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(22) In a company S. had 37. 17s. 2d. more than T. who had six guineas less than R. who had within 16s. 8d. of as much as W. who was known to have 100 guineas, wanting ten marks of 13s. 4d, each. What money had they among them ?

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When the divisor consists of the same figure in all the places; that is, all 9's or all 7's, &c. annex as many ciphers to unit or 1 as there are 9's or 7's, &c. in the given divisor, for a new divisor; and, if the repeating figure be 9, divide the dividend by that divisor, and do the same with the quo tient, till you get O for an integral quotient; then add all the overplusses together, and divide that sum by the given divisor, the overplus thence arising is that required; and the sum of all the integral quotients is the quotient required. For any other figure, divide nine times the dividend so, and the integral quotient by the repeating figure. This gives the true integral quotient; and if the ninth part of the first overplus be added to the second, repeated as the given figure, the sum will be the true overplus.

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X. COMPOUND DIVISION

TEACHETH to divide, by one common divisor, either a simple or compound number into any proposed number of equal parts, whereof each shall be a compound number.

Case 1. When the divisor does not exceed 12.

RULE.

1. Place the divisor and dividend as integers.

2. Write their quotas under each respective dividend. 3. But if there be a remainder after dividing any of the denominations except the least, you must find how many of the next lower denomination it is equal to, by multiplying it by as many of the next less as make one of that, which add to the next, if any, and divide as before.

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(6) Bought 3 cwt. of cheese, for which I gave 74 11s. 6d. At what rate did I give per cwt.?

(7) If 10 dozen of candles cost 31. 17s. Id. what costs one dozen?

(8) Suppose I give my servant fourteen guineas per year, what do his monthly wages come to?

: Case 2. When the divisor exceeds 12, and is such a number that any two figures in the Multiplication Table being multiplied together, will produce it.

RULE.

Divide by component parts, as in Sect. V. Case 4.

EXAMPLES.

(9) Divide 451, 12s. 8d. into 16 equal parts.
(10) Divide 31. 13s. equally amongst 24 persons.

(11) What is cloth per yard, when 36 yards cost 641. 19s. ? (12) What is tobacco per cwt. if 42 cwt. cost 190l. 4s. 6d.? (13) Bought 48 yards of broad cloth for 371. 14s. 8d. I desire to know at what rate I gave per yard?

(14) Suppose a man spends 787. 16s. 8d. in eight months' time, what is that per week?

(15) A prize of 45671. Os. 10d. is to be equally divided amongst 55 persons. What is each man's share?

(16) What is tea per cwt, when 63 cwt. cost 2647. 12s.? (17) If 72 oz. of silver cost 18 guineas, what is it per oz. ? (18) Suppose I have 81 cwt. of cheese, which cost me 1211. 12s. 6d. at what rate did I buy per cwt.?

(19) Divide 1747. 1s. 8d. equally amongst 120 sailors.

Case 3. When the divisor cannot be produced by the multiplication of two small numbers, divide as in Sect. IV. Case 2.

EXAMPLES.

(20) Divide 2147. 17s. 94d. equally among 17 persons. (21) Divide 4767. amongst 145 people.

The following EXAMPLES require three DIVISIONS: (22) I gave 301. 2s. for 112 yards of cambric. At what rate was that per yard?

(23) Divide 10097. equally amongst 350 persons.

(24) Suppose the clothing of 224 charity children comes to 610l. 8s. what is the expense of each?

(25) Divide 14261. equally among 640 persons.

Case 4. If the given quantity, or divisor, consist of 4, ž, or 1.

RULE.

Multiply the given quantity by 4, adding to the product 1 for, 2 for, 3; and it will give the divisor, which divide with, as before; and the quotient multiplied by 4 will give the answer.

EXAMPLES.

(26) Suppose I gave for 64 yards of cambric 127. 12s. 11d. at what rate did I buy it per yard?

(27) Suppose a person in trade to clear 10611. 8s. 93d. equally in 10 years, what was his yearly increase of fortune?

(28) Suppose another to clear 450l. 13s. 11žd. equally in 83 years, what was his yearly profit ?

Of WEIGHTS and MEASURES.

EXAMPLES.

(1) Divide 8 lb. 1 oz. 15 dwts. 8 grs. by 2.
24 tons, 14 cwt. 0 qr. 14 lb. by 3.

(2)

(3)

(4)

(5)

(6)

17 cwt. 2 qrs. 27 lb. 14 oz. 15 drs. by 4.
4 lb. 113. 43. 13. 12 grs. by 5.
214 yds. 3 qrs. 2 na. by 9.
120 ells. Eng. 4 qrs. by 8.
12 lea. 2 m. O fur. 26 p. by 9.
147 yds. 2 f. 11 in. 2 b. c. by 10.
24 W. hhds. 57 gal. by 11.

10 tuns, 1 p. 1 hhd. 60 gal. 3 qts. by 8.
16 tier. 20 gal. 7 pts. by 6.

76 A. hhds. 27 gal. by 5.

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12. B. hhds. 49 gal. 2 qts. by 4.

(14)

61 B. bar. 2 fir. 6 gal. by 3.

(15)

140 A. 2 r. 26 p. by 12

(16)

(17).

60 lasts, 6 qrs. 7 bu. 2 pks. by 7.
146 days, 23 h. 24 m. 56 sec. by 6.

APPLICATION.

(1) An army of 10000 men having plundered a city, took 220000l. What was each man's share?

(2) A certain man intending to go a journey of 336 miles, and to complete the same in twelve days; it is required how many miles he must travel each day?

(3) What number, added to the forty-third part of 4429, will make the sum of 240?

(4) What number, deducted from the twenty-sixth part of 2262, will leave the eighty-seventh part of the same? (5) What number, multiplied by 72084, will produce 5190048 ?

(6) What number, divided by 419844, will quote 9494, and leave just a third part of the divisor remaining? (7) The sum of two numbers is 360, the less is 144. What is their difference, product, and larger quote?

(8) The Spectator's Club of fat people, though it consisted but of 15 persons, is said (No. 9) to weigh no less than 3 tons. How much, on an equality, was that per man?

(9) What number is that, from which if you deduct the 25th part of 22525, and to the remainder add the 16th part of 9696, the sum will be 1440?

(10) What number, multiplied by 57, will produce just what 134 multiplied by 71 will do?

11) Subtract 30079 out of fourscore and thirteen millions, as often as it can be found, and say what the last remainder exceeds or falls short of 21180?

(12) A gentleman at his death left his eldest son once and a half what he allotted his daughter, and to the young lady 13837. less than her mother, to whom he bequeathed four times what he left towards the endowment of Hertford College, Oxon, viz. 1640 guineas. I require what he intended for his youngest son, who claimed under the will half as much as his mother and sister? How much less than 300007, did the testator die worth, after his debts and funeral expenses, being 9887. 10s., were paid?

(13) My purse and money, quoth Dick, are worth 12s. 8d. but the money is worth seven times the purse. Pray what was there in it?

(14) A young fellow owed his guardian 747. 18s. 2d. on balance. He paid off 411. 14s. 8d. and then declared his sister owed the gentleman half as much again as himself. On hearing this, she paid off in part 131. 12s. 10d. and gave out that her uncle William was not then less in arrears than her brother and she together. The uncle hereupon paid in 241. 7s. 3d. and then the uncle's brother, who, by the by, was not the uncle of those children, for 150l. undertook to set them all clear, and had, he said, 351. 15s. 5d. to spare. Can that be true?

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