When the multiplier, or divisor, exceeds 12, the operations of multiplying and dividing are not so easy, unless they be composite numbers; in that case, we may make use of the component parts, or factors, as was done in simple numbers.

Thus 15, in the example 15 being a composite numabove, is a composite number ber, and 3 and 5 its compoproduced by the multiplica-nent parts, or factors, we may tion of 3 and 5, (3 x 5 divide 17 T. 12 cwt. 2 qrs. by 15.) We may, therefore, one of these component parts, multiply 1 T. 3 cwt. 2 qrs. by or factors, and the quotient one of those component parts, thence arising by the other, or factors, and that product by which will give the true the other, which will give the answer, as already taught, true answer, as has been al-(¶ 20.)

ready taught, ( 11.)

OPERATION.

OPERATION. T. cut. gr. 3) 17 12 2

The other factor, 5) 5 17 2
Ans. 1 3 2

5 the other factor.

7 12 2 the answer. 27. What will 24 barrels of flour cost, at 2£. 12 s. 4 d. a barrel?

29. What will 112 lb. of sugar cost, at 74 d. per lb. ?

28. Bought 24 barrels of flour for 62 £. 16 s.; how much was that per barrel ?

30. If 1 cwt. of sugar cost 3 £. 7 s. 8 d., what is that per

Note. 8, 7, and 2, are fac-lb. ?

tors of 112.

31. How much brandy in 32. Bought 84 pipes of 84 pipes, each containing 112 brandy, containing 9468 gal. gal. 2 qts. 1 pt. 3 g.? 1 qt. 1 pt.; how much in a

pipe?

33. What will 139 yards of 34. Bought 139 yards of cloth cost, at 3 £. 6 s. 5dcloth for 461 £. 11 s. 11d.; what was that per yard?

per yard?

139 is not a composite num- When the divisor is such a ber. We may, however, de- number as cannot be produced compose this number thus, by the multiplication of small 139100+30 + 9. numbers, the better way is to We may now multiply the divide after the manner of

price of 1 yard by 10, which long division, setting down will give the price of 10 yards, the work of dividing and reand this product again by 10, ducing in manner which will give the price of lows: 100 yards.

We may then multiply the price of 10 yards by 3, which will give the price of 30 yards, and the price of 1 yard by 9, which will give the price of 9 yards, and these three products, added together, will evidently give the price of 139 yards; thus:

33

4

332 1 99 12 29 17

2 price of 10 yds.

10

8 price of 100 yds.
6 price of 30 yds.
9 price of 9 yds.

as fol

£.

S.

d.

139) 461

11

11 (3£.

417

44
20

891 (6 s.

834

57

12

695 ( 5 d.

695

The divisor, 139, is contained in 461 £. 3 times, (3£.,) and a remainder of 44., which must now be reduced to shillings, multiplying it by 20, and bringing 461 11 11 price of 139 yds. in the given shillings, (11 s.,) Note. In multiplying the making 891 s., in which the price of 10 yards (33£. 4 s. divisor is contained 6 times, 2 d.) by 3, to get the price of (6 s.,) and a remainder of 30 yards, and in multiplying 57 s., which must be reduced the price of 1 yard (3£. 6 s. to pence, multiplying it by 12, 5 d.) by 9, to get the price of and bringing in the given 9 yards, the multipliers, 3 and pence, (11 d.,) together mak9, need not be written down, ing 695 d., in which the dibut may be carried in the visor is contained 5 times, mind.

(5 d.,) and no remainder.

The several quotients, 3£, 6 s., 5 d., evidently make the

answer.

The processes in the foregoing examples may now be pre sented in the form of a

RULE for the Multiplication of RULE for the Division of Com Compound Numbers.

pound Numbers. 1. When the divisor does

I. When the multiplier does not exceed 12, multiply suc-not exceed 12, in the manner cessively the numbers of each of short division, find how denomination, beginning with many times it is contained in the least, as in multiplication the highest denomination, unof simple numbers, and carry der which write the quotient, as in addition of compound and, if there be a remainder, numbers, setting down the reduce it to the next less dewhole product of the highest nomination, adding thereto the denomination.

number given, if any, of that denomination, and divide as before; so continue to do through all the denominations, and the several quotients will be the answer.

II. If the multiplier exceed II. If the divisor exceed 12, 12, and be a composite num- and be a composite, we may diber, we may multiply first by vide first by one of the comone of the component parts, ponent parts, that quotient by that product by another, and another, and so on, if the comso on, if the component parts ponent parts be more than be more than two; the last two; the last quotient will be product will be the product re- the quotient required. quired.

III. When the multiplier III. When the divisor exexceeds 12, and is not a com-ceeds 12, and is not a composite, multiply first by 10, posite number, divide after the and this product by 10, which manner of long division, setwill give the product for 100; ting down the work of diand if the hundreds in the mul-viding and reducing. tiplier be more than one, multiply the product of 100 by the number of hundreds; for the tens, multiply the product of 10 by the number of tens; for the units, multiply the multiplicand; and these several products will be the product required.

EXAMPLES FOR PRACTICE.

1. What will 359 yards of 2. Bought 359 yards of cloth cloth cost, at 4 s. 7 d. per for 83 £.0 s. 44 d.; what was yard? that a yard?

3. In 241 barrels of flour, each containing 1 cwt. 3 qr. 9 lb.; how many cwt.?

5. How many bushels of wheat in 135 bags, each containing 2 bu. 3 pks.?

3 X 9 X 5=135.

4. If 441 cwt. 13 lb. of flour be contained in 241 barrels, how much in a barrel?

6. If 371 bu. 1 pk. of wheat be divided equally into 135 bags, how much will each bag contain?

7. What will 35 cwt. of to- 8. At 759 £. 10 s. for 35 bacco cost, at 3 s. 10 d. per cwt. of tobacco, what is that lb.?

per lb. ?

9. If 14 men build 12 rods 10. If 14 men build 92 rods 6 feet of wall in one day, how 12 feet of stone wall in 7 many rods will they build in days, how much is that per 7 days? day?

T42. 1. At 10 s. per yard, what will 17849 yards of cloth cost?

Note Operations in multiplication of pounds, shillings, pence, or of any compound numbers, may be facilitated by taking aliquot parts of a higher denomination, as already explained in "Practice" of Federal Money, T 29, ex. 10. Thus, in this last example, the price 10 s. of a pound; therefore, of the number of yards will be the cost in pounds. 178428924 £. 10 s. Ans.

2. What cost 34648 yards of cloth, at 10 s. or £. per yard? at 5 s.. per yard?

per yard?

=

at 3 s. 4 d. £. per yard?

at 4 s. =

at 2 s.

Ans. to last, 3464 £. 16 s. sugar, at 6 d. = s. per Ib?

. per yard? 3. What cost 7430 pounds of at 4 d. s. per lb.? s. per ib.?

Vb.? per lb. ?

at 2 d. =

at 3 d.

Ans. to the last, 74.30 s. — 928 s. 9 d. — 46 £. 8s. 9 d. 4. At $1875 per cwt., what will 2 qrs.

what will 1 qr. =

- cwt. cost? what will 8 lbs.

=cwt. cost?

what will 14 lbs.
cwt. cost?

= cwt. cost?

what will 16 lb.

cwt. cost?

Ans. to the last, $1′339.

5. What cost 340 yards of cloth, at 12 s. 6 d. per yard? 10 s. (=£.) and 2 s. 6 d. (.); there.

12 s. 6 d.

1. What distinction do you make between simple and compound nurabers? ( 26.) 2. What is the rule for addition of compound numbers? 3. for subtraction of, &c.? 4. There are three conditions in the rule given for multiplication of compound numbers; what are they, and the methods of procedure under each ? 5. The same questions in respect to the division of compound numbers? 6. When the multiplier or divisor is encumbered with a fraction, how do you proceed? 7. How is the distance of time from one date to another found? 8. How many degrees does the earth revolve from west to east in 1 hour? 9. In what time does it revolve 1°? Where is the time or hour of the day earlier at the place most easterly or most westerly? 10. The difference in longitude between two places being known, how is the difference in time calculated? 11. How may operations, in the multiplication of compound numbere, be facilitated? 12. What are some of the aliquot parts of 1 £.? of 1 s, ? of 1 cwt.? 13. What is this manner of operating usually called?