COMPOUND DIVISION.

Compound Division teaches to find how often one number is contained in another of different denominations.

RULE.*

1. Place the numbers as in Simple Division.

2. Beginning at the left, 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, reduce it to the next lower denomination, and add to it any number, which may be in that denomination ; 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 OF MONEY.

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

1121. 11s. 2d. the quotient.

2. Divide 7511. 14s. 74d. by 3.

Ans. 250. 11s. 6d.

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 numbers. 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. Ild. as by the rule; and the method of carrying from one de nomination to another is exactly the same.

3. Divide 8211. 17s. 93. by 4.
4. Divide 281. 2s. 1 by 6.
5. Divide 1351. 10s. 7d. by 9.

Ans. 2051. 9s. 51d.

Ans. 41. 13s. 81d.

Ans. 151. 1s. 2d.

6. Divide 2271. 10s. 5d. by 11.

Ans. 201. 13s. 8d.

CASE 1.

If the divisor exceed 12, divide continually by its component parts, as in Simple Division.

EXAMPLES.

1. What is cheese per cwt. if 16 cwt. cost 30l. 18s. 8d.? 4)301. 18s. 8d.

4)7 14 8

1 18 8 the answer.

2. If 20cwt. of tobacco come to 1201. 10s. what is that per Gwt.?

3. Divide 571. 3s. 7d. by 35.

4. Divide 851. 6s. by 72.

Ans. 61. 6d.

Ans. 11. 12s. 8d.

Ans. 11. 3s. 84d.

Ans. 6s. 3 d.

6. At 18l. 18s. per cwt. how much

per

lb.?

Ans. 3s. 4 d.

5. Divide 311. 2s. 101d. by 99.

CASE 2.

If the divisor cannot be produced by the multiplication of

small numbers, divide by Long Division.

4. Divide 375mls. 2fur. 7pls. 2yds. 1ft. 2in. by 39.

Ans. 9mls. 4fur. 39pls. 2ft. 8in.

5. Divide 120L. 2qrs. 1bu. 2pe. by 74.

Ans. 1L. 6qrs. 1bu. 3pe.

6. Divide 120mo. 2w. 3d. 5h. 20′ by 111.

Ans. 1mo. 2d. 10h. 12'.

DUODECIMALS.

Duodecimals are so called because they, decrease by twelves, from the place of feet towards the right. Inches are sometimes called primes, and are marked thus'; the next division, after inches, is called parts, or seconds, and is marked thus"; the next is thirds, and marked thus ""; and

so on.

Duodecimals are commonly used by workmen and artificers in finding the contents of their work.

MULTIPLICATION OF DUODECMALS;

OR, CROSS MULTIPLICATION.

RULE.

1. Under the multiplicand write the same names or denominations of the multiplier, that is, feet under feet, inches under inches, &c.

2. Multiply each term in the multiplicand, beginning at the lowest, by the feet in the multiplier, and write each result under its respective term, observing to carry an unit for every 12, from each lower denomination to its next superior.

3. In the same manner multiply every term in the multiplicand by the inches in the multiplier, and set the result of each term one place father toward the right of those in the multiplicand.

4. Proceed in like manner with the seconds and all the rest of the denominations, if there be any more; and the sum of all the lines will be the product required.

Or the denominations of the several products will be as follow:

Feet by feet give feet.

Feet by primes give primes.

Feet by seconds give seconds,
&c.

Primes by primes give seconds.
Primes by seconds give thi.ds,
Primes by thirds give fourthis,
&c.

Seconds by seconds give fourths.
Seconds by thirds give fifths.
Seconds by fourths give sixths,

&c.

Thirds by thirds give sixths.
Thirds by fourths give sevenths.
Thirds by fifths give eights,
&c.

In general thus;

When feet are concerned, the product is of the same denomination with the term multiplying the feet.

When feet are not concerned, the name of the product will be expressed by the sum of the indices of the two factors, or of the strokes over them.