130 The Single Rule of Three in V. Fractions. answer sl 175 answer 861. 9 At 5ts. per oz. what are 16 oz. of silver worth? answer 41 125 Ifqr. 10 'If is C.wt. cost 145** .. what will 7 C.wt. amount. to ? answer 1181 6s 8d.. u If of an ell English be worth of 195. what is the value of 7 answer 77 78 gd rigr. 12 If 8lb. of tobacco cost 4s odos, what is that per Ib. answer 7d. 13 How much cash will purchase 4 pieces of cloth, each 271 yards, at 1565. per yard? answer 852 10s ride 14 Please to tell the quantity and value of 31 pieces of silk, each 245 yards, at 6s od. per yard? answer quantity 856yds. value 25l 145 60.2 gr. 15 If ylb. less by $, cost 13 d. what cost 141b. less by ś of 2lb.? answer 41 93 9i'di 16 Bought 120lb. of tea, at 845. per lb, which being sold: for 70l. required the gain per cent.? answer 351 56 3d. 396.75 17 What will 133lb. cost at the rate of 1765. per C.wt. answer 21 35, in 18 If of a ship be worth 731 Is 3d. what part of her may be purchased for 2501 1os. answer } 19 1f 31 times 3 lb. cost at time ill. what is the value of of 4 of 12 lb.? answer 78 6d. 20 A mercer sold' 44 pieces of silk, each containing 22{yds. at 8250. per yd. what is the amount of his bill? answer 46l os ind. 2 qr. 21 A person having of a ship, sells of his share for 3191. what is the proportional worth of the whole vessel ? answer 5981 25 Oda LNVERSE 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 answers See the last note, The Single Rule of Three in V. Fractions. 130 EXAMPL E S. 1 What quantity of shalloon that is yd. wide, will line 71yds, of cloth, lyd. wide ? First 7='{yds. As.... 15 answer. yd.yd. yd. yd. Second, 1 = {yds. 3 154 Or cancelled ; 15 yds. 2 If 38 yards of cloth, that is yard wide, be sufficient to make a cloak; how much Persian, which is but yards wide, will be required to line it? answer 4yds. 3qrs. 2na. 3 16 men finishing a piece of work in 287 days: the time is required in which 12 men should do it? answer 377 days. 4 In exchanging 20 yards of cloth of 18 yards wide, for some of the same quality of yards wide ; what quantity of the latter makes an equal barter? answer 343 yds. 5 If 3 men can perform a service in 41 hours ; in what time may ten men effect it? answer ihr. 2 i min. 6 When wheat is at 51 shillings per bushel, if the penny loaf weigh 70%. what is it per bushel, when the penny loaf weighs 20%. answer 155 40 39r. 7 If when the price of wheat is 675. per bushel, the penay loaf weighs 90%. what must it weigh, when that grain sells at 4is. per bushel ? answer 120%. 8dr. 8 A piece of tapestry 3 ells Flemish wide, and four long, is to be lined with stuff which is but lyds. 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 45 8yds. 10 How many yards of baize ell English wide, will be sufficient to line żo yards of camelot, that is 4 yards wide ? answer 12 yds. 11 A merchant bartering 5C. of sugar at 6d. per lb. for tea, at 845. per tb. would know what quantity of the katter article he is to receive ? answer 43751b. 12 What 132 The Double Rule of Three in V. Fraction. 12 What number of pieces of merchandize, at 2015. per piece, are equivalent to 2404 pieces, at 12 s. per piece? answer 149112, pieces. 13 A lends to B 100zl. for 6 months; what sum should B lend A for 3 years, to requite his kindness ? answer 141 11s 9d. I gr. 14 How many yards of cloth, at 31s. per yard, must be given for 264 yards, at 5'ss. a yard? answer 17yds. Igr. zna. 4 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 nnmbers. Or, Invert 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 4 of a yard of cloth that is žyds, wide, cost 6. what is the value of yard that is it yard wide, being of the same quality ? Sefyd. I If lyd.] } 중 *** Or, Ax8x2x8x7 =fb=135 4d. 3x7x8x8x8 2 If 9 students spend 1011. in 18 days; what sum will 20 students spend in 30 days? answer 391 18s 4d. ji 3 The labour of 3 men for 197 days comes to 8481. at the same rate, what must 20 men have for working 100% days? answer 3051 Os 82.79 * If 5 persona drink 7 gallons of beer in a week, what quantity will serve 8 persons 221-weeks? ans. 2804 gallons. 5 Fourteen persons upon examining into their expences, for 20 weeks. past, found they had laid out 4051. in what time, at the same rate, may 201.3 be expended by 46 persons ? answer 3711 weeks. 6 If 13}l. in $ of a year, gain li'zl. interest what interest will 50l. gain in e' of a year; and at what rate per cent. per annum? ans. 2l 55 id. 2;qr. at 10 per cent, 7 If sol. in 2 of a year gain 2l 55 id. 2žgr. in what time will 1371. gain It'sh and at what rate per cent. per annum? answer 1 year, at 10 per eent. 8 When 12 persons use 14 pound of tea per month ; how much should a family of 8 persons provide for 1 year? answer 4ilho 9 Two brothers at school compute the expence of their boarding, tuition, &c. for of a year to be 5646. how much will the education of 3 sons for sí years, cost their father at that rate? answer 6ool, DECIMAL FRACTIONS. А DECIMAL Fraction is a part, or parts, of a unit; denoted by a point prefixed to a figure, or res thus, ,4 ,45, 24563 the first figure after the point, denotes so many tenths ofà unit; the second so many huudredths of a unit, or tentbs of one tenth ; which are equal to; and read as, 4, Ho, 18 A mixt number consists of a whole number and a decimal ;. thus, 245, 789; which is, 245 28.05. 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. TABLE, o 9 Note. Ciphers annexed to decimals neither increase nor decrease their value; thus, .25000, and 25 are equal; but prefixed, decrease them in a tenfold proportion ; thus, .5, .05, .005, all express different decimals, and = foi rád, voor 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. E X A M P L E s. Pounds. 763,6821 576,71 38,781 6,64 7036 37,86 4892,204 What is the sum of 450+ 31,47+376,004+1,08+4564 276+,05 ? answer 1315,364 If 2476,8471 + 94,9 + 9,8941 + 867,05 + 84,9 + 271,007 +5,1008+ 1,6789 be added together, what is the sum: answer 3811,3779 SUBTRACTION. |