stocks are equal, the shares are as the times; wherefore, when neither are equal, the shares must be as their products. 2. A, B, and C, company, and put in together £3822; A's money was in 3 months, B's five, and C's money 7 months: they gaved £234, which was so divided, as the of A's gain was equal to of B's gain, and of B's gain was equal to 4 of C's gain: What did each merchant gain, and put in ? Suppose A's gain was £2, then B. must have £3, and C. 4, according to the tenor of the question; which numbers, added together, make 9: then I say, As 9 2.3.4 :: Months. Is a rule compendiously contrived for the speedy operation, or casting up the amount of any sort of goods or merchandize; and, therefore, is of excellent use among merchants, tradesmen, &c. for their quick and elegant despatch of business; and, from its frequent use, is called the rule of practice. This rule is only a contraction of the rule of three direct; for, when the price or value of one is given, and the price of any other quantity is required, the first term, (or number,) being always an unit, the question may more quickly be wrought by the aliquot parts of a shilling or pound, as the nature of the question requires. The following tables are recommended to the learner, to commit to memory, for the more speedy operation of the rule. TABLE 4. Of Aliquot parts of a Cwt. and Qr. PARTS OF A CWT. PARTS OF A QR. 3 10 ៖ 19 0 66 TABLE 5. Of Aliquot parts of a Dollar. 1 cent is = 10 dollar. 1245 is 1 IS 23 TABLE 6. Of Discount per cent. S. d. 11 per cent. is 0 3 £. 0 6 Divide the given number by the denominator of the fraction denoting the rate, as contained in Table 1, viz: if the rate be 1 or 2 farthings, the quotient will be pence, and the remainder will be farthings; or, in dividing by 2, it will be one half penny: then divide the pence by 12, the quotient will be shillings, and the remainder pence; lastly, divide the shillings by 20, the quotient will be pounds, and the remainder shillings. But if the rate be 3 farthings, first multiply the given number by the numerator 3, and then divide as above directed. More ways of working the above examples may be assigned, but the most easy and simple methods are best for an introduction. CASE II. When the rate is pence, under twelve. RULE. Divide the number by the denominator of the fraction denoting the rate, and you will have the answer in shillings; which reduce into pounds. The pence must be some aliquot part of a shilling, and the same time the farthings some aot part of the pence; and if they be not so given, divide the pence into two or more such parts, so as the farthings may be some aliquot part of the lowest division of the pence. Then beginning with the highest division of the pence, divide by the denominators of the fractions denoting the aliquot parts. EXAMPLES. 1. What will 532 yards of cloth 2. What will 2735 yards of Multiply the given number by the numerators of the fractions, and divide the product by the denominators. Or, instead of this general rule, take the two particular ones following. 1. If the rate be an even number of shillings, multiply the given number by half the number of shillings in the rate, always doubling the right hand figure of the product for shillings and the rest will be pounds. 2. If the rate be an odd number of shillings, work for the next lesser even number of shillings as above; and for the odd shilling take of the given number. EYAMPLES. 1. When the rate is an even number of shillings. Ex. 1. 436, at 2s. 1 Ex. 2. 56, at 6s. Ex. 3. 48, at 89. £43 12 0 Ans. 2. When the rate is an odd number of shillings. Ex. 4. 422, at 3s. £19 4 0 Ans. Ex. 6. 124 at 9s. £16 16 0 Ans. Ex. 5. 516, at 7s. £180 12 0 Ans. 49 12 6 4 £55 16 Ans. £63 68. 0 NOTE. By reversing the operation, from the price, and any even rate given, we may readily find the quantity of goods, viz. multiply the price by 10, that is to the price annex a cypher, and divide the product by half the rate. Ex. 1. How many yards of cloth at £49? Half the price 7)490(70 yards, answer. per yard, may I have for 2. How many yards of cloth, at 18 shillings per yard, may be bought for £345? 9)3450(383 yards, answer, and so on universally. CASE V. When the rate is shillings and pence, or shillings, pence, and farthings. RULE 1. If the rate be shillings and pence, which make an aliquot part of a pound, divide the given number by the denominator of the fraction denoting the rate; the quotient will be pounds, and each unit of the remainder, an unit equal to the rate. EXAMPLES. 1. What will 354 yards of cloth|| 2. What will 439 yards of cloth cost at 1s. 8d. per yard? cost at 6s. 8d. per yard? If the rate be no aliquot part of a pound, but may be divided into shillings, and some aliquot part or parts, divide it accordingly, work for the parts separately, and then add. EXAMPLES. 1. What will 427 yards of cloth|| 2. What will 540 yards of cost, at 8s. 6d. cloth cost at 5s. 4d. per yard? If the rate an be not aliquot part of a pound, and cannot readily be divided into such parts, divide it into parts whereof one at least may be an aliquot part of a pound, or some number of shillings, and the subsequent part or parts, each an aliquot part of some prior part. Or, multiply the given number by the shillings, and then, for the pence and farthings, work as before. (in case 3.) EXAMPLES. When the rate is pounds and shillings, or pounds, shillings, pence, and farthings. RULE 1. If the rate be pounds and shillings, multiply the given number by the pounds, and work for the shillings as before. |