DENOMINATE NUMBERS. 193. Denomination is the name of a unit of measure. Thus, feet is the denomination of 6 ft.; pounds, of 25 lb., etc. 194. A denominate number is a number composed of one or more units of any denomination, and may be either simple or compound. 1. A simple denominate number is a number composed of but one denomination. Thus, 7 miles, 10 acres, 5 tons are simple denominate numbers. 2. A compound denominate number is a number composed of two or more denominations of the same nature. Thus, 10 lb. 6 oz., 5 yr. 4 mo., 4 ft. 2 in., are compound denominate numbers. 195. A denominate fraction is a fraction of a denominate number. Thus, of a pound, .9 of a ton, are denominate fractions. REDUCTION. 196. Reduction of denominate numbers is the process of changing their denomination without changing their value. Denominate numbers may be changed from higher to lower, or from lower to higher denominations. In integral numbers and in decimals, the law of increase and decrease is by the uniform scale of 10; but in compound numbers the scale varies. 197. To change a denominate number from higher to lower denominations. 1. How many inches in 26 rd. 3 yd. 2 ft. 9 in. ? EXPLANATION.-Since 1 rod equals 5 yards, 26 rd. 3 yd. equal 26 times 5 yd., plus 3 yd.; 5 yd. × 26 + 3 yd. 146 yards. = 26 rd. 3 yd. 2 ft. 9 in. 51 146 yd. 3 440 ft. 12 5289 inches. PRINCIPLE-A denominate number is changed to lower denominations by MULTIPLICATION. 2. Reduce 7 lb. 10 oz. 16 pwt. 11 gr. to grains. RULE.-1. Multiply the highest denomination of the given number by that number of the scale that will reduce it to the next lower denomination, and to the product add the given number, if any, of that denomination. 2. Proceed in like manner with this and each successive denomination obtained, until the reduction is brought to the required denomination. Reduce 5. 12 mi. 36 rd. 10 ft. to ft. Change 87 T. 9 cwt. 18 lb. to lb. 8. 22 lb. 10 oz. to pwt. 10. 1 common year to min. Change 11. 75 Cd. 6 cd. ft. to cu. ft. 12. 12 hhd. 21 gal. to pt. 13. 24 bu. 3 pk. to quarts. Reduce 14. 5 bundles to quires. 15. 6 G. gro to dozens. 16. 31 gal. to gills. 17. How much is 5 lb. 9 oz. 14 pwt. of gold dust worth, at $.75 a pwt.? 18. How many rods of fence will enclose a farm of a mile square? 19. If 1 barrel will hold 2 bu. 3 pk., how many barrels will be required to hold 1548 bu. 1 pk.? 20/How many boxes, each containing 12 lb., can be filled from a hogshead containing 9 cwt. 60 lb. of sugar? 21. If I buy 9 bu. of chestnuts at $4 a bushel, and retail them at 12 cents a pint, what is my whole gain? 22 If it require 4 reams 10 quires of paper to print a book, how many sheets are required? 23. At 12 cents each, what will be the cost of 2 great gross of writing books? 24. If a clock tick seconds, how many times will it tick during February, 1877 ? 25. How many pint, quart, and 2-quart bottles, of each an equal number, can be filled from a barrel of 314 gallons? 26. What will be the cost of 1 hhd. molasses at $.28 per gal.? 27. How many rods of fence will inclose a farm 14 mi. square? 28. If 14 A. of land are sold from a field containing 50 A., how many square rods does the remainder contain? 29. A man returning from Pike's Peak has 36 lb. 8 oz. of pure gold. What is its value, at $1.04 per pwt.? 30. In the eighteenth century, how many hours? 31. How large an edition of a 12mo book can be printed from 2 bales 2 bundles 15 quires of paper, allowing 8 sheets to the volume? 32. How many pages, 2 pages to each leaf, will there be in an 8vo book, containing 16 fully printed sheets? How many pounds 33. In 361 centals of grain? 34. In 424 bbl. of flour? 35. In 29.5 quintals of fish? 36. In 116 bbl. of salt? 37. In 63.25 kegs of nails? 38. In .75 of 75 bu. of salt? 39. In 125 bu. of wheat? 40. In of 21648 bu. oats? 41. In .7 of 40 bu. corn? 42. In 7.5 casks of lime? 198. 1. Reduce bu. and .645 da. each to integers of lower denominations. 199. To change a denominate number from lower to higher denominations. 1. Change 5722 inches to rods. EXPLANATION.-Since 12 in. 5722 in. 122 ft.=476 ft. 10 in.; make 1 ft. there must be as 476 ft. 158 yd. maining. = Since 3 ft. make 1 yd., there must be as many yards as feet; of 476 ft. is 158 and 2 ft. remaining. Since 5 yd. make 1 rd., there must be 1 51 of 316 half yd. is 28 and 4 yd. remaining. Hence, 5722 in. = 28 rd. 4 yd. 2 ft. 10 in. or 11 as many rods as yards; 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 denomina tion. 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 Reduce 5. Pounds Troy are 85894 gr.? 10. 120400 pens to gro. 6. Tons are 51570 pounds? 11. 2734 eggs to dozens. |