SECT. XIV. OF PRACTICE. PRACTICE is the most expeditious rule in arithmetic, and, is of general ufe among men of bufinefs, as it readily dif covers the value of any number of integers from having the value of one. By this rule are anfwered all queftions 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 fame denomination of which the divifor is a part. An aliquot part of a number is fuch 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; 55. 2d. is not an aliquot part, for it is not exactly contained any number of times in a pound without leaving a remainder. but Before the learner can perform this rule, he must perfectly understand the following tables of aliquot parts, and retain them in his memory. These tables are fo plain as to need no explanation; their ufe 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 fhillings and pounds by divifion; except the given price be 3 farthings, then it is brought into fhillings, and answered at once by dividing by 16. Example 1. What is the amount of S047lb. of old iron, at a halfpenny per pound?" 2)8047 12)4023 1 2,0) 33,5 3 16 15 Here I divide the given number 8047 by 2, as 2 farthings is the half of a penny, and the quotient 4023 is the price of the iron in pence, and 1 remains, which is 1 halfpenny, for the remainder is always of the fame name with the divifor; I then reduce the pence into fhillings by dividing by 12, and the quotient is 335 fhillings, and 3 remains, which is pence; and then reducing the fhillings into pounds, the answer is 161. 15s. 3d. Example 2. What is the value of 5763 yards of trimming, at 3 farthings per yard? In this example I divide the given number by 16, as before directed, as 3 farthings is the fixteenth part of a fhiliing, and the quotient is 360 fhillings, which reduced into pounds is 181. os. 24d. for the 3 that remains in the first divifion is 3 fixteenths of a shilling, or 3 times 3 farthings, equal to 24d. 2,0) 16)5763(36,0 48 96 96 18 2. 3. What comes 445, at d. ?—Anf. 9s. 3‡d. Cafe Cafe 2. When the price is an aliquot part of a shilling, divide the given number by fuch aliquot part, and the quotient is the answer in fhillings, which must be reduced into pounds. Example 5. What is the value of 879lb. of cheese, at 4d. per lb. ? Here the given number of pounds is divided by 3, as 4d. is of a fhilling, and it quotes 293 fhillings, which are brought into pounds; and the Answer? is 14%. 135. 3)879 2,0)29,3 fhillings 14 13 24. 6. What is the value of 297lb. of tallow at 3d. per lb.?-Here the given number must be divided by 4, as 3d. is of a fhilling, and the Anfwer is 31. 145, 3d. Example 7. What is the value of 3cwt. of fugar, at 6d. per lb?-Anf. 81. 85. 2)336 2,0)16,8 8 Example 8. What is the value of 2178lb. of alum, at d per lb. Anf. 137. 125. 3d. 8)2178 2,0) 27,22 13 12 Example 9. What is the value of 4861b. at 2d. per lb.? Anf. 44. 15. 6)486 2,0) 8,1 4. I Cafe 3. When the price of the integer, is pence and farthings, and not an aliquot part of a fhilling, find what aliquot part of a fhilling 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 confider what part it is of the the given price, and divide the quotient by it; and if there be ftill a remainder of the given price, confider what aliquot part this is of the laft, and divide the laft quotient thereby; then add all the quotients together for the answer. Example 10. What is the value of 5cwt. of butter, at Std. per lb. ? 6. is of a filling 2)616 equal to 5 cwt. [equal to 4d. 2d. is of 6d. therefore divide by 3)308 d. is. of 2d. therefore divide by 4) 102 remains 2, or of 62. 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 2d. in the price, and it quotes 1025. which is the price of the article at 2d. per lb. and 2 remains; and for the halfpenny I divide the laft quotient by 4, as one halfpenny is the fourth part of 2d. and the quotient is 25. which is the price of the butter at a halfpenny per lb.: the three quotients added together give the answer. i Example 11. What is the value of 137 yards of cloth, at 1044. per yard? 1 For the 6d. I divide by 2)137. For the 3d. I divide by 2) 68 remains 1, or 64. 3 Qu. 12. What is the value of 5zolb. of foap, at 7d.per lb.?Anf. 161. 55. Qu 13. What is the value of 860 yards of linen, at 114d. per yard?—Anf. 41). 46, 2d. V Cafe 20. Cafe 4. When the price is any number of fhillings under Firft. If it be an even number of fhillings, multiply the given number by half the price, and double the first figure on the right hand, which will be fhillings, and all the other figures are pounds. Secondly. If the price be an odd number of fillings, multiply the quantity by half the next lefs number, which will be an even number, then for the odd fhilling add of the given number to the laft product, and the fum of these two quantities will be the answer. Qu. 14. What is the value of 476 yards of cloth, at 45. per yard? to be added to the next product, faying, 2 times 7 is 14, and I carried is 15, 5 and carry 1; then 2 times 4 is 8, and 1 is 9; then I cut off the first figure 4 for fhillings, and the rest are pounds. Example 15. What is the value of 462 yards of cloth, at 75. per yard? . Anfwer 2,0)46,2 3 138,12 23 2 161 14 In this example, 7 being an odd number, I take 3 for the multiplier (being the half of 6 the next even number), and multiply as in the former example, doubling the firft number for fhillings, and the product is 138. 125. which is the price of the cloth at 6s. per yard; then for the other fhilling I take a twentieth part of the given number, and the quotient is 237. 25. which is the price of the cloth at 1s. per yard, and which, added to the former price at 65. gives 1617. 145, the answer. |