After disposing of the fractions as before directed, I consider that lo of a year being a longer time than 1, it will not require so much principal lent, therefore the greater of the first and third numbers must be the divisor (as in whole numbers); the third fraction therefore must be inverted, and the question will stand thus : If of a year of 1000l. of a year? Anfwer 3950, or 15613, equal to 15$l. 145. 7110. Questions both in this rule and the former are proved by back-stating the question, as in whole numbers; thus the foregoing example may be proved by saying, if 10 of :cool. principal require y of a year, what will of 10col. require? and the answer is zo, or of a year. Qu.2. How much shalloon will it require at of a yard wide to line the garments made with 101 yards of cloth at * 1* yard wide ? Auf, , or 2, equal to 24 yards. Qu. 3. If 12 men can mow 245, acres in 103 days, how many days will 6 men require to do the same? - Answer 21 days. Qu. 4. If a board be * of a foot in breadth, how inany inches in length will make a square foot? - Ans. 16 inches. From what has been delivered in this section concerning vulgar fractions, it is plain that every other rule in ariihmetic may be wrought by vulgar fractions as well as by whole numbers, as the operation in both cafes depends upon the same principle; thus, in the ruie of three direct in vulgar fractions, inverting the first fraction, and multiplying it by the second and third, is the same as multiplying the second and third fractions together, and dividing by the first : and in the inverse rule, inverting the third fraction and multiplying it by the first and second, is equal to dividing the product of the first and second fractions by the third, as the learner may prove at his leisure. SECT. XIV. OF PRACTICE. PRACTICE is the most expeditious rule in arith:metic, and is of general use among men of business, as it readily difcovers the value of any number of integers from having the value of one. By this rule are answered all questions in the rule of three direct that have an unit for their firft number. Rule. Divide the given number of integers by one or more aliquot parts of a penny, fhilling, or pound, or any two or three of them; and the quotient will be the answer, and of the same denomination of which the divisor is a part. An aliquot part of a number is such a part, that being taken any number of times, will exactly measure that number without a remainder : thus 2 is an aliquot part of 6, for it is contained exactly 3 times in 6; and 5s. is an aliquot part of a pound, for it is contained exactly four times in a pound; but 55. 2d. is not an aliquot part, for it is not exactly con. tained any number of times in a pound without leaving a remainder. Before the learner can perform this rule, he must perfectly understand the following tables of aliquot parts, and retain them in his memory. The aliquot Parts. d. d. half o) 6 8 fourth fixth 3 6 10 2 of a shilling. 4 O O O O O O O O of a pound. 2 tzlixteenth 2 half 1 1 fowith } or of a penny. 1 of 16 15 These tables are so plain as to need no explanation; their use is to discover by what number to divide any given number of integers. Cafe 1. When the price is less than a penny, divide the given number by the aliquot parts of a penny equal to the given price, and the quotient gives the answer in pence, which reduce into shillings and pounds by division ; except the given price be 3 farthings, then it is brought into thillings, and answered at once by dividing by 16. Example 1. What is the amount of 80471b, of old iron, at a halfpenny per pound!!! Here I divide the given number S047 by 2, 2) 8047 as 2 farthings is the half of a penny, and the 12) 4023 2 quotient 4023 is the price of the iron in pence, 2,0) 33,5 3 and i remains, which is 1 balfpenny, for the remainder is always of the fame name with the divisor; I then reduce the pence into thillings by dividing by 12, and the quotient is 335 shillings, and 3 remains, which is pence; and then reducing the fhillings into pounds, the answer is 161. 155. 3 d. Example 2. What is the value of 5763 yards of trimming, at 3 farthings per yard? In this example I divide the given number 2,0) by 16, as before directed, as 3 farthings is the 1615763(39,0 18 fixteenth part of a fhilling, and the quotient is 360 millings, which reduced into pounds is 181. os. 2 d. for the 3 that remains in the first division is 3 fixteenths of a shilling, or 3 times 3 farthings, equal to 2 d. Qu. 3. What comes 445, at $d. ?-Anf. gs. 31d. 24. 4. What is the value of 3379, at 14.1--Anf. 71. 54. Call 48 96 96 mil Case 2. When the price is an aliquot part of a shilling, divide the given number by such aliquot part, and the quotient is the answer in shillings, which must be reduced into pounds. 1 j Example 5. What is the value of 8791b. of cheese, at 4d. per lb. Here the given number of pounds is 3)879 divided by 3, as 41. is, of a fhilling, 2,0)29,3 shillings and it quotes 293 fhillings, which are 14 brought into pounds; and the Answer 13 is 141. 134 Qa. 6. What is the value of 2971b. of tallow at 3d. per ib.?—Here the given number must be divided by 4, as 3d. is of a Avilling, and the Anfwer is 3l. 145. 3d. Example 7. What is the value of 3cwt. of sugar, at 6d. per lb 1-Anf. 81. 85, 2)336 2,016,8 8 Example 8. What is the value of 21781b. of alum, at 11d. per lb, ?-Anf. 131. 128. 3d. 8)2178 2,0). 27,22 Example 9. What is the value of 4861b. at 2d. per lb.: – Anf. 41. is. : 16)486 4 I Cafe 3. When the price of the integer is pehce and farthings, and not an aliquot part of a shilling, find what aliquot put of a Milling is the nearest to the given price, and less than it, and divide the given number by that aliquot part; and for the remainder of the price consider what part it is of the the given price, and divide the quotient by it; and if there be still a remainder of the given price, consider what aliquot part this is of the laft, and divide the last quotient thereby ; then add all the quotients together for the answer. '., Example 10. What is the value of sicwt. of butter, at sid. per lb. ? 6d. is į of a shilling 2)616 equal to sicwt. 2d. is of 6d. therefore divide by 3) 308 {equal to 4d. It. is of 2d. therefore divide by 4)102 remains 2, or of 6d. 25 remains 2, or of2d. 2,0) 43,5 equal to id. In this example, I divide the given number first by 2, as 6d. is the nearest aliquot part to the price, and the quotient is 308s, which is the price at 6d. per lb. : I then divide that quotient by 3, for the other ad. in the price, and it quotes 102s. which is the price of the article at 2d. per lb. and 2 remains; and for the halfpenny I divide the last quotient by 4, as one halfpenny is the fourth part of 2d, and the quotient is 255. which is the price of the butter at a halfpenny per lb. : the three quotients added together give the answer. Example 1r. What is the value of 137 yards of cloth, at 10 d. per yard? For the 6d. I divide by 2)137 3 105 24. 12. What is the value of 520lb. of soap, at 72 d. per Ib.? ---Anf. 161.55. Qu. 13. What is the value of 860 yards of linen, at 1144. per yard ?--Anf: 411. 45. 2d. Cafe |