Ans. 31cwt. 2qrs. 20lb. 1. What is the weight of 4 hogsheads of sugar, each weighing cwt. 3qrs. 19lb. ? 2. What is the weight of 6 chests of tea, each weighing 3cwt. 2qrs. 9lb.? Ans. 21cwt. 1qr. 26lb. 3. If I am possessed of 14 dozen of silver spoons, each weighing 3oz. 5pwt.-2 dozen of tea spoons, each weighing 15pwt. 14gr. -3 silver cans, each 9oz. 7pwt.-2 silver tankards, each 21oz. 15pwt. and 6 silver porringers, each 11oz. 18pwt. pray what is the weight of the whole? Ans. 18lb. 4oz. 3pwt. 4. In 35 pieces of cloth, each measuring 273 yards, how many yards? Aus. 9711 yards. 5. How much brandy in 9 casks, each containing 45gal. 3qts. 1pt.? Ans. 412gal. 3qts. 1pt. 6. If I have 9 fields, each of which contains 12 acres, 2 roods and 25 poles; how many acres are there in the whole? Ans. 113A. 3r. 25p COMPOUND DIVISION* IS the dividing of numbers of different denominations: In doing which, always begin at the highest, and when you have divided that, if any thing remain, reduce it to the next lower denomination, and so on, till you have divided the whole, taking care to set down your quotient figures under their respective denominations. INTRODUCTORY EXAMPLES, * To divide a number consisting of several denominations by any simple number whatever, is the same as dividing all the parts or members of which that number is composed, by the same number. And this will be true when any of the parts are not an exact multiple of the divisor; for, by conceiving the number, by which it exceeds that multiple, to have its proper value by being placed in the next lower denomination, the dividend will still be divided into parts, and the true quotient found as before: Thus £41 17s. (d. divided by, will be the same as £36 1178. 4 d. divided by f, which is equal to £6 18. 7d. as by the rule. lu the first example, having divided the pounds, the 4, which remains, is 4 pounds, which are equal to 30 shillings, and 17 in the shillings make 97; I then find 5 is contained 19 times in 97, and 2 over: I set down 19 under the shillings, and reduce the 2 shillings, which remain, into pence, and they make 24, and the 9 pence, in the question, added, make 33: Then how often 5 in 33; I find it 6 times, and 3 over: I set down 6 under the pence, and reduce the 3 pence, which remain, to farthings, and they make 12; then, how often 5 in 12; I find it to be twice: I therefore set down d. and the 2 which remains, is of a farthing, which I make no account of. 25. Suppose that two places lie east and west of each other, and it is found by observation that it is noon at the former 2 hours, 6′ 30" sooner than at the latter; how many degrees are they asunder? 4'2h. 6' 30" Reduce the hours and minutes to minntes, then, minutes divided by 4′ give de 31° 37′ 30′′ Ans. grees in the quotient.* Because 360°, the whole circumference of the carth. divided by 24, the hours in a day, give 15° for one hour or 60 minutes: and 60÷15=4' for onc degree. 26. The longitude of Cambridge is 4h. 44' 17", and that of Philadelphia, 5h. 0' 43"; how many degrees difference. PRACTICAL QUESTIONS. CASE I. 4° 6' 30" Ans. Having the price of any number of yards, pounds, &c. which is within the pence table, or is a composite number, to find the price of one yard, pound, &c. use the following rule. If the quantity do not exceed 12, proceed by setting down the price, and dividing it by the quantity; which quotient will be the price of one yard, required; but if the quantity exceed 12, then divide by such numbers, as, when multiplied together, will produce the quantity, and the last quotient will be the value of 1 yard, required. el? EXAMPLES. 1. If 9 yards of cloth cost £4 3s. 74d. what is it per yard? £ S. d. Q 9 31 Ans. 2. If 7 ells cost £5 17s. 5d. what cost 1 ell? 3. If 11 sheep cost £6 5s. 9d. what did each cost? Ans. 11s 54d. 4. If 12 gallons of rum cost £8 11s. 91d. 5. If 84 cows cost £253 13s. what is the 6. If 132 bushels of corn cost £20 12s. 6d. what is it per gallon? Ans. 14s. 3 d. price of each ? Ans. £3 Os. 43d. what is that per bushAns. 3s. 1 d. 7. If 11 sheep cost $25.63c. what is the price of each ? Ans. $2.33c. 8. If 84 cows cost $363.52c. what is the price of one? Ans. $10.28c. 9. If 132 bushels of corn cost $66 what is the price of a bushel? Ans. 50c. Note. If there be a remainder after the division by one of the parts of a composite number before the last, that remainder must be divided according to the rule for division of fractions, as in the following example. 10. If 35 yards cost £37 11s what is the price of one yard? 35=5X7 £ 8. 5)37.. 11 1 5 133qr. Ans. Now 63 In dividing the farthings by 7, there is a remainder of 63qrs. which is to be divided by 7 to obtain the whole answer. 3, and 3-7, which must be annexed to farthing in the last quotient. 11. If 42 bushels of wheat cost $48.57c. what costs one bushel? Ans. $1.15, c. 12. What do I pay a pound for cotton, when 99lbs. cost £6 2s. 4d. Ans. 1s. 213d. CASE II. : Having the price of a hundred weight, to find the price of 1 Divide the given price by 8, that quotient by 7, and this quetient by 2, and the last quotient will be the price of 1 b required. EXAMPLES. 1. If 1 cwt. of flax cost £2 7s. 8d. what is that per 8) £2 7s. 8d. 7)0 5 11/ 2)0 0 10d.0 qr. 5d. price of 1 pound. 2. At £3 10s. per cwt. what cost 1? CASE III. 玷? Having the price of several hundred weight, to find the price per : Divide the whole price by the number of hundreds, which will give the price per cwt. and then proceed as in the last Case. EXAMPLES. 1. If 3 cwt. of sugar cost £13 8s. 4d. what is that per ? 5) £13 8s. 4d. 0 0 5 price of 1 ib. 2. If 8 cwt. cocoa cost £15 17s. 4d. what is that per 3. If 31 cwt. of sugar cost £9 17s. 2d. what is that 4. If 13 cwt. of cotton wool cost £6 10s. 8d. what is ? Ans. 44d. per ? Ans. 6d. that per it? Ans. 8d. 5. If 3 cwt. of raisins cost $50.52c. what cost 1 ? $ 7. If 114 cwt. cost $87.33c. what cost 1 ? 8. If 31 cwt cost $3.64, what cost 1 ? Ans. 1c. Note. This Case proves the 6th in Compound Multiplicalion. CASE IV. Having the price of any number of yards, &c. to find the price of 1 yard: Divide the price by the quantity, beginning at the highest denomination, and, if any thing remain, reduce it into the next, and every inferiour denomination, and, at each reduction, divide as before, remembering each time, to add the odd shillings, pence, &c. if there be any, and you will have the value of unity required. Note. If there be, or of a yard, pound, &c. multiply both the price and quantity by 4, and then proceed as above directed; or, in federal money, work by decimals. EXAMPLES. $55 59c. 31m. what are they per it? £ S. d. Price 16 13 63 Produces 382 for a divisor. Product £66 14 250 4 3 for a dividend. 382)66 14 3 (0 3 5 3 per 1b. |