EXAMPLES FOR PRACTICE. Ans. 16916. Ans. 29lbs. 6oz. 5 pwts. 1. In £17 12s. 5d. how many farthings? 2. In 7085 put. how many pounds, &c.? 3. In 2lbs. 8oz. Sput. of silver, how many table spoons, weighing 22put. each, and tea spoons, each 5pwt. may be made, and an equal number of each sort? 4. In 9cwt. 3qrs. 13lbs. of indigo, how many ounces? 5. In 4lb. 53. how many drams? 6. In 500 nails, how many Ells English? Ans. 24. Ans. 17680. Ans. 424. Ans. 25. 7. The highest mountain in the known world is the Himmaleh in Asia, which is 5m. Ofur. 3rds. 3 yds. 2ft.., how many feet is that? Ans. 26462. 8. The next highest is Chimborazo, in South America, which is 21450 feet, how many miles is that? Ans. 4m. Ofur. 20rds. Ans. 16. Ans. 17C. 57ft. and pint bottles, of 9. In 2560 square rods, how many acres? 10. In 2233 feet, how many cords, &c.? 11. How many two quart bottles, quart bottles, cach an equal number, may be filled from a pipe of wine? Ans. 144. 12. In 242 pints, how many bushels, &c.? Ans. 3bu. 3pks, 1qt. 13. The latitude of Boston is 42° 23′ 2′′ north; how many seconds is that? Ans. 152582. 14. The latitude of Rio Janeiro amounts to 82739" south, how many degrees, &c.? Ans. 22° 58' 59" 15. In a silver tankard, weighing 3lbs. 11oz. 19pwt. 23gr., how many grains? Ans. 23039. 16. The distance from New-York to Albany is 141 miles, how many inches is that? Ans. 8933760. 17. In a hogshead of tobacco, weighing 5cwt. 3qrs. 26lbs., how many pounds? Ans. 670. 18. A boy found a gold medal, weighing 3oz. 17pwt. 21grs., and finding no owner, he disposed of it at 1 penny per grain. What did he get for it? Ans. £7 15s. 9d. 19. In 256 boxes of raisins, each weighing 19lbs., how many hundred weight, &c? Ans. 43cwt. 1gr. 20lbs. 20. In 1tb. 23.23.19., how many scruples? Ans. 343. 21. The distance from the earth to the sun is 95,000,000 of miles; how long would a cannon ball be in passing that distance at the rate of 8 miles per minute? Ans. 22y. 216d. 12h. 40m. 22. How many inches will reach round the globe, it being 360 degrees? Ans. 1585267200. 23. If the British national debt be 13 hundred millions of pounds sterling, how long would it take to count it, at the rate of £50 a minute, reckoning without intermission 12 hours each day, and 365 days to the year? Ans. 98y. 341d. 1h. 20m. ADDITION OF COMPOUND NUMBERS, COMMONLY CALLED COMPOUND ADDITION. 103. COMPOUND ADDITION is finding the sum of two or more proces, it will be sem, commies in adding up Larm column. dividing the sum by as KAFT OF SOLO Of the saxx to maka 1993 of the west higher, setting down the VER., BAË DETTyung am QUEMENT. 104. Beace, for the anticion of comPS UND NUMBERS, we have this BULE L Place the numbers so that the SAME DENOMINATIONS Anay stand directly under each other. IL Add up the numbers of each denomination, reduce their SUM to the NEXT HIGHER, set down the REMAINDER, and carry The QUOTIENT. Paoor. The same as in simple addition ENGLISH MONEY. £ d. gre. 293 14 5 197 10 18 2. A merchant began trade with £1755 13 4d in goods £459 12s. 3d. in good 3 debts-and be cleared the first year £249 19% 10d; what was be worth at the year's Ans. £2465 5s. 5d. 2 12 6 1 put. gr. end? TROY WEIGHT. 4 If an ingot of gold weigh 7/bs, 9oz. 11put. 20 19gr a gold medal 401. 17prt. 21grs., and 17 18 another lump 5. Sez. 17put. 6grs., what is 21 the whole weight? 13 32012 Ans. 13/bs. 11oz. 6put. 22grs. grs. 6. An apothecary would make a compound AVOIRDUPOIS WEIGHT. 14 8 19 15 7 3 0 27 17 13 9 6 19 0 1 13 4 13 Yds. gre. na. 3 8. Bought tobacco 6cut 2qrs. 27lbs., raisins 23cut. 1gr. 20lbs, sugar 11cut, 18lbs. ;-what is their amount? CLOTH MEASURE. Ans. 4lcut. 1gr. 9lbs. 10. Bot. 3 pieces of cloth, one containing 72yds. 3qrs. 2na., another 87yds. 1gr. 3na., and a third 54yds. 2na.; how much in all? LONG MEASURE. 9. 175 2 Ans. 214yds. 1gr. 3na. LAND OR SQUARE MEASURE. 13. A man owns 87A. 2R. 27rds.; he buys a 12. 18 3 29 piece adjoining, 32A. 16rds., another, 67A. 3R. 17 21 15 21rds., and a third, 21A. 2R. 96rds.; how much did he then own? Ans. 219A. 1R. 20rds: 14. 13 17 19 25 SOLID OR CUBIC MEASURE. in. 15. Sold to one man 3 loads of wood; 1st load 187 57ft. 1142in., 2d load 49ft. 703 980 Bbl. gal. qts. 16. 17 26 2 WINE MEASURE. 1327in., 3d load 62ft. Ans. 1C. 42ft. 297in. 17. A man has 4 casks, containing as follows: 3 1st. 28gal. 3qts. 1pt., 2d 27gal. 2qts., 3d 29gal. Ipt., and 4th 15gal. 3qts. 1pt.; how much will 1 they all hold? Ans. 3bbl. 6gal. 3qts. 1pt. B. pks. qts. 18. 16 14 7 6 DRY MEASURE. 19. Bot. 3 parcels of grain, one containing 21B. 3pks. 1qt., another 17B. 2qts., a third 19B. 2pks. Tqts.; how much in all? Ans. 58B. 2pks. 2qts. TIME. THEORETICAL QUESTIONS. What is compound addition? In what does it consist? What is the first part of the rule? What the second? the PROOF? SUBTRACTION OF COMPOUND NUMBERS, COMMONLY CALLED COMPOUND SUBTRACTION. 105. COMPOUND SUBTRACTION is finding the DIFFERENCE between two COMPOUND NUMBERS. Here it is plain that we find the difference, for 6d. from 9d. leaves 3d., and 10s. from 15s. leaves 5s. Therefore Henry evidently has 5s. 3d. the most. Here we cannot take 9d. from 6d., but we can borrow one of Oliver's (17) shillings, and taking 9d. from this, the rem. is 3d.; 3 and 6 (the number of pence above) is 9; set down 9d. Now as we have borrowed 1 from the 17s., it is evident that we must either call 17 one less, or carry 1 to 13 (the number below,) and take the SUM from 17. The latter mode is most convenient. 106. Hence, TO SUBTRACT COMPOUND NUMBERS, we have this RULE I. Place the LESSER number under the greater, and the SAME DENOMINATIONS under EACH OTHER. III. Begin at the right hand, and take the number of each denomination in the lower line from the number above it; and set the remainder underneath. III. If the number in the lower line EXCEED that above it, take it from AS MANY as it takes of that denomination to make one of the NEXT higher, and add the remainder to the upper number; set the result underneath, CARRY ONE to the next lower number, and proceed as before. PROOF. The same as in simple subtraction. EXAMPLES. 1. In account with Wm. Trusty on my book, he stands Dr. to £112 8s. 3d., Cr. to £87 15s. 9d.; what is the balance, and in whose favour? 2. Purchased an ingot of gold, weighing 5lbs. 4oz. 17pwt.; sold 2lbs. 11oz. 6pwt.; how much is there left? and what will it come to at 3d. per grain? Ans. to the last, £177 6s. Ans. £34 13s. 4d. 3. Bot. 13cwt. 15lbs. of sugar; sold 5cwt. 2qrs. 23lbs., what will the balance come to, at 10d. a pound? 4. Bot. muslin, 217yds. 2qrs.; sold 158yds. 3qrs. 2na.; how much reremains? Ans. 58yds. 2qrs. 2na. 5. A certain town is 21m. 3fur. 25rds. long, and 15m. 5fur. 17rds wide; how much longer is it than wide? Ans. 5m. 6fur. 8rds. 6. A man has a farm of 217A. 2R. 12rds.; he sells 39A. 3Ř. 33rds.; how much has he left? 7. From a lot of wood containing 526 C. 72ft. 1125in.; how much remains? 8. Bot. a cask of wine containing 57gal. 3qts. 19gal. 2qts.; how much remains? 9. Put up in my bin, 736B. 1pk. of wheat; 3pks.; how much remains? deg. m. fur. rds. yds. ft. 10. From 38 41 3 29 2 1 Ans. 177A. 2R. 19rds. 1017in., sold 87 C. 98ft. Ans. 438 C. 22ft. 1620in. 1pt.; out of which I sold Ans. 38gal. 1qt. 1pt. having sold 379 B. Ans. 356B. 2pks. and in. b. c. 7 35 5 31 3 1 9 and prove the result. Subtract 19 11. My note against Peter Pencil, given May 20th, 1825, is this day to be settled-April 21, 1828: For how long time must interest be reckoned? Y. mo. d. We begin with the last date, and set down the year (1828), no. 1828 4 21 of the month (4), and day of the month (21). Then with the 1825 5 20 first date, we set down the year (1825), no. of the month (5), and day of the month (20) UNDERNEATH; and, subtracting, obtain 2y. 11mo. 1d., the answer.. Avs. 2 11 1 107. Hence, to obtain the DIFFERENCE OF TIME between any two given dates, we have this RULE. Begin with the last date, and set down the YEAR, number of the month, and day of the month; under which set down the first date in the SAME WAY, and subtract as before directed. NOTE. In casting interest, each month is reckoned 30 days. 12. What difference of time between Sept. 18, 1821, and June 16, 1828? 13. Between Aug. 17, 1815, and June 1, 1829? 14. Between Oct. 26, 1817, and Feb. 21, 1829 ? Ans. 6y. Smo. 28d. Ans. 13y. 4mo. 15d. Ans. 11y. 3mo. 23d. 15. Bot. a hogshead of sugar, weighing 9cwt. 2qrs. 17lbs.; sold at three several times, as follows, viz: 2cwt. 1qr. 11lbs. 5oz.; 2qrs. 18lbs. 10oz.; 25lbs. 6oz.; what weight remains unsold? Ans. 6cwt. 1gr. 17lbs. 11oz. 16. A merchant receives 75 7. 1qr. 20lbs. of iron at one time, and 60 7. 15cwt, 3qrs. at another; he then sells 10 T. 3qrs. 8oz.; how much has he left? Ans. 125 T. 15cwt. 1gr. 19lbs. 8oz. THEORETICAL QUESTIONS. What is compound subtraction? What the first part of the RULE ?—the second ?-the third the PROOF? What is the rule for finding the DIFFERENCE OF TIME between any two given dates? 108. Which is a method of 109. Which is a method of repeating a COMPOUND NUMBER dividing a cOMPOUND NUMBER into any given number of parts. any given number of times. At 8s. 6d. per yard, what will yards come to? 6, cost of 1 yard. Ans. £0 8 6, cost of 1 yard. £1 5 6, cost of 3 yards, Ans. Here we evidently reverse the process As the cost of lyd. is 88. 6d., it is eviin the left hand column, and divide the dent, that the cost of 3yds. must be three COST of the given number of yards by times as much. We, therefore, evidently THAT number; saying 3 in £1 0 times. but £1 is 20s. and 5 (the number of the multiply the cost of ONE yard by the NUMnext less) is 25s.; 3 in 25 8 times, and 18. BER of yards; saying 3 times 6 is 18d.; 18d. is 1s. and 6d. We set down the 6d., the next less....saying 1s. is 12d. and 6 (the over we set down 8, and reduce the 1s. to and carry the 1s. to the product of the next ....saying 3 times 8 is 24, and 1 we had to number of the next less) is 18d.; 3 in 186 carry is 25s.; 25s. is £1 5s. Set down times: set down 6. Therefore, Ans. 8s. 6d. the 5s., and carry the £1 to the product This process may be used in all cases where the divisor does NOT EXCEED 12. of the next.....3 times 0 is 0, but 1 we had Wherefore we have this to carry is £1. Therefore, Ans. £1 58. 6d. This process may be used in all cases 111. RULE. After placing where the multiplier does NOT EXCEED the numbers as above, begin with the highest denomination, and 110. RULE. After placing find how often the divisor is the numbers as above, begin with contained in it; set the quotient the lowest, and multiply EACH denomination by the multiplier, der (if any) to the next less observing to set down and carry denomination, adding in the next as in COMPOUND ADDITION. less, and proceed as before. 12. Wherefore we have this underneath, reduce the remain From what has been said, it is plain, that 112. THESE TWO RULES mutually prove each other. |