q.m. A. R. sq.r. sq.y. sq.ft. sq.in. sq.m. A. R. sq.r. sq.y. sq.ft. 204. ILL. Ex. Required the time from June 5, 1862, to Jan. 1, 1863. y. mo. d. 1853 1 1 Jan. being the 1st m. and June the 6th, we siotract 1862 y. 6 m. 5 d. from 1863 y. 1 m. 1 d., allowing 30 days for one month and 12 months for a Ans. 6 m. 26 d. year, and have for the answer 6 m. 26 d. 1862 6 NOTE. This method is not so exact as that illustrated in Art. 196, but is one in common use. 20. Required the time from the landing of the Pilgrims, Dec. 22, 1620, to the Declaration of Independence, July 4, 1776. 21. From the Declaration of Independence to the present time. 22. Nathaniel Bowditch was born March 26, 1773, and died March 16, 1838; what was his age? 23. Horace Mann was born May 4, 1796, and died Aug. 2, 1859; what was his age? 24. Lafayette was born Sept. 6, 1757, and died May 19, 1834; what was his age? 25. Required the time between the births of Tycho Brahe, Dec. 4, 1546, and La Place, March 23, 1749. 26. Required the time between the births of Benjamin Franklin, Jan. 17, 1706, and George Washington, Feb. 22, 1732. 27. How old was Washington when he died, Dec. 14, 1799? 28. How old was Lafayette when that event took place? For Dictation Exercises, see Key. 205. ADDITION AND SUBTRACTION COMBINED. 1. 3 qr. 9 lb. 8 oz. +7 cwt. 9 lb. 2 oz. +28 cwt. 2 qr. =? 2. 9 tb, 93, 13, 19, 9 gr. - 2 lb, 11 3, 43, 2, 18 gr. =? 3. 17 £. 9 s. 6 d. 3 qr. + 2 £. 12 s. 8 d. 2 qr. 7 £. 15 s. 8 d. 3 qr.=? 4. 28 cd. 2 cd. ft. 14 cu. ft. 19 cd. 6 cd. ft. 2 cu. ft. 4 cd. 5 cd. ft. 14 cu. ft.+ 18 cd. 3 cd. ft. 9 cu. ft.? 3.1848 cu. yd. 9 cu. ft. 1700 cu. in. (118 cu. yd. 7 cu. ft. 176 cu. in.+50 cu. yd. 960 cu. in.) =? f. 19 lb. 5 oz. 12 pwt. 19 gr. + 9 lb. 3 oz. 18 pwt. 2 gr. +7 lb. 8 oz. 17 pwt. 22 gr. (13 lb. 3 oz. 12 pwt. 18 gr. 2 lb. 12 wt. 16 gr.)? Ans. 25 lb. 3 oz. 8 pwt. 17 gr. 7. 7 T. 5 cwt. 2 qr. 20 lb. + 2 T. 8 cwt. 3 qr. 7 lb. 7 cwt. 18 lb. 1 T. 19 cwt. 24 lb. 10 oz.) = ? 3. 3° 7′ 18′′ +9° 12′ 40′′ +40° 12′ + 90° — 7° 2′ 8′′ 3' 10" 12° 3' 13") =? 9. 9 y. 22 w. 3 d. 10 h. 12 h. 10. 8 2 m. y. 25 w. (19° 5 d. 3 h. +8 y. 45 w. 4 y. 7 w. 6 d. 2 h. ? 3 d. 7 f. 12 r. 4 y. 1 ft.+ 4 f. 3 r. + 4 m. 5 f. 30 r 2 y. 3 m. 7 f. 38 r. 5 y. 1 ft. 4 in. =? 11. 3 sq. m. 204 A. 5 sq. r. 9 sq. yd. † 98 A. 3 R. 2 sq. rd. 4 3q. yd. — (140 A. 2 R. 34 sq. rd. 28 sq. yd. + 278 A. 1 R. 39 8. yd.)? 12. 384 cu. yd. 19 cu. ft. 1700 cu. in. 18 cu. in. - 116 cu. yd. 18 cu. ft. 394 cu. in.) +504 cu. yd. 24 cu. ft. 89 cu. in. =? 13. Mr. Day having 49£ ready money, pays to one man a debt of 5£. 7 s. 8 d.; to another, 10£. 15 s. 6 d. to the third, 18£. 12 s. 9 d.; how much money has he left? 9 Ans. 9° 34' 54". 14. What is the difference of latitude between Boston and Charleston? 15. Between Washington and London? 16. Between Philadelphia and Paris? 17. Between Quebec and St. Petersburg? 18. Between Portland and Cape Horn? † 19. Between Cape Horn and Cape Good Hope? 20. What is the difference of longitude between Boston and Montreal? 21. Between New Orleans and New York? 22. Between Mexico and Paris ?† * From the American Almanac and New American Cyclopedia. †The difference of latitude between places on opposite sides of the equator is found by adding the latitudes. The difference of longigitude between places on opposite sides of the first meridian is found by adding the longitudes. If their sum exceeds 180°, the difference of long tude equals 360° minus that sum. 23. Between Constantinople and Chicago? 24. Between Canton and San Francisco? For Dictation Exercises, see Key. 207. ADDITION AND SUBTRACTION OF DENOMINATE FRAC TIONS. ILL. EX., I. cwt. + qr. = what? These fractions, being of different denominations, must first be reduced to the same denomination. The fraction & cwt. may be changed to quarters, or the qr. may be changed to parts of a cwt., and then addition can be performed. In the first case, the answer will be in qr.; in the second, in cwt. Another excellent method is first to reduce both fractions to integers of lower denominations, if necessary (Art. 198), and then add. Thus, Perform the following examples, and give the answers, as far as possible, in whole numbers of lower denominations. 208. ILL. Ex. 1 pt. 3 gi. X 7 OPERATION. pt. gi. 1 3 7 6 qt. 0 pt. 1 gi. MULTIPLICATION. what? 7 X 3 gi.21 gi.=5 pt.+1gi.; we write 1 gi. under gi. in the multiplicand, and reserve the 5 pt. to add with the pints in the product. 7×1 pt.: with the pt. reserved 12 pt. 6 qt. 0 pt. 1 gi. Hence the 7 pt., which = 6 qt. 0 pt. Ans. RULE FOR MULTIPLICATION OF COMPOUND NUMBERS. Multiply the number of the lowest denomination by the multiplier, and divide the product thus obtained by the number it takes of that denomination to make one of the next higher; write the remainder under the term multiplied, and add the quotient with the product of the next higher denomination; and thus continue till all the terms of the multiplicand are multiplied. EXAMPLES. 1. 7 bu. 4 pk. 3 qt. 1 pt. X 5 = ? Ans. 40 bu. 2 pk. 1 qt. 1 pt. 2. 28 gall. 2 qt. 1 pt. 3 gi. × 17 = ? 3. 20 T. 16 cwt. 4 lb. 15 oz. X 25 =? × 37 = ? 5. 24 lb. 8 oz. 16 pwt. 5 gr. X 78 = ? 6. 118° 24' 52′′ × 55 = ? 7. 18 y. 37 d. 23 h. 14 min. 7 sec. X 12 = ?* 8. 36 y. 48 w. 5 d. 7 h. 3 m. 10 s. × 21 =? 10. 7 £. 6 s. 3 d. 2 qr. × 73 = ? 11. 4 m. 7 f. 35 rd. 3 yd. 2 ft. 11 in. × 29 = ? 12. 118 cd. 4 cd. ft. 1 cu. ft. X 35 = ? 13. 76 cu. yd. 12 cu. ft. 184 cu. in. × 24 =? 14. 4 sq. m. 320 A. 3 R. 25 sq. rd. 25 sq. yd. 7 sq. ft. 117 sq in. X 9 = ? 15. How much land in 9 gardens each containing 34 sq. rd. 4 sq yd. 8 sq. ft. 67 sq. in. ? * Art. 195, Note. |