(20) How many pounds of silver are there in a half-dozen of dishes, each weighing 51oz. 10dwts., and a dozen of plates each weighing 15oz. 15dwts. 22grs.? Answer: 41lbs. 6oz. 11dwts.

(21) If a wheel of 5yds. 1ft. 6in. in circumference make 64640 revolutions, what space will it pass over? Answer: 202 miles.

IV. COMPOUND DIVISION.

63. RULE. Having placed the divisor and dividend as in integers, find how often the divisor is contained in the highest denomination of the dividend, put down the quotient; and reduce the remainder, if any, to the next inferior denomination, adding to it the number of that denomination in the dividend, and repeat the division : so proceed through all the denominations.

Ex. Divide 41 wks. 6days. 19hrs. by 11.

and the operation may be proved by that of multipli

cation.

When the divisor is greater than 12, the process may be conducted as in Article (42), if it be a composite number, and by long division, if it be incomposite.

Ex. To divide £1478. 13s. 83d. into 77 equal portions, we may use either of the subjoined methods:

The division may also be effected by reductions analogous to those alluded to in Multiplication.

Examples for Practice.

(1) Divide £189. 8s. 4d. by 5 and 8.

(2) Find the quotients of 182cwt. 3qrs. 7lbs. by 7 and 9.

(3) Divide 1658yds. 1ft. by 6 and 10.

(4) Find the quotients of 238ac. 2ro. 32po. by 8 and 11.

(5) Divide 13wks. 5days. 19hrs. 30min. by 3 and 4. (6) Divide 739 qrs. 4bush. 2pks. 1gal. into 11 equal portions.

(7) What is the twelfth part of 22wks. 4 days. 20hrs. 43min. 24sec.?

(8) Divide £1738. 12s. 7 d. by 18; and £1279. 13s. 8 d. by 23.

Answers: £96. 11s. 9 d., and £55. 12s. 94d.

(9) Divide 425tons. 15cwt. 2qrs. 12lbs. by 27; and 2374cwt. 1qr. 12lbs. 12oz. by 38.

Anwers: 15tons. 15cwt. 1qr. 16lbs., and 62cwt. 1qr. 26lbs. 2oz.

(10) Find the quotient of 1361mi. 4fur. 28po. by 28; and of 3179lea. Imi. 5fur. 16po. by 46.

Answers: 48mi. 5fur. 1po., and 69lea. 2fur. 36po.

(11) If 41cwt. cost £52. 10s. 74d., what is the price of a cwt.?

Answer: £1. 5s. 74d.

(12) What will be the price of 1lb., when 1cwt. costs £137. 18s.?

Answer: £1. 4s. 7 d.

(13) If a soldier's pay for a year of 365 days be £9. 2s. 6d.; how much is that for a day?

Answer: 6d.

(14) If a person's yearly income be £65. 12s. 6d., and he lay by £20. a year; how much does he spend each day?

Answer: 2s. 6d.

(15) If 145 sheep cost £169. 3s. 4d.; what is the price of a score at the same rate?

Answer: £23. 6s 8d.

(16) A wheel makes 514 revolutions in passing over 1mi. 467yds. 1ft.; what is its circumference? Answer: 4yds. 1ft.

(17) If a person complete a journey of 422mi. 3fur. 38po. in 37days; what distance does he travel each day? Answer: 11mi. 3fur. 14po.

(18) If 8 packages of cloth, each consisting of 4 parcels, each parcel of 10 pieces, and each piece of 26. yards, cost £6656.; what is the price of a yard?

Answer: 16 shillings.

(19) If the clothing of 754 soldiers come to £3178. 11s. 74d.; how much is that for each man?

Answer: £4. 4s. 3 d.

(20) A vintner bought 138gals of wine at 10s. a gallon, of which he retained 18gals. for his own use: at what rate per gallon must he sell the remainder, that he may have his own for nothing?

Answer: 11s. 6d.

(21) A ship's crew of 50 men have a supply of water for 30 days at 2 quarts a head: if they lose 125 gallons, and find that they will be 50 days at sea, what must be each man's daily allowance?

Answer: 1 quart.

64. The multipliers and divisors in the last two rules have been regarded as abstract numbers: and though it is impossible to determine the product of two concrete quantities as such, the quotient of one concrete magnitude by another of the same kind will be an abstract number, being merely the number of times one of them must be repeated to make up the other. See the Appendix.

Ex. The sum £263. 8s. 111⁄2d. is distributed equally among a number of persons, so that the share of each is £37. 12s. 8d.: find the number of persons.

Here, the dividend = 252910 farthings:

and the divisor 36130 farthings:

=

whence, the quotient is found to be 7, by common division: or, £37. 12s. 84d. being repeated 7 times, amounts to £263. 8s. 11 d., and the number of persons is 7.

Hence, one concrete magnitude may be a measure or a multiple of another of the same kind.

CHAPTER III.

THE RULE OF THREE,

SOMETIMES CALLED THE GOLDEN RULE.

65. DEF. THE object of the Rule of Three is, by means of three quantities given, to determine a fourth, which shall be the same multiple, part or parts of one of them, that one of the remaining quantities is of the other; and it therefore follows that the operation, by which this may be accomplished, will depend upon those of Multiplication and Division already considered.

Ex. 1. If 1lb. of any commodity cost 3s. 44d., it is required to find the price of 12lbs.

Here, it is evident that the required price will be the same multiple of 3s. 44d., that 12lb. is of 1lb., which may therefore be found by Multiplication: thus,

and this result may be obtained by means of a Slatement and Operation in the following form: