1 11 What is the value of ,092 of 3A. 2R. ? answer 1R. 11,52per. 12 What is the value of ,3 of a year? answer 109da. 13hr. 48min. 13 What is the value of ,6875 of a yard ? answer 2qr. 3na. 14 What is the value of ,3375 of an acre ? answer 1R. 14per. 15 Find the value of ,785 of a L. by inspection. answer 15s. 8d.. 16 Find the value of ,875 of a £. by inspection. answer 17s. 6d. 17 What is the value of a tenement for nine years; at 12,41. per annum? answer 111. 12s. 18. Sold 25 yards of superfine scarlet cloth, at 2,75l. per yard: what was its value answer 681. 15s. 19 What is the sum of ,48 of a L. and,16 of a shilling? answer 9s. 9,12d. 20 What is the sum of,17 of a lb. troy, and ,84 of an oz.? answer 2oz. 17dwt. 14.4gr. 21 What is the sum of ,177.,19 C.wt. ,17qr. ,7lb? answer 3C.wt. 2qr. 15,54lb. 22 What is the sum of ,78 acres, and ,67 rood? answer 3R. 31,6per. 23 What is the difference between ,171. and 7s. ? answer 2s. 8d. 1,6qr. 24 What is the difference between ,41 days, and,16 of an hour? answer 9hr. 40min. 48sec. THE SINGLE RULE OF THREE IN DECIMALS. The operation both in direct and inverse proportions are agreeably to those rules in pages 59 and 63, having regard to placing the points. DIRECT PROPORTION. EXAMPLES. 1 If 1,4lb. of mace cost 14,5s. what cost 75,31lb. ? 2 If 1,6C. of sugar sell for 31. 12,76s. what is the proportional cost of 3hhds. each 11C. 3qr. 10,12lb. answer 801. 15s. 3d. 3,36qr. 3 If 1,50z. of silver be worth 7,8s. what is the value of . 9,7lb.? answer 20l. 5s. 3d. 1,44qr. 4 If 1,47 C. of sugar be worth 4,5l. what is that for 1,7lb. P answer 11,1d. 5 Sold 12,5 hhds. of wine, at 1,2s. per pint; query the amount? answer 3781. 6 Bought S pieces of cloth, each 21,5 yards, at 12,3s. per yard; please to cast up the cost. facit 39l. 13s. 4,2d. 7 If 8,4lb. of tobacco cost 16s. 4.6d. what is the value of 3hhds. each 4C. 2qr. 7,4lb. answer 1491. 12s. 3d. 8 How many yards are in a piece of cloth which brings 6l. 13,12s. at 4s. 2,6d. per yard? answer 31,569yds. 9 Bought 5,8 tons of oil for 60,41. whereof 50,9 gallons leaked out; what must the rest be sold for per gallon, that the purchaser may be no loser ? answer 10,27d. 10 A grocer bought 7,6C.wt. of sugar, at 40,1s. per C.wt. which he sold at 4,5d. per lb. whether did he gain or lose, and how much? answer gained 14s. 5d. 1,12gr. 11 Bought 3C. 1,5gr. of cloves, at 2,75s. per lb. which was sold for 60l. 11s. 6d. query the gain? answer 8l. 12s. 12 When a merchant buys 436 yards of cloth at 8,5s. per yard, what will he gain by disposing of it at 10,75s. per yard? answer 491. 1s. 13 A owes B 296,851. but compounds for 7,5s. in the L. what sum must B receive? answer 111l. 6s. 4d. 2qr. 14 How many English ells of linen may be bought for 25l. 18s. Id., at 7s. 9d. per yard? answer 53E. 1qr. 15 If a yard of ribband sell for 4,5 cents, how many dollars will buy 345 yards? answer 15,525, i.e. 15D. 521c. D. d. c. m. 16 When 675 yards cost 12,8 2 5, how many yards may be had for 38 mills ? answer 2 yards. . D. d. c. 17 If 19 yards of calico bring 25,7 5; what will 435,5 yards come to ? D. d. c. m. answer 590,2 17% 18 What 18 What must be paid for 7 yards of broad cloth, at 51 dollars per yard ? answer 40,5625D. or 40D. 564cts. 19 How does broad cloth sell per yard when 73 yards cost 40D. 564 cents. ? answer 5,5D. 20 The French foot is just 1,068ft. English; how tall then would a 6ft. Philadelphian be at Paris? answer but 5,618ft. INVERSE PROPORTION. EXAMPLES. 1 How many men can do as much work in,4 of a month, as 16 could in a month and a half? mo. men. mo. men. As 1,5 16,4: 60 answer. 2 If, when wheat flour is as high as 6l. per C.wt. the half penny cake weighs 1,13330z. what should be the weight of it, when flour is only 1,81251. per hundred weight? Oz. oz. dr. answer 3,75=3 12 3. If a board be,75 foot broad, what length will it require to measure 12 square feet? answer 16ft. 4 How much Persian ,75yd. wide will line 25,5 yards of five quarter cloth? 5 A had 40,7 yards of linen for ells of Holland, valued at 4,5s. per rated per yard? answer 42,5yds. which B. gave him 25,6 how was A's linen answer 2s. 9d. 3,8qr. ell; 6 How many dollars of 7,5s. each, should be given in exchange for 100 French guineas, at 34,5s. P answer 460 7 What sum has A at interest, when it yields as much in 71⁄2 months, as B's 450l. do in 15 ? answer 9001. THE DOUBLE RULE OF THREE IN DECIMALS. Questions in this rule are wrought as in whole numbers, placing the points agreeably to the preceding directions. EXAMPLES. 1 If 3 men receive 8,91. for 19,5 days labour; how much must 20 men have for 100,25 days? If 4 13, Ma. } 8,91. {100,29da.} answer £.305 0 8,2 2 If 2 persons receive 4,625s for one day's labour, how much should 4 persons have for the work of 10, days? answer 41 17s 1d. 3 If 16s 4d. be the porterage of 5,25 hundred weight for 20 miles; what must be paid for carrying 17,75 hundred weight 7,5 miles ? answer 1l Os 8d. 4 How many men should reap 417,6 acres in 12 days, when 5 persons cut down of that quantity in half the time? answer 20 men. 5 Suppose the interest of 76,941. for 9,5 months to be 15,251. what principal will gain 6l. in 12,75 months? answer 221 11s 1d. 6 When 12 oxen graze down 16,25 acres, in 20 days; how much, of like pasture, would suffice 24 such cattle for 100 days? answer 162,5 acres. 7 What money, at 31 per cent. per annum, will clear 381 10s. in a year and a quarter? answer 8801. 8 A cellar which is 22,5ft. long, 17,3 wide, and 10,25 deep, being dug in 2 days, by six men, working 12,3 hours a day; how many days, of 8,2 hours, should 9 men take to excavate one which measures 45, by 34,6 by 12,3 feet? answer 12 days. INVOLUTION; OR THE RAISING OF POWERS. A POWER is the product arising from multiplying any given number into itself continually a certain number of times; thus, 2x2 4 is the second power, or square of 2. 2×2×2= 8 the third power, or cube of 2. 2× 2×2×216 the fourth power of 2, &c. The number denoting the power is called the index, or the exponent of that power. If two or more powers are multiplied together, their product is that power whose index is the sum of the exponents of the factors; thus, 2X2-4 the square of 2; 4x4-16-4th power of 2; and 16x16-256-8th power of 2, &c. N TABLE 1953125 51251125 625 3125| 15625] 78125 390625 61362161296] 7776| 46656| 279936] 1679616| 10077696 749 343 2401|168071117649 823543 5764801 40553607 864512 4096 32768/262144/2097152/16777216|13421772891811729 6561159049 531441 4782969 43046721/S87420489 EXAMPLES. 1 What is the fifth power of 7? 7X7X7X7X716807-fifth power. 2 What is the third power or cube of 35? 3 What is the fourth power of ? answer 42875 ,000000020511149 answer 10190,005304479729 17851 6 What is the eighth power of 32 ? EVOLUTION: OR THE EXTRACTING OF ROOTS. TH HE root of any number, or power, is such a number, as, being multiplied into itself a certain number of times, will produce that power. Thus 2 is the squareroot of 4, because 2×2=4; and 4 is the cube root of 64, because 4X4 X4-64, and so on. |