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with the given grains, 128, which, divided by 8, give 16 for a quotient ; thus you have the same number for an answer in this operation, which was given in multiplication, consequently, compound multiplication and division prove each other, the same as simple multiplication and division do.

Pup. All this appears very plain, and the similarity of the compound to the simple rules is so great that I think it will require only a little practice to make them perfectly familiar.

Tut. The compound rules are not so difficult as they at first appear to be, provided you understand them well; if you have not got the tables well, and do not understand the nature of the rules, they will always trouble you, and you had beiter not leave them without a full acquaintance with their principles.

Divide 48 lb. 8 oz. 12 pwt. 14 grs. by 9.

Ans. 5 lb. 4 oz. 19 pwt, 45 grs. Divide 4 T. 16 cwt. 2 qr. 24 lb. by 6.

Ans. 16 cwt. O qr. 13} lb.

When the divisor is so large as to make it inconvenient dividing by it, and it can be produced by the multiplication of two or more numbers, divide first by one of those numbers, and then that quotient by one of the others, and so on with the whole ; when the last quotient will be the

answer.

Divide 168 cwt. 3 qrs. 14 lb. by 56.

8)168 3 14

7)21 0

12 4

3 0 1 12

Ans. 3cwt. Oqr. llb. 1202. Here by dividing 168cwt. 3qrs. 141b. by 8 we obtain one eighth of this number, and then dividing this quotient by 7, we get one seventh of the quotient, and }

of į is to

H

Divide 1061cwt. 2qrs. by 28.
Divide 156d. 18h. by 36.

Aps. 37cwt. 3qrs. 181b.
Ans. 4d. 8h. 50'.

When the divisor cannot be produced by the multiplication of two or more numbers; the division must be performed by dividing by the whole number at once.

If the quotient which is sought, were known, we might, by adding it to, or subtracting it from the dividend a certain number of times, and increasing or diminishing the divisor at the same time by as many units, alter the question so that the divisor might be resolved into factors, which would give the same quotient, and the analogy between multiplication and division preserved. But the quotient being unknown before the operation, this cannot be done.

Divide 249cwt. Oqr. 261b. by 17.

17)249 0 26(14 2 18

17

79 68

11 4

44
34

10 28

80 20 26

306

17

136
136

In this example, I begin and divide 249 as in simple pumbers ; obtain 14 for a quotient, and have 11 remainder, which I reduce to quarters; divide them by the divisor, and get 2 for a quotient, which I place so as to be kept separate from the 14cwt. The 10 remaining / reduce to pounds, and again divide, and obtain 18 for a quotient.

Pup. I understand this, and think it is very plain, there being nothing different in the principles of the rule from what I have been taught before.

Divide 126cwt. 3qrs. 21lb. by 26.

Aos. 4cwt. 3qrs. 141b: Divide 26cwt. 2qrs. 14lb. by 13.

Ans. 2cwt. Oqr. 5lb. 6oz. ? dr.

When the price of several hundred weight is given, and you wish to find the price of one hundred weight; divide the whole price by the number of hundred weight given, and the quotient will be the answer:

If, having the price of sereral hundred weight given, you wish to find the price of a quarter, a pound, &c. ; first find the price of a hundred weight, and then the price of the lower denominations, by dividing this price by those numbers which will reduce a number from a hundred weight to the denomination for which you wish to find a price. If 8 cwt. sugar cost $48, what is that

per

cwt. ?
8)48
Ans. $ 6

If 16 cwt. sugar cost $148, what is that per pound ?
16)148(9,25 price of cwt.
144

4)9,25
10

28)231(8,2 32

224 80

70 80

56

Ans. $0,082 14

If I give $450, for 210 cwt. raisins, what do they cost per cwt. ?

Ans. $2,142.

When the given quantity consists of several denominations, as of hundreds, quarters, pounds, &c. and the price of the whole given, to find the price of any particular denomination, first reduce the given quantity to the denomination for which you wish to find a price, and divide the price of the whole by it, when the quotient will be the answer. If the given quantity consist of lower denominations than the one for which you wish to find the price ; reduce the given quantity to the lowest denomination mentioned, and find the price for that, and then find the price for the other denominations, by multiplying this price by such numbers as will reduce a number from this denomination to the denomination for which a price is wanted.

If I give $124 for 16 cwt. 2 qr. of sugar, what is that per quarter?

16 2
4

[blocks in formation]

By reducing the whole quantity to quarters and dividing the price by that number, you get the price of one quarter; for if 66 quarters cost $124, one quarter will cost one sixty sixth part of the whole price. The ciphers annexed to the remainders reduce them to cents and mills, and the quotients arising from them are the same.

If 126 cwt. 2 qr. 14 lb. 12 oz. cost $482,50, what is it. worth per quarter ?

126 2 14 12

4

506
28

4062 1012

14182

16

85104 14182

226924)482,500(2,1262 the price of an ounce.

453348

[blocks in formation]

141912 $0,952,5376 pr. of 1 qr.

Ans. $0,952 per gr. Here we find that one ounce is worth 2 mills and 0,1262 of a mill; this price, multiplied by 16, gives the price of one pound, viz. $0,340,192 ; which, multiplied by 28, gives the price of one quarter, viz. $0,952. T'he price of one quarter, multiplied by 4, will give the price of one hundred weight, and the price of cwt. multiplied by the number of cwt. will give the price of the given hundreds, which, with the prices of the other given denomis nations, will be the price of the whole as it was givene

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