11 Divide of 4 by 44, 12 Divide of 6 by of of 4. 14 What is the quotient of of divided by 1⁄2 of 7 ÷ ? answer 7 I 15 What is the quotient of 52054 divided by 4 of 91? answer 715 THE SINGLE RULE OF THREE IN VULGAR FRACTIONS. DIRECT PROPORTION. RULE. Prepare the given terms, if recessary, by reduction, and state them as in whole numbers; multiply the second and third terms together, and divide that product by the first; Or, Invert the dividing term, and multiply the three together for the fractional answer. Note. When the dividing term is inverted, the note to case 5 in reduction is applicable here. EXAMPLES. 1 If of a yard cost of a . what cost yards? As 335== 35 4d. answer. 7 Or, Cancelled; 8131 3 16 14 6 3 X 2 2 If ¡¡b. of sugar costs. what cost 131.? answer 4d. 39r. 1 3 8 3 3. If 4 of an ell English cost. what is that per ell? answer 18s 10d. 4 When 20%. of silver cest 16. what is the value of answer 6s id 3qr. 5 If 64 yards cost 18s. what buys 94 yards? answer il 5s 7d. 1gr.75 6 Sold 500 bushels of wheat, at 563d. per lu. what sum passes to the credit of that article? answer 1171-18 14 130 The Single Rule of Three in V. Fractions. 7 If 1 yard cost 9s. what is the value of 161 yards? answer 51 8 What sum pays for 100yds. of cloth, at 17s. per yd.? answer &62 9 At $1s. per oz. what are 16oz. of silver worth? to? answer 41 12s 13gr. 10 If C.wt. (cost 14. what will 7 C.wt. amount answer 1181. 6s 8d. 11 If of an ell English bo worth of 195. what is the value of ells? answer 71 7s gd. 11gr. 12 If 86. of tobacco cost 4s gd.3, what is that per 15. ansaver 7d. 13 How much cash will purchase 4 picces of cloth, each 27 yards, at 15. per yard? answer 851 10s 11d 14 Please to tell the quantity and value of 3 pieces of silk, each 24 yards, at 6s od. per yard? answer quantity 85 yds. value 257 14s 6d. 2{qr. 15 If lb. less by, cost 13 d what cost 146. less by } of 2lb.? ancwer 41 98 92'zd. 16 Bought 120lb. of tea, at 8s. per lb. which being sold for 70. required the gain per cent? answer 351 55 3d. 3gr.{} 17 What will 133b. cost at the rate of 17 per C.ut. answer 21 38 Dia 18 If of a ship be worth 73 is 3d. what part of her may be purchased for 250l 10s.? answer 19 If 3 times 3lb. cost 1 time 14. what is the value of of of 124lb.? answer 7s 6d. 20 A mercer sold 4 pieces of silk, each containing 22 yds. at 84s. per yd. what is the amount of his bill? answer 461 9s 11d. 21qr. 21 A person having of a ship, sells of his share for 3214. what is the proportional worth of the whole vessel ? auswer 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 e fractional answer. See the last note. EXAMPLES. 1 What quantity of shalloon that is yd. wide, will line. 7yds. cloth, 1yd. wide? First, 7yd. Or, cancelled; As 3... 15: 4. 15 answer. 2 2 If 3 yards of cloth, that is 1 yard wide, be sufficient to make a cloak; how much Persian which is but yard ide will be required to line it? answer 4yds. 3qrs. zna. 3 16 men finishing a piece of work in 28 days: the time is required in which 12 men should do it? answer 377 days. 4 In exchanging zo yards of cloth of 14 yard wide, for some of the same quality of 34 yards wide; the latter makes an equal barter? 5 If 3 men can perform a service in 4 time may ten men effect it? what quantity of answer 34% yds. hours; in what answer thr. 21 min. 6 When wheat is at 5 shillings per bushel, if the penny loaf weigh 70%. what is it per bushel, when the penny loaf weighs 20%. 15s 4d 39r. 7 If when the price of wheat is 61s. per bushel, the penny loaf weighs 9oz. what must it weigh, when that grain sells at 44. per bushel? answer 1202 8dr. 8 A piece of tapestry 3 ells Flemish wide, and four long, is to be lined with stuff which is but yd. wide; how many yards are sufficient? ansiver gyds. 9 Suppose 275 yards of cloth, that is 11 yard wide, make coats for 130 men; what number of yards of shalloon of yards wide will be requisite to line them? answer 4584 yds. 10 How many yards of baize ell English wide, will be sufficient to line 20 yards of camlber, that is 11 A merchant bartering 5C. of sugar yard wide? Answer 12 yds. at 6d. per for tea, at 8s. per lb. would know what quantity of the latter article he is to receive? answer 43lb. 12 What 132 The Double Rule of Three in V. Fractions. 12 What number of pieces of merchandize, at 204s. per piece, are equivalent to 240 pieces, at 12s. per piece? answer 149 pieces. 13 A lends to B 10031. for 63 months; what sum should B lend A for 3 years to requite his kindness? answer 141 11s 9d. 155gr. 14 How many yards of cloth, at 81s. per yard, must be given for 26 yards, at 5s. a yard? answer 17yds. 1gr. 3na.43 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, 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 cafe 5, in reduction, may be applied here. EXAMPLES. 1 If of a yard of cloth that is yd. wide cost 6. what is the value of 4 yard that is 14 yard wide, being of the sante quality? If yd. {syd.} 2 If 9 students spend 107. in 18 days; what sum will 20 students spend in 30 days? answer 391 18s 4d.20 3 The labour of 3 men for 194 days, comes to 8181. at the same rate, what must 20 men have for working 100% days? answer 3051 Os 8d2 4 If 5 persons drink 74 gallons of beer in a week, what quantity will serve 8 persons 22 weeks? ans. 280 gallons. 5. ΙΣ 1 5 Fourteen persons upon examining into their expences, for 20 weeks past, found they had laid out 40%. in what time, at the same rate, may 2013 be expended by 46 persons? 5.6 answer 3 weeks, 6 If 13 in of a year, gain 1 interest what interest will 5ol gain in of a year; and at what rate per cent. per annum? ans. 2/ 5$ Id. 23gr. at 10 per cent. If 50l. in, of a year in 2/ 5s 1d. 23. in what time will 133 gain 1. and at what rate per cent. per annum? answer year, at 10% per cent. 8 When 12 persons use 14 pound of tea per month ; how much should a family of 8 persons provide for year? Two brothers at school compute the bding, tuition, &c. for 2 of a year to will the education of 3 sons for 5 at that rate? answer 44lb. expence of their be 561. bow years cost their answer bool. A DECIMAL FRACTIONS. 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 ter 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 4 45 456 read as, 100, 1000: A mixt number consists of a whole number and a decimal; thus, 245, 789; which is, 245 7000 789 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. |