to ? :7 If 14 yards cost 98. what is the value of 164 yards? answer 51 17s. 8 What sum pays for 100 yds. of cloth, at 17 s. per yd ? answer 861. 9 At 5 s. per oz. what are 164oz. of silver worth? answer 4l 12s I qr. 10 If o C.wt. cost 14%, L. what will 71 C.wt. amount answer 1181 6s 8d. 11 If of an ell English be worth of 198. what is the value of 7 ells ? answer 71 73 92.1 qr. 12 If 8lb. of tobacco cost 48 9d. what is that per lb.? answer 7d.} 13 How much cash will purchase 4 pieces of cloth, each 273 yards, at 15 s per yard ? answer 851 10s 11d. 14 Please to tell the quantity and value of S4 pieces of silk, each 24 yards at 6s Od. per yard ? answer quantity 85 yds. value 25l 14s 6d. 24qr. 15 If lb. less by , cost 13s įd. what cost 14lb, less by of 2lb. answer 41 9s 9. 16 Bought 120lb. of tea, at 8ks. per lb. which being sold for 70L. required the gain per cent ? answer 351 5s 3d. 3qr. 17. What will 13 lb. cost at the rate of 17L, per C.wt. answer 21.3873 18 If of a ship be worth 731 1s 3d. what part of her may be purchased for 2501 10s. F answer i 19 If 3 times 3 lb : cost 1 time ill. what is the value of of of 12tlb? answer 7s 6d. 20 A mercer sold 44 pieces of silk, each containing 22fyds. at 8 s. per yard, what is the amount of his bills answer 461 9s 11d 25gr. 21 A person having of a ship, sells of his share for 3191. what is the proportional worth of the whole vessel ? answer 5981 2s 6d. INVERSE PROPORTION. RULE. After the necessary preparations, multiply the first and second terms together, and divide that product by the third term; or, Invert the dividing term, and multiply them together for the fractional answer. See the last note. EXAMPLES. 1. What quantity of shalloon that is lyd. wide, will line 7}yds. cloth, 1żyds. wide ? First, , 73-*yds.} As :::: 15 answer. yd. yd. yd.yd. 3 15 4 = 15 yds. Ķ 3 2 If 34 yards of cloth, that is 1} yard wide, be sufficient to make a cloak; how much Persian which is but yard wide will be required to line it? answer 4yds. 3qrs. 2na. 3 16 men finishing a piece of work in 281 days: the time is required in which 12 men should do it answer 377 days. 4 In exchanging 204 yards of cloth of 14 yard wide, for some of the same quality of 33 yards wide; what quantity of the latter makes an equal barter ? answer 34žyds. 5 If 3 men can perform a service in 41 hours ; in what time may ten men effect it? answer 1hr. 21 min. 6 When wlieat is at 51 shillings per bushel, if the penny loaf weigh 7oz. what is it per bushel, when the penny loaf weighs 27 oz.? answer 158 4d. 3qr. 7° If when the price of wheat is 64s. per bushel, the penný loaf weighs 9oz what must it weigh, when that grain sells at 4 s. per bushel ? answer 12oz. 8dr. 8 A piece of tapestry 3 ells Flemish wide, and four long, is to be lined with stuff ' which is but žyds. wide ; how many yards are sufficient? answer Syds. 9 Suppose 275 yards of cloth, that is 14 yard wide, make coats for 130 men ; what number of yards of shalloon of yards wide will be requisite to line them? answer 458}yds. 10 How many yards of baize ell English wide will be sufficient to line 20 yards of camelot, that is yards wide? answer 12yds. 11 A merchant bartering 5C. of sugar at 6 d. per lb. for tea, at 845. per lb. would know what quantity of the latter article he is to receive ? answer 43 lb. 12 What 12 What number of pieces of merchandize, at 2015. per piece, are equivalent to 2404 pieces, at 12fs. per piece answer 149 124 pieces. 13 A lends to B 10041. for 6 months; what sum should B lend A for 3 years to requite his kindness answer 141 11s 9d. 18qr. 14 How many yårds of cloth, at 8{s. per yard, must be given for 264 yards, at 5 gs. a yard? answer 17yds. Igr. 3na. 14 THE DOUBLE RULE OF THREE IN VULGAR FRACTIONS. RULE. Prepare the terms, if necessary; then state, and work them agreeably to the directions given in whole numbers. Or, Ínvert the dividing terms, and multiply the upper figures continually for the numerator, and those below for the denominator, of the fractional answer. Note. The Note to case 5, in Reduction, may be applied here. EXAMPLES. 1 If of a yard of cloth that is Zyd. wide cost L. what is the value of yard that is 14 yard wide, being ofthe same quality? Syd. 2 2l138 L=13s 4d; 2 If 9 students spend 107. in 18 days; what sum will 20 students spend in 30 days? answer 391 18s 4d.fi 3 The labour of 3 men for 194 days comes to 81%. at the same rate, what must 20 men have for working 1001 days? answer 3051 Os 3d.no If {yd.? { Or, 4 If 5 persons drink 7 gallons of beer in a week, what quantity will serve 8 persons 224 weeks ? answer 2804 gallong. 5 Fourteen persons, upon examining into their expences for 20 weeks past, found they had laid out 40l. in what time, at the same rate, may 2031. be expended by 46 persons? answer 31163 weeks. 6 If 13 l. in of a year gain 1 Bl. interest, what interest will 501. gain in fe of a year; and at what rate per cent, per annum ? answer 21 5s 1d. 2 qr. at 10% per cent. 7 If 501. in of a year gain 22 5s id. 2}qr. in. what time will 135l. gain 1. jl. and at what rate per cent. per annum ? answer year, at 105 per cent. 8 When 12 persons use 13 pound of tea per month ; how much should a family of 8 persons provide for 1 year answer 4 lb. 9 Two brothers at school compute the expence of their boarding, tuition, &c. for of a year to be 561l. how much will the education of 3 sons for 5 years cost their father at that rate ? answer 6001. DECIMAL FRACTIONS. A DECIMAL Fraction is a part, or parts of a unit, denoted by a point prefixed to a figure, or figures, thus, .4, .45, 456; the first figure after the point denotes so many tenths of a unit'; the second so many hundredths of a unit, or tenths of one tenth, which are equal to, and read as, to 1 100 A mixt number consists of a whole number and a decimal; thus, 245, 789; which is, 245 2 As whole numbers, counting from the right to the left, increase in a ten fold proportion ; so decimals, counting towards the right, decrease in the same proportion; which is exemplified in the following: 7 8 9 TABLE. 9 8 7 6 5 4 3 1.1 2 3 4 5 6 7 Note. Ciphers, annexed to decimals, neitner increase nor decrease their value; thus, ,25000, and ,25 are equal, but prefixed, decrease them in a tenfold proportion ; thus; .5, .050.005, all express different decimals, and=10,1 osiood ADDITION OF DECIMALS. RULE. Place the numbers according to their value; viz. units under units, tenths under tenths, &c. and add as in addition of integers ; putting the point in the sum total exactly under those in the example. EXAMPLES. Pounds. 763.6821 576.71 38.781 2718.94 6.64 619.473 37.86 21.66 3.4782 7.8 7.36 4892.204 What is the sum of 450 +31.47 +376.004+1.08+456+ 76+.05? answer 1315.364 If 2476.8471 + 94.9 + 9.8941 + 867.05 + 84.9 + 271.007 +5.1008+1.6789 he added together, what is th answer 3811.3779 SUBTRACTION sum ? |