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COMPOUND MULTIPLICATION.

Compound Multiplication teacheth to find the amount of any given number of different denominations by repeating it any proposed number of times.

RULE.*

1. Place the multiplier under the lowest denomination' of the multiplicand.

2. Multiply the number of the lowest denomination by the multiplier, and find how many ones of the next higher denomination are contained in the product.

3. Write down the excess, and carry the ones to the product of the next higher denomination, with which proceed as before; and so on, through all the denominations to the highest, whose product, together with the several excesses, taken as one number, will be the whole amount required.

The method of proof is the same as in simple multiplication.

EXAMPLES

The product of a number consisting of several parts, or denominations, by any simple number whatever, will evidently be expressed by taking the product of that simple number and each part by itself, as so many distinct questions: thus, 251. 12s. 6d. multiplied by 9 will be 2251. 108s. 54d. = (by taking the shillings from the pence, and the pounds from the shillings, and placing them in the shillings and pounds respectively) 230l. 12s. 6d. which is the same as the rule; and this will be true, when the multiplicand is any compound number whatever.

EXAMPLES OF MONEY.

1. 9lb. of tobacco, at 2s. 8d. per lb.

2s. 8d.

1 9

11. 4s. 41d. the answer.

2. 3lb. of green tea, at 9s. 6d. per lb. 3. 5lb. of loaf sugar, at Is. 3d. per lb. 4. 9cwt. of cheese, at 11. 11s. 5d.

Ans. 11. 8s. 6d.
Ans. 61. 35.

per cwt.

Ans. 141. 2s. 9d.

5. 12 gallons of brandy, at 9s. 6d. per gallon.

Ans. 51. 145.

CASE I

If the multiplier exceed 12, multiply successively by its component parts, instead of the whole number at once, as in simple multiplication."

EXAMPLES.

1. 16cwt. of cheese, at 11. 18s. 8d. per cwt,

Il. 18s. 8d.

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2. 28 yards of broad cloth, at 19s. 4d. per yard.

Ans. 271. Is. 4d.

3. 96 quarters of rye, at 11. 3s. 4d. per quarter.

4. 120 dozen of candles, at 5s. 9d. per doz.

Ans. 112.

Ans. 34. 10s.

5. 132 yards of Irish cloth, at 2s. 4d. per yard.

Ans. 151. 8.

6. 144 reams of paper, at 13s. 4d. per ream.

Ans. 961.

7. 1210

7. 1210 yards of shalloon, at 2s. 2d, per yard.

CASE II.

Ans, 1311. Is. 8d.

If the multiplier cannot be produced by the multiplication of small numbers, find the nearest to it, either greater or less, which can be so produced; then multiply by the component parts as before; and for the odd parts, add or sub. tract according as is required.

EXAMPLES,

1. 17 ells of holland, at 7s. 8d. per ell, 7s. 8d.

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£6 II of the answer.

2. 23 ells of dowlas, at 1s. 6d. per ell.

Ans. 11. 155, 54d,

3. 46 bushels of wheat, at 4s. 74d. per bushel.

Ans. 10l. 11s. 91d.

4. 59 yards of tabby, at 7s. 10d. per yard.

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Yds. qr. nls. T. hhd. gal. pt. W. qr. bu. pe.

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II

COMPOUND DIVISIÓN,

Compound Division teacheth to find how often one given number is contained in another of different denominations,

RULE.*

1. Place the numbers as in simple division.

2. Begin at the left hand, and divide each denomination by the divisor, setting the quotients under their respective dividends,

3. But if there be a remainder, after dividing any of the denominations except the least, find how many of the next lower denomination it is equal to, and add it to the num ber, if any, which was in this denomination before; then divide the sum as usual, and so on, till the whole is finished. The method of proof is the same as in simple division.

EXAMPLES

* To divide a number consisting of several denominations, by any simple number whatever, is evidently the same as dividing all the parts or members, of which that number is composed, by the same simple 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 251. 12s. 3d. divided by 9, will be the same as 181. 144s. 99d. divided by 9, which is equal to 21. 16s. 11d. as by the rule; and the method of carrying from one denomination to another is exactly the same.

EXAMPLES OF MONEY.

1. Divide 2251. 2s. 4d. by 2. 2)2251. 2s. 4d.

112l. 11s. 2d. the quotient.

2. Divide 7511. 14s. 74d. by 3.
3. Divide 8211. 178. 94d. by 4.
4. Divide 281. 2s. 1d. by 6.
5. Divide 1351. 10s. 7d. by 9.
6. Divide 2271. 10s. 5d. by 11.
7. Divide 13321. 11s, 81d. by 12.

Ans. 250l. 11s. 6d.
Ans. 2051. 9s. 54d.
Ans. 41. 13s. 8d.
Ans. 151. Is. 2d.
Ans. 201. 13s. 8d.
Ans. 111. 11d.

CASE I.

If the divisor exceed 12, divide continually by its com ponent parts, as in simple division,

EXAMPLES.

1. What is cheese per cwt, if 16cwt, cost 30l. 18s. 8d. 4)30l. 18s. 8d.

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2. If 20cwt. of tobacco comes to 120l, 10s. what is

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If the divisor cannot be produced by the multiplication of small numbers, divide it after the manner of long division.

EXAMPLES.

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