199. To change a denominate number from lower to higher denominations. 1. Change 5722 inches to rods. Since 3 ft. make 1 yd., there must be as many yards as feet; of 476 ft. is 158 and 2 ft. remaining. 1 Since 5 yd. make 1 rd., there must be or as many rods as yards; 51 of 316 half yd. is 28 and 4 yd. remaining. Hence, 5722 in. = 28 rd. yd. 2 ft. 10 in. In order to divide by 51, both dividend and divisor may be reduced to halves before dividing. In this case the remainder, if any, is halves, which may be reduced to integers. PRINCIPLE. A denominate number is changed to higher denominations by DIVISION. 2. Reduce 6048 gills to hogsheads. 3. In 3199 pints, how many bushels? 4. In 31556926 seconds, how many days? RULE.-1. Divide the given denomination by that number of the scale which is equal to a unit of the next higher denomination. 2. In like manner, divide this and each successive quotient, until the denomination required is reached. The last quotient, with the remainders annexed, will be the required result. How many 5. Pounds Troy are 85894 gr.? to gro. Reduce 33. Of 1 T. 15 cwt. 36 lb. of sugar, at 9 cents a pound? 34. Of 2 lb. 8 oz. 12 pwt. of gold dust, at $.72 a pwt.? 35. Of 3 mi. of telegraph wire, at 12 cents a foot? 36. Of 1 hhd. of wine, at 40 cents a pint ? 37. Of 2 bu. 1 pk. 6 qt. grass seed, at 14 cents a quart? 38. Of 2760 lb. of wheat, at $1.50 a bushel? 39. Of 12 weeks board, at $2.62 a day? 40. Of 1 half acre of land, at 25 cents a square foot ? 50. Of 3 T. 17 cwt. 20 lb. of hay, at $222 a ton? 51. At 12 cents a pint, how much molasses can be bought for $8.52? 52. What is the cost of a load of oats weighing 1960 lb., at. $.56 a bushel? 200. 1. What decimal of a pound Troy are 2 oz. 14 pwt.? 240 pwt. 2 oz. 14 pwt. 240 lb..225 lb. In order to find what part one com- Thus, 2 oz. 14 pwt. are equal to lb. 1. If the given number contain a fraction, the denominator of this fraction must be regarded as the lowest denomination. 2. The pupil may be required to give the answers either in the form of a fraction, or of a decimal, or both. What part of 2. 1wk. is 3 da. 2 hr. 40 min.? 9. 2 lb. Avoir. is 10 oz.? What decimal of 10. 2 cd. is 4 cd. ft. 8 cu. ft.? 18. From a hhd. of molasses 28 gal. 2 qt. were drawn. What part of the whole remained? 19. What part of 1 barrel of flour is 243 lb. ? 20. What part of 15 cwt. 21 lb. is 2 cwt. 11 lb. ? 21. What part of 4 gal. 3 qt. is 3 qt. 2 gi.? 22. What part of 54 cords of wood are 4800 cu. ft. ? 23. What part of 3 bbl. of flour are 110 lb. 4 oz. ? 01. To find the sum of two or more denominate mbers, or denominate fractions. Denominate numbers are added, subtracted, multiplied, and divided by the same general methods as are employed for like operations in Simple Numbers. The corresponding processes are based upon the same principles. The only modification of the rules needed is that which is required by a varying scale instead of the uniform or decimal scale of 10. The principles will be made sufficiently plain in the solutions and explanations to enable the pupil readily to construct a rule for each. 1. What is the sum of 32 bu. 2 pk. 6 qt.; 24 bu. 1 pk. 4 qt.; 16 bu. 3 pk. 7 qt. ? EXPLANATION.-Write the numbers so that units of the same denomination stand in the same column, and begin at the right to add. The sum of the quarts is 17 qt., equal to 2 pk. 1 qt. Write the 1 qt. under the column of quarts, and add the 2 pk. to the column of pecks. Add, in like manner, the column of pecks and bushels. bu. pk. qt. 32 2 6 24 16 74 2. What is the sum of wk., & da., and hr.? 4. A farmer received $.75 a bushel for 4 loads of corn; the first contained 48.4 bu., the second 2626 lb., the third 363 bu., and the fourth 41 bu. 52 lb. What did he receive for the whole? 5. Bought 3 loads of hay at $15 a ton. The first weighed 1.125 T., the second 13 T., and the third 2750 lb. What did the whole cost? 6. A tailor used in one year, 2 gross 5 doz. 10 buttons, another year 3 gross 7 doz. 9, and another year 4 gross 6 doz. 11; how many did he use in the three years? 7. What is the sum of § of a day added to of an hour? 8. To of a hhd. add § of 10 gal. 9. What is the sum of 224 cwt., 267 lb., and 14 oz.? 10. Add 5 Cd. 7 cd. ft., 2 Cd. 2 cd. ft. 12 cu. ft., 6 cd. ft. 15 cu. ft., 73 Cd., and 3 Cd. 2 cu. ft. 11. Add 7 yd. 2 ft., 5 yd. 14 ft., 2 ft. 91⁄2 in., 3 yd. 1 ft. 6 in., 2 ft., and 4 yd. 12. What is the sum of 1 hhd., 36 gal. 3 qt. 14 pt., gal., 2 qt. pt., and 1.75 pt. ? 202. To find the difference between any two denominate numbers, or denominate fractions. 1. From 16 lb. 8 oz. 6 pwt. 10 gr., take 7 lb. 4 oz. 12 pwt. 9 3 14 4 Since 12 pwt. cannot be subtracted from 6 pwt., take 1 oz., equal to 20 pwt., from the 8 oz., leaving 7 oz., and add it to the 6 pwt., making 26 pwt.; 12 pwt. from 26 pwt. leaves 14 pwt., which write under the pennyweights. Since 1 oz. was taken from 8 oz., subtract 4 oz. from 7 oz., and write the difference, 3 oz., under the ounces. 7 lb. from 16 lb. leaves 9 lb.. which write under the pounds. Hence, etc. |