The grain is the same in the three weights, Avoirdupois, Troy, and Apothecaries'. It is obtained by taking a certain fraction (very nearly) of the weight of a cubic inch of distilled water at its greatest density (39.2° nearly). REDUCTION OF DENOMINATE NUMBERS 200. Changing numbers to larger denominations is reduction ascending. 201. Changing numbers to smaller denominations is reduction descending. 202. Oral 1. Find the number of cubic inches in one quart, liquid measure. 2. A fountain contains four barrels of water. gallons does it contain? How many hogsheads? How many 3. A grocer bought green peas at two dollars a bushel, and retailed them at ten cents a quart. What did he gain on three bushels? 4. What is a grocer's profit on half a ton of coffee bought at $15 per hundredweight and sold at 20 cents a pound? 5. A gold dollar weighs 25.8 grains. dollars will weigh 25.8 pennyweights? How many gold 6. A druggist bought 10 lb. (Avoir.) of oxalic acid. How many grains did he buy? 7. A can contained 20 ounces (Apoth.) of quinine sulphate. How many pounds (Apoth.) did it contain? How many drams? How many scruples? How many grains? 8. A field is 20 rods wide. How many feet wide is it? How many yards? 9. The perimeter of a square yard is how many inches? 10. A 100-acre farm contains how many square chains? 11. A cubic yard of earth is sometimes called a load. How many cubic feet of earth are there in twenty such loads? 12. Name the leap years from 1890 to 1920 inclusive. 13. What is the exact number of days from 2 o'clock P.M., Jan. 19, 1904, to 2 o'clock P.M., April 1, 1904? 14. A gross of 2-pound cans of baking powder will fill how many cases, each holding 48 cans? How much will the baking powder weigh? 15. How many clothespins are there in a box containing 10 gross? 16. Four gallons of ammonia water will fill how many 4-ounce bottles? 17. How many quires of paper will a lady use in writing thirty letters if she uses two sheets of paper for each letter? 18. The earth makes one complete rotation every 24 hours. How many degrees does it turn in 1 hour? 19. A wheel in a factory makes 240 revolutions per minute. How many revolutions does it make in one second of time? Through how many degrees does it revolve in of a second? 20. A wheel has eight spokes that make equal angles at the center. How many degrees are there in each of the angles? Two of these angles together form what kind of angle? 21. A crown is an English coin equal to five shillings. A sovereign is a gold coin whose value is £1. Mr. Denham has in his purse a sovereign, two crowns, one half crown, a shilling, and a sixpence. All the money in the purse is equal to how many shillings? 22. 38,476 centimes are equal to how many francs and centimes? 23. 46 francs are equal to how many centimes? 24. 86.75 marks are equal to how many pfennigs? 25. At the rate of 20 pfennigs apiece, how many oranges can be bought for 4 marks? 26. Without a rule, draw a line 5 feet long on the blackboard. Measure and correct it. 27. Estimate, then measure: a. The number of feet from the front door of your schoolhouse to the sidewalk. b. The width of the sidewalk. d. The dimensions of the schoolroom windows. e. The dimensions of the schoolroom doors. 203. 1. Reduce 22 A. 7 sq. yd. to square feet. 2. Reduce 392,429 sec. to larger denominations. 60 392429 sec. 60 6540 min. 29 sec. 24 109 hr. 4 da. 13 hr. 4 da. 13 hr. 29 sec. Ans. NOTE.- Compound numbers, other than those expressing time, or arc and angle measure, are seldom expressed in more than two denominations. Extended reductions are rarely needed. In actual business, the work of reduction is performed by short and direct processes. For example, surveyors, in measuring land, use a metallic tape from fifty to one hundred feet in length, marked off in feet and tenths of a foot, or a chain with links one foot in length, marked in tenths. With this they obtain the dimensions of a piece of land in feet and tenths of a foot, and the area in square feet and hundredths of a square foot. The area in square feet divided by 43,560 (the number of square feet in one acre) gives the number of acres. Feet are reduced to miles by dividing by 5280 instead of dividing successively by the numbers in the scale of linear measure. Bushels are reduced to quarts by multiplying directly by 32. In all measurements and computations, decimals are more generally used than formerly, taking the place of common fractions and the smaller units of denominate numbers. In the following examples, use short and direct processes where possible. 204. Written 1. Reduce: a. 14 wk. 3 da. to hours. b. 5 T. 7 cwt. to pounds. c. 4900 min. to higher denominations. d. 7 mi. to inches. e. 18 bbl. 13 gal. to pints. f. 193,479 cu. in. to higher denominations. i. 86,240 pwt. to pounds. j. 9 oz. Apoth. to grains. k. 84,763d. to pounds, shillings, and pence. 1. £5 108. 11d. to pence. m. 48° 50' 19'' to seconds. n. 12 common years to minutes. o. 190,113 in. to higher denominations. p. 5040 pt. to hogsheads. (Use 30 da. for one month.) (Use 365 days for a year.) q. 3 yr. 7 mo. 21 da. to minutes. u. 118,096 sq. yd. to higher denominations. 2. 12,480 in. are what part of a mile? This problem may be solved in two ways: a. 12480 × 1 × 332 3 × 320 ? = = b. 13488? (There are 63,360 in. in a mile.) 63360 In what other way could this problem be solved? (1 lb. Troy how many grains?) = 4. Change 1⁄2 cu. yd. to cubic inches. 5. 270 sec. are what part of a day? |