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the 2far., and divide the amount, 18far., by 9, and obtain 2far, for a quotient, which we place under the 2far. in the dividend. Thus we find the answer to be 14£. 58. 8d. 2far.
RULE. Divide as in division of simple numbers, each denomination in its order, beginning with the highest.
If there be a remainder, reduce it to the next lower denomination, adding in the number already of this denomination, if any, and divide as before.
PROOF. The same as in simple numbers.
NOTE. - When the divisor and dividend are both compound numbers, they must be reduced to the same denomination, and the division then is that of simple numbers.
0)12 14 4 2 6)1143 % 731093
Ib. 5 7) 0
g 18 3 17 10 14 15 3 12
18 15 8 3
13. fur. rd. ft. in.
8)145 3 3 2 103 9)213 2 0 9
10)98 0 4 2
NOTE. — The answers to the following questions are found in the corresponding numbers in Multiplication of Compound Numbers.
14. What costs 1 yard of cloth, when 7yd. can be bought for 6£. 11s. 3d. ?
15. If a man, in 9 days, travel 112m. 1fur. 21rd., how far will he travel in 1 day?
16. If 8 acres produce 21T. 5cwt. 2qr. 2lb. of hay, what will 1 acre produce ?
- What is the rule for division of compound numbers ?
17. If a family consume in 1 year 598 gal. 2qt. of molasses, how much will be necessary for 1 month ?
18. John Smith has 12 silver spoons, weighing 3lb. 10oz. 11pwt. ; what is the weight of each spoon ?
19. Samuel Johnson bought 7 loads of timber, measuring 55T. 19ft.; what was the quantity in each load ?
20. If the moon, in 10 days, move in her orbit 45. 11° 55' 50”, how far does she move in 1 day?
21. If $9 will buy 2411 83 33 19 10gr. of ipecacuanha, how large a quantity will $1 purchase ?
22. When $12 will buy 34A. OR. 32p. Syd. 5ft. 48in. of wild land, how much will $1 buy?
23. Joseph Doe will cut 24 cords 105 feet of wood in 9 days; how much will he cut in 1 day?
24. When 8 acres of land produce 25ch. 17bu. 3pk. 4qt. of grain, what will 1 acre produce ?
Art. 110. When the divisor is a composite number, and none of its factors exceed 12.
Ex. 1. When 24 yards of broadcloth are sold for 57£. 10s. Od., what is the price of 1 yard ?
Ans. 2£. 78. 11d.
We find the component £.
parts, or factors, of 24, 6) 57 10 0 price of 24 yards. are 6 and 4. We there4) 9 11 8=price of 4 yards.
fore divide the price by
one of these numbers, and 2 7 11= price of 1 yard. the quotient by the other.
RULE. — Divide by the factors of the composite number in succession.
EXAMPLES FOR PRACTICE.
2. If 360 tons of iron cost 6409£. 10s. Od., what is the cost of 1 ton ?
3. If a man travel 117m. 7fur. 20rd. in 30 days, how far will he travel in 1 day?
4. If 84 loads of hay weigh 201 tons 6cwt. Oqr. 121b., what will 1 load weigh ?
5. When 72 ladies require 567yd. Oqr. Ona. for their dresses, how many yards will be necessary for one lady?
QUESTIONS. — Art. 110. How does it appear that dividing by 6 in Ex. 1 gives the price of 4 yards ? How do you divide by a composite number?
6. When 132 sailors require 470yd. lqr. of cloth to make their garments, how many yards will be necessary for 1 sailor ?
Art. 111. When the divisor is not a composite number, and exceeds 12, or, if a composite number, and any of its factors exceed 12, the whole operation can be written down, as in the following example : Ex. 1. If 23cwt. of iron cost 171£. ls. 3d., what cost lcwt. ?
Ans. 7£. 8s. 9d.
23)171 1 3(7£.
We divide the pounds by 23, and obtain 7 for the quotient, and 10£. remaining, which we reduce to shillings, and add the ls., and again divide by 23, and obtain 8s. for the quotient. The remainder, 178., we
luce to pence, and add the 3d., and again divide by 23, and obtain 9d. for the quotient. Thus, the method of operation is the same as by the general rule (Art. 109), excepting more of the work is written down; and, by uniting the several quotients, we find the answer to be 7£. 88. 9d.
per ton ?
2. If $62 will buy 1095lb. 14oz. 6dr. of beef, how much may be obtained for $1 ?
3. Paid 280£. 58. 9fd. for 97 tons of lead; what did it cost
4. If a man travel 662m. 4fur. 28rd. 3yd. 2ft. 2in. in 38 days, how far will he travel in 1 day?
5. When 98 acres produce 2739 bu. lpk. 5qt. of grain, what will 1 acre produce ?
6. A tailor made 347 garments from 2732yd. 2qr. 2na. of cloth; what quantity did it take to make 1 garment ?
7. When 19 tons of iron will purchase 262A. 3R. 37p. 25yd. ift. 40in. of land, how much may be obtained for 1 ton ?
8. If 451 tons of copper ore will purchase 8003T. 17cwt. lqr. 121b. 10oz. of iron ore, how much will 1 ton purchase ?
Ans. 17T. 14cwt. 3qr. 181b. 14oz.
QUESTION. — Art. 111. When the divisor is large, and not a composite num ber, how is the division performed ?
♡ XVI. MISCELLANEOUS EXAMPLES IN MULTI
PLICATION AND DIVISION OF COMPOUND NUMBERS.
1. Bought 30 boxes of sugar, each containing Scwt. 3qr. 20lb., but having lost 68cwt. 2qr. Olb., I sold the remainder for 1£. 17s. 6d. per cwt. ; what sum did I receive ? Ans. 375£.
2. A company of 144 persons purchased a tract of land containing 11067A. 1R. 8p. John Smith, who was one of the company and owned an equal share with the others, sold his part of the land for 1s. 93d. per square rod; what sum did he receive?
Ans. 1101£. 12s. 1d 3. The exact distance from Boston to the mouth of the Columbia River is 2644m. 3fur. 12rd. A man, starting from Boston, travelled 100 days, going 18m. 7fur. 32rd. each day; required his distance from the mouth of the Columbia at the end of that time.
Ans. 746m. 7fur. 12rd. 4. James Bent was born July 4, 1798, at 3h. 17m. A. M.; how long had he lived Sept. 9, 1807, at 11h. 19m. P. M., reckoning 365 days for each year, excepting the leap year 1804, which has 366 days?
Ans. 3353da. 20h. 2m. 5. The distance from Vera Cruz, in a straight line, to the city of Mexico, is 121m. 5fur. If a man set out from Vera Cruz to travel this distance, on the first day of January, 1848, which was Saturday, and travelled 3124rd. per day until the eleventh day of January, omitting, however, as in duty bound, to travel on the Lord's day, how far would he be from the city of Mexico on the morning of that day?
Ans. 43m. 4fur. Srd. 6. Bought 16 casks of potash, each containing 7cwt. 3qr. 181b., at 5 cents per pound. I disposed of 9 casks at 6 cents per pound, and sold the remainder at 7 cents per pound; what did I gain ?
Ans. $182.39. 7. A merchant purchased in London 17 bales of cloth for 17£. 18s. 10d. per bale. He disposed of the cloth at Havana for sugar at 1£. 178. 6d. per cwt. Now, if he purchased 144cwt. of sugar, what balance did he receive?
Ans. 35£. Os. 2d. 8. A and B commenced travelling, the same way, round an island 50 miles in circumference. A travels 17m. 4fur. 30rd. a day, and B travels 12m. 3fur. 20rd. a day; required how far they are apart at the end of 10 days.
Ans. lm. 4fur. 20rd.
9. Bought 760 barrels of flour at $5.75 per barrel, which I paid for in iron at 2 cents per pound. The purchaser afterwards sold one half of the iron to an axe manufacturer; what quantity did he sell?
Ans. 54T. 12cwt. 2qr 10. Bought 17 house-lots, each containing 44 perches, 200 square feet. From this purchase I sold 2A. ŽR. 240ft., and the remaining quantity I disposed of at ls. 2 d. per square foot; what amount did I receive for the last sale ?
Ans. 5914£. 19s. 5 d. 11. J. Spofford's farm is 100 rods square. From this he sold H. Spaulding a fine house lot and garden, containing 5A. 3R. 17p., and to D. Fitts a farm 50rd. square, and to R. Thornton a farm containing 3000 square rods; what is the value of the remainder, at $1.75 per square rod?
Ans. $6235.25. 12. Bought 78Ā. 3R. 30p. of land for $7000, and, having sold 10 house-lots, each 30rd. square, for $8.50 per square rod, I dispose of the remainder for 2 cents per square foot. How much do I gain by my bargain?
$ XVII. PROPERTIES AND RELATIONS OF
An odd number is a number that cannot be divided by 2 without a remainder; thus, 3, 7, 11.
An even number is a number that can be divided by 2 without a remainder; thus, 4, 8, 12.
Numbers are also either prime or composite.
A prime number is a number which can be exactly divided only by itself or 1; as 1, 3, 5, 7.
À composite number is a number which can be exactly divided other than by itself or 1; as 6, 9, 14.
Numbers are prime to each other when they have no factor in common; thus, 7 and 11 are prime to each other, as are, also, 4, 15, and 19.
QUESTIONS. — Art. 112. What is an integer? What are all numbers? What is an odd number? What is an even number? What other distinctions of numbers are mentioned? What is a prime number? When are numbers primo to each other? What is a composite number?