Ex. 5. Reduce 49 acres, 28 poles, 10 yards, 8 feet, 112 inches, to inches. Prove the result. Now, since 30 or 121 sq. yds.=1 sq. po., we multiply by 4, which reduces the sq. yds. into quarters of sq. yds., and then divide that result by 121, or 11 × 11, which brings it into sq. poles. Therefore in 308471296 sq. in., there are 49 ac., 28 sq. po., 10 sq. yds., 8 sq. ft., 112 sq. in. Ex. 6. How many half-guineas are there in 537 half-crowns? By Rule 1, 537 half-crowns = (537 × 5) sixpences = 2685 sixpences. Next, to find how many half-guineas there are in 2685 sixpences. therefore in 537 half-crowns, there are 127 half-guineas and 18 sixpences. Ex. XXXIII. (1) Reduce (verifying each result); 1. £57 to pence; and 613 guineas to farthings. 2. £15. 128. to pence; and 5000 guineas to pence. 3. 88. 4 d. to half-pence; and £1. Os. 3 d. to farthings. 4. £83. 15s. 6d. to farthings; and £393. Os. 111d. to half-pence. 5. 738 half-crowns to farthings; and 570 crowns to fourpenny pieces. 6. 2673 half-guineas to farthings; and 221 guineas to sixpences. (2) Find the number of pounds in 5673542 farthings, and prove the truth of the result. (3) How many half-crowns, how many sixpences, and how many fourpences, are there in 25 pounds? (4) In 6300 fourpences, how many half-crowns are there, and how many half-guineas? (5) In 351 seven-shilling-pieces, how many half-guineas are there, and how many moidores? (6) Reduce, verifying the result in each case, the following: 1. 59 lbs., 7 oz., 14 dwts., 19 grs. to grains; and 37400157 grs. to lbs. 2. 56332005 scrs. to lbs. Troy; and 536 lbs. to drams and scruples. 3. 7 tons, 15 cwt., 2 qrs., 16 lbs. to ounces; and 7563241 drs. to tons. 4. 5838297 oz. to tons; and 33 tons, 17 cwt., 3 qrs., 27 lbs., 15 drs. to drams. 5. 17 lbs. 2 3., 2. to grains; and 34678 grs. Apoth. to oz. Troy. 8. 1364428 in. to leagues; and 74 m., 3 fur., 4 yds. to inches. 14. 3 ro., 37 po., 26 yds. to inches; and 3 ac., 30 po. to feet. 16. 29 cub. yds. to feet; and 158279 cub. in. to yards. 17. 17 cub. yds., 1001 cub. in. to inches; and 26 cub. yds., 19 cub. ft. to inches. 18. 563 gals. to pints; and 365843 gills to gallons. 19. 5 pipes, 1 hhd., 35 gals. to pints; and 487634 gills to tierces. 20. 6 hhds., 1 bar. of beer to pints; and 2307621 pints of wine to hhds. 21. 760 bus., 3 pks. to quarts; and 2 qrs., 1 coomb, 3 pks. to gallons. 24. 56 reams, 19 quires to sheets; and 52073 sheets of paper to reams. 25. 36 wks., 5 d., 17 hrs. to seconds; and 1 mo. of 30 days, 23 hrs., 59 sec. to seconds. (7) How many barrels, gallons, quarts, and pints are there in 1336381 half-pints? (8) One year being equivalent to 365 days, 6 hours, find how many seconds there are in 27 years, 245 days. (9) From 9 o'clock P.M., Aug. 5, 1852, to 6 o'clock A.M., March 3, 1853, how many hours are there, and how many seconds? (10) In England there are 50535 square miles; in Wales, 8125 square miles; in Scotland, 29167 square miles: how many square acres do they all contain? COMPOUND ADDITION. 117. COMPOUND ADDITION is the method of collecting several numbers of the same kind, but containing different denominations of that kind, into one sum. RULE. "Arrange the numbers, so that those of the same denomination may be under each other in the same column, and draw a line below them. Add the numbers of the lowest denomination together, and find by reduction how many units of the next higher denomination are contained in this sum. Set down the remainder, if any, under the column just added, and carry the quotient to the next column: proceed thus with all the columns." Ex. 1. Add together £2. 4s. 7 d., £3. 58. 101d., £15. 15s., and £33. 12s. 11 d. Proceeding by the Rule given above, The sum of 2 farthings, 1 farthing, and 2 farthings,=5 farthings, =1 penny, and 1 farthing; we therefore put down, that is, one farthing, and carry 1 penny to the column of pence. Then (1 +11+10+7)d. = 29d. = (12 × 2 + 5)d. or 2 shillings, and 5 pence; we therefore put down 5d., and carry on the 2 to the column of shillings. Then (2+12+15+5+4)s = 38s. = (20 × 1+18)s. = £1., and 188.; we therefore put down 18s., and carry on the 1 pound to the column of pounds. Then (1+33 +15+3+2) pounds = £54. Therefore the result is £54. 18s. 51d. Note. The method of proof is the same as that in Simple Addition. Ex. 2. Add together 34 tons, 15 cwt., 1 qr., 14 lbs. ; 42 tons, 3 cwt., 18 lbs. ; 18 tons, 19 cwt., 3 qrs. ; 7 cwt., 6 lbs.; 2 qrs., 19 lbs.; and 3 tons, 7 lbs. (10) Find the sum of £28. 14s. 63d., £27. 18s. 41d., £79. 12s. 6d., £19. 18s. 101d., and £85. 14s. 32d.; also of £678. 10s. 2d., £325. 6s. 5d., £487. 18s. 9d., £507. Os. 11d., and £779. 10s. 8d.; also of £568. 10s. 31d., £259. 19s. 51d., £188. 11s. 41d., £157. 9s. 32d., £13. 13s. 51d., and £779. 8s. 83d.; also of £941. 14s. 2d., £888. 17. 9åd., £309. 19s. 101d., £679. 2s. 11 3d., £455. 16s., and £447. Os. 7 d.; also of £3966. 16s. 94 d., £2. 11s. 7åd., £3795. Os. 23⁄4d., £37. 178. 0åd., £48. Os. 0åd., and £59000. 14s. 6åd.; also of £6491, £3651. 10s. 3₫d., £8000. Os. 11ąd., £5510. 19s. 10§d., £50430. 12s. 1 d., £316. 14s. 5 d., and £4850. 18s. 4d.; also of £306217. 13s. 9 d., £55. Os. Id., £450812. 15s. 2 d., £9837. 1s. 51⁄2d., and £2939. 3s. 11åd.; and prove the result in each case. (11) Add together 2 lbs., 9 oz., 1 dwt., 23 grs.; `8 lbs., 6 oz., 4 dwts., 20 grs.; 1 lb., 10 oz., 5 dwts., 12 grs.; 14 lbs., 11 oz., 14 dwts., 19 grs.; and 21 lbs., 8 oz., 13 dwts., 11 grs.: also 22 lbs., 7 dwts., 15 grs.; 15 lbs., 11 oz., 18 grs.; 34 lbs., 9 oz., 12 dwts.; 74 lbs., 1 oz., 1 dwt., 20 grs.; and 46 lbs., 11 oz., 16 dwts., 19 grs.: also 1740 oz., 9 dwts., 19 grs.; 4179 oz., 11 dwts, 14 grs.; 8497 oz., 12 dwts., 22 grs.; 5629 oz., 19 dwts., 17 grs.; and 1038 oz., 4 dwts., 14 grs.: verify each result. (12) Add together 3 drs., 2 scr., 19 grs.; 2 drs., 2 scr., 11 grs.; 7 drs., |