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The use of this table is, to find how often the divifor is contained in any particular dividend; thus, in this example, after having pointed off the first nine figures in the dividend 243098249 (because the first eight figures are lefs than the divifor), I caft my eye on the table, and find that the next lefs number is 238994464, and which I find by the table contains the divifor 8 times; I therefore place 8 in the quotient, and the multiple of 8, taken from the table, I place under the dividend, and fubtract it therefrom, and to the remainder bring down the next figure 3 for a new dividend: then, by the table, I find the divifor is contained in this dividend but once, I place I in the quotient, and fubtract the multiple of 1 (or the divifor) from fuch dividend as before, and to the remainder I bring down the next figure 7: in this dividend (by the table) I find the divifor is contained 3 times, which I place in the quotient, and take the multiple of 3 from the table to be fubtracted from the last dividend, to which remainder I bring down the laft figure 2: and, by the table, I find the divifor is contained in the last dividend 7 times; and the multiple of 7 being fubtracted from this last dividend, there remains 11005176 after the work is ended.

When the divifor has a cypher or cyphers towards the right hand, the dividend may be divided by the fignificant figures only, and the cyphers feparated from the divifor by a stroke of the pen; in which cafe there must be as many figures separated from the right hand of the dividend, as there are feparated cyphers, and fuch feparated figures are to be fet down at the last as a remainder and if there be any other remainder, the separated figures are to be fet on the right hand thereof. When the divifor has an unit only on the left hand, with nothing but cyphers on the right hand thereof, the divifion is performed at once, by cutting off as many figures from the right hand of the dividend as there are cyphers in the divifor the remainder of the dividend is the quotient. See the following examples :X 2

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Divifion of divers denominations is performed by dividing each denomination in the dividend by the divifor, placing the quotient of each denomination under the fame denomination in the quotient, and carrying the overplus of each denomination to be added to the next, as follows:

Divide 4374, 195, 10d, among 24 men,

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195.

In this example, I first divide the 4371. by 24, the quotient of which is 18. and there remains 54, which, added to the makes 1195. for a new dividend; then the divifor is cou tained 4 times in 119, wherefore I fet down 45, in the quotient, and 234. remain, which added to the 10d. make 286d. for the next dividend; in which the divifor is contained i times, and there remains 22d, or 88. farthings, in which the divifor is contained 3 times. Thus the quotient is 184, 45.11ŝd. and there remains 16 farthings.

Sums of this nature may also be more expeditiously wrought, if the divifor be a commenfurable number, and can be refolved into two parts, as in the following example:

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Qu. 1. If the expense of a country feast be 2631. 105. 6d. to be paid by 28 ftewards, what must each steward pay ?-La this example I divide by 4, and the quotient thence ariling by 7, which is equal to dividing by 28, and the answer is found to be gl. 8s. 2d, for each steward to pay.

Qu. 2. If a gentleman spend 3471. 155, 9d. in the space of one year and eight weeks, it is defired to know how much it is per week on an average ?-Here I divide the whole fum by 5, and the quotient thence arising by 6, and that quotient by 2; which is equal to dividing by 60 (the number of weeks in one year and eight weeks), and the answer is 54 155. 11d. per week, as in the example.

Qu. 3. If the capital stock of a tontine amount to 43721. 145. od. and there be in it 160 fhares, what will be the amount of each fhare-In this example I divide by 4, and that quotient by 10, and the quotient thence arifing by 4, which is equal to dividing by 160; as 4 times. 10 is 40, and 4 times 40 is 160, and the answer is 271. 6s. 7d. for each flare.

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To find the exact remainder in fums where there are two or more divifors, as in the foregoing ones, the rule is to multiply the first divifor by the laft remainder, adding thereto the first remainder, if any, and the product will be the true remainder; as if it had been divided by the long method: thus in the first of the foregoing examples, I multiply 4, the first divifor, by 5, the laft remainder, which produces 20, to which adding 2, the first remainder, the true remainder is found to be 22, which may be proved at leifure.

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Qu. 4. There is a piece of land, having 4 fides, containing 1398 acres, 3 roods, 35 perches, and 240 feet in breadth, it is defired to know how many feet it is in length?

Qu. 5. There is a piece of timber, the folid contents of which is 600 feet, its length is 40 feet, and its depth 3 feet; it is required to know its fuperficial contents?

Question 4.

A. R. P.

4)1398 3 35

6) 349 2 383 10) 58 I 62

5 3 12 6

Question 5.
31600

200

In the fourth queftion I divide the contents of the land, first by 4, and that quotient by 6, and the next quotient by ro, which is the fame as dividing at once by 240; and the anfwer is found to be 5 acres, 3 roods, and 12 perches, for the length of the piece of land.

In the last queftion I divide the folid contents of the piece of timber by 3, the depth, and the quotient 200 feet, is the fuperficial contents, which if divided again by 40 feet, the length, would give 5 feet for the breadth.

In the fame manner as the foregoing examples are wrought divifion of other denominations may be performed, having respect to the table of quantity belonging to the fame.

But in this fpecies of divifion, if the divifor be not a commenfurable number, or one which cannot be divided into parts exactly, the divifion must then be performed by one divifor.

Divifion alfo teacheth how to bring small denominations into great ones; but as this part more properly belongs to Reduction, I have deferred treating of it till I come to that rule..

SECT.

SECT. VI.

OF REDUCTION.

REDUCTION is only the application of the rules of multiplication and divifion, and teacheth how to bring numbers of one denomination into another denomination without altering their value.

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Reduction is either defcending or afcending. Reduction defcending is performed by multiplication, and ferves to bring great denominations into fmall ones; as pounds into fhillings, pence, or farthings; hundred-weights into pounds or ounces," &c. Reduction afcending is performed by divifion, and brings small denominations into great ones; as farthings into pence, fhillings, or pounds; drams or ounces into pounds, hundredweights, &c.

Shillings in 1 pound

250

20

Rule. In reduction defcending, multiply the number by the number of units of the next lower denomination which make an unit of the next greater, and multiply fuch product by the number of units of the next lower denomination which' make one of the next greater; and proceed in this manner till the number be reduced to the denomination required. EXAMPLE 1. Reduce 250l. os. od. into farthings. In this example, I first multiply the 250 by 20, which is the number of units of the next lower denomina. tion which make an unit of the next higher; that is, the number of fhillings contained in a pound, and the product fhews the number of fhillings contained in 250%.; which product must be again multiplied by 12, the number of units of the next lower denomination which make one of the next greater, or the number of pence contained in one filling, and the product gives the number

121

Shillings in 250%. 5000
Pence in 1 fhilling
Pence in 250/. 60000

Farthings in 1 penny

Answer 240000

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