manner as fol 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 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 5 price of 1 yd. 10 2 price of 10 yds. 10 8 price of 100 yds. £. 8. d. 139) 461 11 11 ( 3£. 417 44 891 (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 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 presented in the form of a RULE for the Multiplication of RULE for the Division of ComCompound Numbers. pound Numbers. I. When the multiplier does I. When the divisor 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. 41 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 5135. 7. What will 35 cwt. of tobacco cost, at 3 s. 10 lb.? 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? S. At 759 £. 10 s. for 35 d. per cwt. of tobacco, what is that per lb. ? 9. If 14 men build 12 rods 6 feet of wall in one day, how many rods will they build in 7 days? 10. If 14 men build 92 rɔds 12 feet of stone wall in 7 days, how much is that per 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. 178498924 £. 10 s. Ans. 2. What cost 34648 yards of cloth, at 10 s. or £. per yard? at 5 s.. per yard? at 4 s. =£. at 3 s. 4 d. per yard? at 2 s. £. per yard? b. ? 3. What cost 7430 pounds of sugar, at 6 d. = s. per lb? at 3 d. = s. per s. per lb.? Ans. to the last, 14.30 s. 928 s. 9 d. 46 £. 8 s. 9 d. 4. At $1875 per cwt., what will 2 qrs. = cwt. cost? what will 1 qr. = † cwt. cost? cwt. cost? what will 8 lbs. 5. What cost 340 yards of cloth, at 12 s. 6 d. per yard? 10 s. (=£.) and 2 s. 6 d. (= 12 s. 6 d. fore, £.); there 1. What distinction do you make between simple and compound numbers? ( 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 numbers, 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? EXERCISES. 1. A gentleman is possessed of 12 dozen of silver spoons, each weighing 3 oz. 5 pwt.; 2 doz. of tea spoons, each weighing 15 pwt. 14 gr.; 3 silver cans, each 9 oz. 7 pwt. ; 2 silver tankards, each 21 on 15 and 6 silver porringers, each 11 oz. 18 pwt.; what is the weight of the whole ? Ans. 18 lb. 4 oz. 3 pwt. Note. Let the pupil be required to reverse and prove the following examples: 2. An English guinea should weigh 5 pwt. 6 gr.; a piece of gold weighs 3 pwt. 17 gr.; how much is that short of the weight of a guinea? 3. What is the weight of 6 chests of tea, each weighing 3 cwt. 2 qrs. 9 lb. ? 4. In 35 pieces of cloth, each measuring 27 yards, how many yards? 5. How much brandy in 9 casks, each containing 45 gal. 3 qts. 1 pt.? 6. If 31 cwt. 2 qrs. 20 lb. of sugar be distributed equally into 4 casks, how much will each contain? 7. At 44 d. per lb., what costs 1 cwt. of rice? 3 cwt.? 2 cwt.? Note. The pupil will recollect, that 8, 7 and 2 are factors of 112, and may be used in place of that number. 8. If 800 cwt. of cocoa cost 18 £. 13 s. 4 d., what is that per cwt.? what is it per lb. ? 9. What will 94 cwt. of copper cost at 5 s. 9 d. per lb. ? 10. If 6 cwt. of chocolate cost 72 £. 16 s., what is that per lb. ? 11. What cost 456 bushels of potatoes, at 2 s. 6 d. per bushel? Note. 2 s. 6 d. is of 1 £. (See T 42.) 12. What cost 86 yards of broadcloth, at 15 s. per yard? Note. Consult T 42, ex. 5. 13. What cost 7846 pounds of tea, ats. 6 d. ner lb. ? at 14 s. per lb. ? at 13 s. 4 d. ? 14. At $94 25 per cwt., what will be the cost of 2 qrs. of tea? of 3 qrs.? of 16 lbs. ? Note. of 14 lbs. ? of 24 lbs. ? Consult T 42, ex. 4 and 5. of 21 lbs. ? |