8. Reduce of a mile to integers of lower denominations. Process. mi.of 320 rd. = 2440 rd. = 2037 rd. yd. there is of 3 ft. of a ft. there is of 12 in. Therefore, of a mile =203 rd. 3 yd. 1 ft. 6 in. Reduce to integers of lower denominations: 1 ft. Since there are 12 in. in 1 ft., in 6 in. Reduce to a decimal of the highest denomination : 16. 14 cwt. 9 lb. 12 oz. 22. What part of a ton is 19. 124 rd. 4 yd. 2 ft. 8 in. 20. 56 gal. 3 qts. 1 pt. 2 gi. 21. 87° 29' 52". 14 cwt. 72 lb. 12 oz. ? lb. 12 oz. = 12 × 1 400 = 40 58 to which the 14 cwt. given are added Analysis. Since 1 oz. is of a lb., 12 oz. are + lb. = lb., to which the 72 lb. given are added. Since 1 lb. is Too of a cwt., 722 lb. are 481 cwt., = 1428 cwt. Since 1 cwt. is of a ton, 1428 cwt. is 5888 of a ton. Therefore, 14 cwt. 72 lb. 12 oz. = 5881 T. Reduce to a fraction of the highest denomination : 23. 3 pk. 7 qts. 1 pt. 24. 80° 14' 18". 26. 185 rd. 4 yd. 2 ft. 25. 36 sq. rd. 18 sq. yd. 28. 18s. 6d. 3 far. Addition of Denominate Numbers. 1. What is the sum of 12 lb. 8 oz. 11 pwt. 9 gr.; 8 lb. 7 oz. 8 pwt. 8 gr.; 21 lb. 6 oz. 19 pwt.; 27 lb. 5 oz. 21 gr.? 20 pwt. 8 pwt. 11 pwt. are 39 pwt., equal to 1 oz. and 19 pwt. We write 19 under the column of pwt., and add 1 oz. to the column of oz. to 2 lb. and 3 oz. 6 oz. 6 oz. 7 oz. and 8 oz. are 27 oz., equal We write 3 under the column of oz., and add 2 to the column of lb. 29 lb. 21 lb. 8 lb. and 12 lb. are 70 lb., which we write under the column of pounds. 2. Find the sum of 13s. 1d.; £99 2s. 5d. £18 11s. 7d.; £110 18s. 9d.; £188 3 far.; £90 8d. 2 far. 3. What is the sum of 18 mi. 88 rds. 5 yds. 1 ft. 9 in.; 19 mi. 5 yds. 2 ft. 11 in.; 74 mi. 200 rds. 4 yds. 2 ft. 6 in.; 144 rds. 5 yds. 7 in.? 4. What is the sum of 18 bush. 3 pks. 6 qts.; 23 bush. 4 qts.; 11 bush. 1 pk. 7 qts. 1 pt.; 3 pks. 1 pt.; 40 bush. 4 qts. 1 pt.; 29 bush. 6 qts. 11⁄2 pts.; 77 bush. 2 pks. 4 qts.? 5. Add 15° 28′ 47′′; 24° 36′ 52"; 5 S. 20° 51′ 11′′; 9 S. 15° 34' 54". 6. Add 3 A. 110 sq. rds. 10 sq. yds.; 4 A. 3 sq. rds. 11 sq. yds.; 120 sq. rds. 20 sq. yds. 10. Illustrate addition of denominate numbers by a problem in long measure. 11. Illustrate addition of denominate numbers by a problem in cubic measure. Subtraction of Denominate Numbers. ART. 235.—1. From 33 gal. 2 qts. 1 pt. 3 gi. take 27 gal. 3 qts. 1 pt. and 2 gi. from 1 pt. leaves 0 pts., which we write under the column of pts. 3 qts. cannot be taken from 2 qts., so we increase 2 qts. by 1 gal., making 6 qts. 3 qts. from 6 qts. leaves 3 qts., which we write under the column of qts. Since we increased the minuend by 1 gal., we increase the subtrahend by 1 gal. 28 gal. from 33 gal. leaves 5 gal., which we write under the column of gallons. Subtract: 2. 121 lb. 1 oz. 11 pwt. 17 gr. from 144 lb. 2 oz. 10 pwt. 18 gr. 3. 99 hhd. 24 gal. 3 qts. from 100 hhd. 20 gal. 1 pt. 4. 180 mi. 220 rds. 4 yds. 1 ft. 9 in. from 202 mi. 218 rds. 3 yds. 1 ft. 8 in. 5. A jeweler having 11 lb. of gold, used 1 lb. 2 oz. 5 pwt. 5 gr. in making watch chains, and 7 lb. 9 oz. 9 pwt. 20 gr. in other articles: how much gold was left? 6. General U. S. Grant died July 23, 1885, and General G. B. McClellan, October 29 of the same year: what is the difference between the two dates ? 7. Sir Moses Montefiore was born October 24, 1784, and died July 28, 1885: what was his age when he died? 8. The steamship Alarm left New York at 4.15 P.M. December 19, 1885, and reached the Galveston bar at midnight December 25: what was the time occupied in the passage? 9. Alaska was ceded by Russia to the United States, June 20, 1867: how long was that after the discovery of America by Columbus, October 12, 1492 ? 10. How many years between the breaking out of the American Revolution, April 19, 1775, and the declaration of war against Great Britain, June 19, 1812 ? 11. War was declared against Mexico, May 13, 1846, and closed February 2, 1848: how long did the war last? 12. The war for the Union began at Fort Sumter, April 14, 1861, and General Lee surrendered April 12, 1865 how long did the war last? 13. The Military Academy at West Point was founded by Congress, March 16, 1802, and the Naval Academy at Annapolis was opened October 10, 1845: how much time. between the dates ? 14. The first passenger railroad was opened in England, September 27, 1825: how long was that after the arrival of the Savannah (the first steamer which crossed the Atlantic) at Liverpool, May 24, 1819 ? 15. The first public telegram that ever passed over a wire was sent from Baltimore to Washington, May 27, 1844 how long ago was it? 16. Washington was inaugurated first President April 30, 1789: how long was that previous to the first success of the telephone, May 14, 1877 ? 17. How long after the surrender of Cornwallis at Yorktown, October 19, 1781, was fought the battle of Waterloo, June 18, 1815 ? 18. Illustrate by an original problem subtraction of denominate numbers. |