubical contents of a box of goods, a pile of wood, &o., found? |