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139. Preparatory direction. Write down the given number, namely, the number which expresses the quantity of goods of which you want to find the value, and to the left of it draw three perpendicular lines sufficiently wide apart to contain a column of figures in each of the two intervals; then, having (if necessary) broken the given price into sums which are respectively aliquot parts of some greater whole, and of one another, you are to place these sums in their proper order under one another in the left hand interval; and opposite each, in the right hand interval, place the number expressing what aliquot part it is; then, work according to the directions given in the rule to which the particular question belongs.
140. When the price is an aliquot part of a penny.
RULE I. Having drawn the lines, and placed the price and the aliquot part as above directed, divide the given number by the aliquot part, and the quotient will be the answer in pence; these (if there be a sufficient number) must be divided by 12 and 20, to reduce them into pounds.
II. If when you have divided by the aliquot part there be a remainder, it will be pence, and must be reduced to farthings, which being divided by the aliquot part, will give farthings".
1. What is the value of 3571 yards of tape, at ; d. per yard 2
• Nothing can be easier to understand than the rules of Practice. In the rule here given let us take Example I; where, if 3571 yards had cost a penny each, they would evidently have amounted to 3571 pence; but as they cost only #d. each, it is plaim that they will amount to half that number of pence. And in Example 2,9867 pears at #d. each will, it is plain, amount to one quarter that number of pence: wherefore this rule is evident. *
2. What cost 9867 pears, at 4d. each.
Operation. z Explanation. + | + |9867 A farthing is one fourth of a penny; I 12 2466 3. therefore divide by 4; the 3 remainder are oln/ToonTETo pence, which reduced are 12 farthings, which 2|0|205 6 12 divided by 4 give +. I then divide by 12 and
141. When the price is an aliquot part of a shilling.
RULE. Having placed the price, and its corresponding aliquot part, as before directed, divide by the aliquot part, and the quotient will be shillings, which reduce to pounds by dividing it by 20. If there be a remainder after the first division, it is shillings; reduce it to pence, which divide by the aliquot part, and the quotient is pence P.
7. What is the worth of 826 lemons, at 3d, each 2
OPERATIon. Earplanation. d. Here 3d. by table 2, is + of a shilling; I 3 || 3 |826 therefore divide by 4; the quotient is shillings, 2|o 206 6 and the remainder 2 I make 24 pence, which di
- vided by 4 gives 6 pence; the quotient I then Answer 10l. 6s. 6d. divide by 20, which gives the answer.
p Here if we consider the articles as worth a shilling each, they will cost in the whole as many shillings as there are articles given; wherefore if they cost an aliquot part of a shilling each, the whole will evidently amount to the same part of so many shillings: thus, in Example 7, 826 lemons at 1s. each will cost 826 shillings; but at 3d. each (since 3d. is + of a shilling) they will amount to # of 826 shillings; and the like in other cases,
142. When the price is an aliquot part of a pound.
Rule I. Having placed the price and the aliquot part as before, divide by the aliquot part, and the quotient will be pounds.
II. The remainder (if any) must be reduced to shillings, and divided by the aliquot part for shillings; if there be a second remainder reduce it to pence, and divide for pence; if a third, reduce it to farthings, and divide for farthings".
17. What must be given for 135 pullets, at 2s. 6d. each
Earplanation. OPERATION. Here by table 3, 2s. 6d. is # of a pound; I s. d. divide by 8, and the quotient is 16 pounds; the |2 6| + |135 remainder 7 turned into shillings is 140, which
divided by 8 gives 17 shillings, with 4 remainder; the latter brought into pence is 48, which divided by 8 gives 6 pence.
* The observations in the two foregoing notes are equally applicable to this rule; thus, in Example 17, 135 pullets at ll, each will cost 135l. ; but since the price (2s. 6d.) is # of a pound, it is evident that the whole will amount to # of 135l. : and the like may be shewn of the other Examples,
RULE I. Divide the price into sums which are aliquot parts of the whole, (viz. of a shilling, or a pound, as the case may be,) or of which one is an aliquot part of the whole, and the rest aliquot parts either of the whole, of this, or successively of one another.
II. Divide by these several aliquot parts, and the quotients being added together, the sum will be the answer in shillings, if the aliquot parts are of a shilling; and in pounds, if they are aliquot parts of a pound".
* This rule will be evident from an explanation of the 29th Example, where if 37 loz. had cost 1s. each, the whole would have cost 371 shillings; but at 3d. each (since 3d. is + of a shilling) they will cost 4 of 371 shillings, or 92s. 9d.; and at #d. each (since #d. is + of 3d.) they will cost + of their value at 3d., that is ; of 92s. 9d., or 15s. 5d.;; wherefore, if the value at 3d. each be added to the value at #d. each, the sum will evidently be the value at 3d.; each : and the like may be shewn in every other case.
29. What is the value of 371 ounces of tobacco, at 3d.; per ounce • ?
Or thus; by 20. d. In the second operation, I divide the given price 2 | + |371 3d.; differently; I take 2d., which is #, and 14.4, , I-FT- which is +, both aliquot parts of a shilling; I 14| + | 61 10 therefore divide the top line by both, add the quo46 4+ tients together, and divide by 20, which gives the 2]o 10|8 23 answer the same as in the first operation.
31. What sum will pay for 215 cheeses, at 17s. 10d. each?
OPERATIon. &. Erplanation. 10 || 3 |215 When there are several aliquot parts, we are not 5 || 4 || 107 10 - obliged to take each part out of the neart preceding 2 i 53 15 one; we may take it out of any of the preceding s" parts, as may be most convenient. In this exam10d # 21 10 ple 2s. is + (not of 5s, but) of 10s.; I therefore
• To prove this example, multiply 371 by 3d:#, and divide by 12 and 20. “To prove operations of this kind, multiply the given price by the number of particulars (Art. 105); in the present instance it will be 17s.6d. x 123.